Twin Cities campus
 
Twin Cities Campus

Mathematics B.S.Math.

School of Mathematics
College of Science and Engineering
  • Program Type: Baccalaureate
  • Requirements for this program are current for Fall 2017
  • Required credits to graduate with this degree: 120
  • Required credits within the major: 73 to 93
  • Degree: Bachelor of Science in Mathematics
The mission of the program is to provide high-quality mathematics instruction in a stimulating intellectual atmosphere. The goal is to educate students at all levels to provide cultural enrichment, to give them the analytic tools they need to become responsible citizens, and to prepare them for careers involving mathematics. The School of Mathematics offers a program leading to the bachelor of science degree. The course of study is flexible and may be adapted to satisfy a wide variety of interests and needs. Students may prepare for graduate study in mathematics or emphasize various fields of interest, such as preparation for secondary school teaching, actuarial science, or programs in applied mathematics, including industrial mathematics, biology, mathematics applicable to computer science, and numerical analysis.
Program Delivery
This program is available:
  • via classroom (the majority of instruction is face-to-face)
Admission Requirements
Students must complete 5 courses before admission to the program.
Freshman and transfer students are usually admitted to pre-major status before admission to this major.
Successful completion of five (5) courses is required for admission to upper division as a math major: three (3) calculus courses: Calculus I (1371/1271/1571H), Calculus II (1372/1272/1572H), and one 2xxx level Calculus course - either Linear Algebra & Differential Equations (2373/2243/2574H/3592H) or Multivariable Calculus (2374/2263/2573H/3593H) - plus two (2) Calculus-based Physics courses (see list below).
For information about University of Minnesota admission requirements, visit the Office of Admissions website.
Required prerequisites
Calculus Sequence
CSE Calculus Sequence
Either MATH 2373 Linear Algebra & Differential Equations (here) or MATH 2374 Multivariable Calculus (see program requirements) can be taken to meet the requirement for admission to upper division.
Calculus I
MATH 1371 - CSE Calculus I [MATH] (4.0 cr)
or MATH 1271 - Calculus I [MATH] (4.0 cr)
or MATH 1571H - Honors Calculus I [MATH] (4.0 cr)
Calculus II
MATH 1372 - CSE Calculus II (4.0 cr)
or MATH 1272 - Calculus II (4.0 cr)
or MATH 1572H - Honors Calculus II (4.0 cr)
2xxx Level Calculus Course
MATH 2373 - CSE Linear Algebra and Differential Equations (4.0 cr)
or MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or MATH 2374 - CSE Multivariable Calculus and Vector Analysis (4.0 cr)
or MATH 2263 - Multivariable Calculus (4.0 cr)
or 2xxx or 3xxx Level Honors Calculus Course
MATH 2574H - Honors Calculus IV (4.0 cr)
or MATH 3592H - Honors Mathematics I (5.0 cr)
Required prerequisites
Physics
PHYS 1301W - Introductory Physics for Science and Engineering I [PHYS, WI] (4.0 cr)
or PHYS 1401V - Honors Physics I [PHYS, WI] (4.0 cr)
or PHYS 1501V - Honors Introduction to Mechanics [PHYS, WI] (4.0 cr)
PHYS 1302W - Introductory Physics for Science and Engineering II [PHYS, WI] (4.0 cr)
or PHYS 1402V - Honors Physics II [PHYS, WI] (4.0 cr)
or PHYS 1502V - Honors Introduction to Electricity and Magnetism [PHYS, WI] (4.0 cr)
General Requirements
All students in baccalaureate degree programs are required to complete general University and college requirements including writing and liberal education courses. For more information about University-wide requirements, see the liberal education requirements. Required courses for the major, minor or certificate in which a student receives a D grade (with or without plus or minus) do not count toward the major, minor or certificate (including transfer courses).
Program Requirements
Students must complete eight (8) upper division math courses at 4xxx and above plus a computer science course (see list below) and two (2) technical elective courses at the 3xxx level or above with the prerequisite of Calculus I. The School of Mathematics will accept STAT 5101 and 5102 as part of the eight-course upper division mathematics requirement. The content of STAT 5101 is the same as MATH 5651. STAT 5102 does not fulfill the analysis requirement. No other courses from other departments may be used as part of the eight-course math requirement, although other courses may be used as technical electives. MATH 3113, 3116, 3118, 4113, 4116, 4118, 3283W, 4005, 4067W, 49xx and 59xx math courses neither satisfy upper division math course requirement nor the technical electives requirement. In addition to the specializations described below, students who wish to pursue a pure mathematics track or are planning to go to graduate school in mathematics should consult their advisor about appropriate course choices.
Remaining Required Lower Division Calculus Courses
2xxx Level Calculus Course
MATH 2374 - CSE Multivariable Calculus and Vector Analysis (4.0 cr)
or MATH 2263 - Multivariable Calculus (4.0 cr)
or 2xxx or 3xxx Level Honors Calculus Course
MATH 2573H - Honors Calculus III (4.0 cr)
or MATH 3593H - Honors Mathematics II (5.0 cr)
Sequences, Series, & Foundations
MATH 3283W - Sequences, Series, and Foundations: Writing Intensive [WI] (4.0 cr)
or MATH 2283 - Sequences, Series, and Foundations (3.0 cr)
Upper Division Writing Intensive within the major
Students are required to take one upper division writing intensive course within the major. If that requirement has not been satisfied within the core major requirements, students must choose one course from the following list. Some of these courses may also fulfill other major requirements.
Take 0 - 1 course(s) from the following:
· MATH 3283W - Sequences, Series, and Foundations: Writing Intensive [WI] (4.0 cr)
· MATH 4067W - Actuarial Mathematics in Practice [WI] (3.0 cr)
· MATH 4997W - Senior project (Writing Intensive) [WI] (1.0 cr)
Specializations in Mathematics
Mathematics (No Specialization)
Students who do not choose one of the specializations must complete the basic mathematics major course requirements listed here. For the technical electives requirement, students must take at least 6 credits of courses that meet the following criteria: prerequisite of calculus; 3xxx level or higher; courses form a coherent part of the student's program.
Algebra Requirement
Both courses can be from the theoretical algebra list.
Take 2 or more course(s) from the following:
Theoretical Algebra
Take 1 or more course(s) from the following:
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
· Applied Algebra
Take 0 or more course(s) from the following:
· MATH 4242 - Applied Linear Algebra (4.0 cr)
· MATH 5705 - Enumerative Combinatorics (4.0 cr)
· MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
· MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
· MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
Analysis Requirement
Take 2 or more course(s) from the following:
· MATH 4567 - Applied Fourier Analysis (4.0 cr)
· MATH 4603 - Advanced Calculus I (4.0 cr)
· MATH 4604 - Advanced Calculus II (4.0 cr)
· MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
· MATH 5583 - Complex Analysis (4.0 cr)
· MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
· MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
· MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
· MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
· MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
· MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
· MATH 5654 - Prediction and Filtering (4.0 cr)
· STAT 5101 - Theory of Statistics I (4.0 cr)
Computer Science Requirement
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
Third Semester Physics Requirement
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
Mathematics Electives Requirement
Courses from the algebra and analysis lists which have not already used to fulfill those requirements may be taken to fulfill the mathematics elective requirement.
4xxx/5xxx Level Mathematics Courses
Take 4 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
Technical Electives Requirement
Any mathematics, science, or engineering course of technical nature that is not listed below and is not already used to fulfill specific BS mathematics requirements may be used as a technical elective course by permission. Contact the MATH director of undergraduate studies.
Technical Electives Courses: Mathematics
Complete 6 credits of technical elective courses at the 3xxx level or above which have Calculus I (1271/1371/1571H) as a prerequisite. Technical electives are selected by consultation with and approval of the math faculty advisor. Courses for this requirement must form a coherent part of a student's program.
Take 2 or more course(s) totaling 6 or more credit(s) from the following:
· MATH 4152 - Elementary Mathematical Logic (3.0 cr)
· MATH 5165 - Mathematical Logic I (4.0 cr)
· MATH 4567 - Applied Fourier Analysis (4.0 cr)
· MATH 5467 - Introduction to the Mathematics of Image and Data Analysis (4.0 cr)
· MATH 5345H - Honors: Introduction to Topology (4.0 cr)
· MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
· MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
· MATH 5654 - Prediction and Filtering (4.0 cr)
· MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
· MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
· MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
· MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
· MATH 5583 - Complex Analysis (4.0 cr)
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
· MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
· MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
· MATH 5447 - Theoretical Neuroscience (4.0 cr)
· MATH 5378 - Differential Geometry (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
· MATH 5335 - Geometry I (4.0 cr)
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 4653 - Elementary Probability (4.0 cr)
· MATH 4707 - Introduction to Combinatorics and Graph Theory (4.0 cr)
· MATH 5705 - Enumerative Combinatorics (4.0 cr)
· MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
· MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 4603 - Advanced Calculus I (4.0 cr)
· MATH 4604 - Advanced Calculus II (4.0 cr)
· MATH 4512 - Differential Equations with Applications (3.0 cr)
· MATH 4242 - Applied Linear Algebra (4.0 cr)
· MATH 4428 - Mathematical Modeling (4.0 cr)
· MATH 4065 - Theory of Interest (4.0 cr)
· MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I (4.0 cr)
· MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II (4.0 cr)
· MATH 5067 - Actuarial Mathematics I (4.0 cr)
· MATH 5068 - Actuarial Mathematics II (4.0 cr)
or Chemistry Technical Elective
CHEM 4501 - Introduction to Thermodynamics, Kinetics, and Statistical Mechanics (3.0 cr)
CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy (3.0 cr)
or Computer Science Technical Elective
Take 2 or more course(s) totaling 6 or more credit(s) from the following:
· CSCI 4011 - Formal Languages and Automata Theory (4.0 cr)
· CSCI 4041 - Algorithms and Data Structures (4.0 cr)
· CSCI 4061 - Introduction to Operating Systems (4.0 cr)
· CSCI 4611 - Programming Interactive Computer Graphics and Games (3.0 cr)
· CSCI 5106 - Programming Languages (3.0 cr)
· CSCI 5304 - Computational Aspects of Matrix Theory (3.0 cr)
· CSCI 5607 - Fundamentals of Computer Graphics 1 (3.0 cr)
· CSCI 5608 - Fundamentals of Computer Graphics II (3.0 cr)
· CSCI 5403 - Computational Complexity (3.0 cr)
· CSCI 5421 - Advanced Algorithms and Data Structures (3.0 cr)
· CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming (3.0 cr)
· CSCI 5511 - Artificial Intelligence I (3.0 cr)
· CSCI 5512 - Artificial Intelligence II (3.0 cr)
· CSCI 5521 - Introduction to Machine Learning (3.0 cr)
or Economics Technical Elective
ECON 3101 - Intermediate Microeconomics (4.0 cr)
ECON 3102 - Intermediate Macroeconomics (4.0 cr)
or ECON 4261 - Introduction to Econometrics (4.0 cr)
or Physics Technical Elective
Take 2 or more course(s) totaling 6 or more credit(s) from the following:
· PHYS 4001 - Analytical Mechanics (4.0 cr)
· PHYS 4002 - Electricity and Magnetism (4.0 cr)
· PHYS 4051 - Methods of Experimental Physics I (5.0 cr)
· PHYS 4101 - Quantum Mechanics (4.0 cr)
· PHYS 4201 - Statistical and Thermal Physics (3.0 cr)
· PHYS 4511 - Introduction to Nuclear and Particle Physics (3.0 cr)
· PHYS 5001 - Quantum Mechanics I (4.0 cr)
or Statistics Technical Elective
Take 2 or more course(s) totaling 6 or more credit(s) from the following:
· STAT 3021 - Introduction to Probability and Statistics (3.0 cr)
· STAT 3022 - Data Analysis (4.0 cr)
· STAT 5021 - Statistical Analysis (4.0 cr)
· STAT 5031 - Statistical Methods for Quality Improvement (4.0 cr)
· STAT 5302 - Applied Regression Analysis (4.0 cr)
· STAT 5303 - Designing Experiments (4.0 cr)
· STAT 5421 - Analysis of Categorical Data (3.0 cr)
-OR-
Actuarial Specialization
Complete the requirements for the actuarial sub-plan.
-OR-
Mathematics Education Specialization
Complete the requirements for the mathematics education sub-plan.
-OR-
Computer Applications Specialization
Complete the requirements for the computer applications sub-plan.
-OR-
Mathematical Biology: Genomics
Complete the requirements for the genomics sub-plan.
-OR-
Mathematical Biology: Physiology
Complete the requirements for the physiology sub-plan.
Program Sub-plans
A sub-plan is not required for this program.
Actuarial Science
The BS mathematics with actuarial specialization requires a minimum of 8 upper division (4xxx level and above) mathematics courses, as indicated in the lists below. Students pursuing the actuarial specialization may want to include MATH 4067W, which fulfills an upper division writing intensive requirement, although it does not fulfill any of the upper division math course requirements. It is recommended in this specialization to plan for a summer internship after the junior year. For the actuarial specialization, students must complete specific courses in economics, accounting, insurance, and finance. Thus, these required courses in economics and finance take the place of a technical electives package for students who successfully complete the actuarial specialization. A third semester of physics is not required for the actuarial specialization.
Mathematics Course Requirements
Algebra Requirement
Theoretical Algebra
Take 1 or more course(s) from the following:
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
Applied Algebra
MATH 4242 - Applied Linear Algebra (4.0 cr)
Analysis Requirement
Theory of Probability & Statistics
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Stochastic Processes
MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
Actuarial Mathematics Requirement
MATH 4065 - Theory of Interest (4.0 cr)
MATH 5067 - Actuarial Mathematics I (4.0 cr)
MATH 5068 - Actuarial Mathematics II (4.0 cr)
Additional Math Requirements for Actuarial Specialization
Courses recommended for this specialization are MATH 5075, 4428, 5485, 5076.
4xxx or 5xxx Level Math Courses offered in Fall
Take 1 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
· MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I (4.0 cr)
· MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
or 4xxx or 5xxx Level Math Courses offered in Spring
Take 1 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
· MATH 4428 - Mathematical Modeling (4.0 cr)
Computer Science Requirement
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
Economics and Business
Introductory Economics
ECON 1101 - Principles of Microeconomics [SOCS, GP] (4.0 cr)
ECON 1102 - Principles of Macroeconomics (4.0 cr)
Economics and Finance
ACCT 2050 - Introduction to Financial Reporting (4.0 cr)
ECON 3101 - Intermediate Microeconomics (4.0 cr)
ECON 4261 - Introduction to Econometrics (4.0 cr)
FINA 3001 - Finance Fundamentals (3.0 cr)
Insurance
Take 2 or more course(s) from the following:
· INS 4100 - Corporate Risk Management (2.0 cr)
· INS 4101 - Employee Benefits (2.0 cr)
· INS 4200 - Insurance Theory and Practice (2.0 cr)
Computer Applications
The upper division (4xxx level or above) mathematics courses, a 3rd semester of physics, and a minimum 24 credits of math and computer science courses relating to computer applications (from the courses listed below) are needed to fulfill the requirements for the BS mathematics with computer applications specialization. Students who complete the computer applications specialization may meet the requirements for a minor in computer science.
Mathematics Course Requirements for Computer Applications
Algebra Requirements
Theoretical Algebra
Take 1 or more course(s) from the following:
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
Applied Algebra
MATH 5485 - Introduction to Numerical Methods I (4.0 cr)
Analysis Requirements
Numerical Methods
MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
Additional Analysis Course
Take 1 or more course(s) from the following:
· MATH 4567 - Applied Fourier Analysis (4.0 cr)
· MATH 4603 - Advanced Calculus I (4.0 cr)
· MATH 4604 - Advanced Calculus II (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5583 - Complex Analysis (4.0 cr)
· MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
· MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
· MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
· MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
· MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
· MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
· MATH 5654 - Prediction and Filtering (4.0 cr)
· STAT 5101 - Theory of Statistics I (4.0 cr)
Mathematics Electives
Mathematics courses in the algebra, analysis, or computing-related mathematics lists which are not used to fulfill those requirements may be taken as mathematics elective courses.
Take 2 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
Computing-Related Mathematics
Mathematical Logic Requirement
MATH 5165 - Mathematical Logic I (4.0 cr)
Computer-Related Mathematics Electives
Take 1 or more course(s) from the following:
· MATH 4242 - Applied Linear Algebra (4.0 cr)
· MATH 5166 - Mathematical Logic II (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
· MATH 5705 - Enumerative Combinatorics (4.0 cr)
· MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
· MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
Computer Applications Lower Division Requirements
Introduction to Computing and Programming Concepts
CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
CSCI 1933 - Introduction to Algorithms and Data Structures (4.0 cr)
or Introduction to Computer Programming
CSCI 1913 - Introduction to Algorithms, Data Structures, and Program Development (4.0 cr)
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
Discrete Structures
CSCI 2011 - Discrete Structures of Computer Science (4.0 cr)
Computer Science Courses & Technical Electives
Upper division computer science courses may be counted as technical electives.
Take 2 or more course(s) from the following:
· CSCI 4011 - Formal Languages and Automata Theory (4.0 cr)
· CSCI 4041 - Algorithms and Data Structures (4.0 cr)
· CSCI 4511W - Introduction to Artificial Intelligence [WI] (4.0 cr)
· CSCI 5607 - Fundamentals of Computer Graphics 1 (3.0 cr)
· CSCI 5608 - Fundamentals of Computer Graphics II (3.0 cr)
· CSCI 5421 - Advanced Algorithms and Data Structures (3.0 cr)
· CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming (3.0 cr)
· CSCI 5511 - Artificial Intelligence I (3.0 cr)
· CSCI 5512 - Artificial Intelligence II (3.0 cr)
· CSCI 5521 - Introduction to Machine Learning (3.0 cr)
Third Semester Physics Requirement
A physics course from the following list should be taken during the the second year to fulfill this requirement.
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
Mathematics Education
Preparation for teaching mathematics in secondary education.
The eight (8) required upper division (4xxx level or above) mathematics courses for the mathematics education specialization include courses that meet admission requirements for the secondary teaching licensure program in mathematics. Additional requirements for the BS mathematics with mathematics education specialization include a 3rd semester of physics, a minimum of one (1) computer science course, and a technical electives course package. MATH 4653 is recommended to meet admission requirements for the Math Education Licensure Program, but it does not fulfill the analysis requirement for the major. Courses that are recommended for this specialization (but not required) include MATH 5652 Stochastic Processes, STAT 5102 Theory of Statistics II, and MATH 5336 Geometry II.
Mathematics Education Specialization Requirements
Algebra Requirements
Theoretical Algebra
MATH 4281 - Introduction to Modern Algebra (4.0 cr)
or MATH 5248 - Cryptology and Number Theory (4.0 cr)
or MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
or MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
Applied Algebra: Combinatorics
Note: MATH 4707 fulfills the applied algebra requirements only for the mathematics education specialization.
MATH 4707 - Introduction to Combinatorics and Graph Theory (4.0 cr)
or MATH 5705 - Enumerative Combinatorics (4.0 cr)
or MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
Geometry
MATH 5335 - Geometry I (4.0 cr)
Probability and Statistics
MATH 5651 or STAT 5101 may be used to fulfill this requirement.
MATH 4653 - Elementary Probability (4.0 cr)
Analysis Requirements
Take 2 or more course(s) from the following:
· MATH 4567 - Applied Fourier Analysis (4.0 cr)
· MATH 4603 - Advanced Calculus I (4.0 cr)
· MATH 4604 - Advanced Calculus II (4.0 cr)
· MATH 5486 - Introduction To Numerical Methods II (4.0 cr)
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
· MATH 5583 - Complex Analysis (4.0 cr)
· MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
· MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
· MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
· MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
· MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
· MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
· MATH 5654 - Prediction and Filtering (4.0 cr)
· STAT 5101 - Theory of Statistics I (4.0 cr)
Mathematics Education Electives Requirement
Recommended math elective courses for this specialization are MATH 5336, MATH 4242, MATH 5652, STAT 5102. Courses from the algebra or analysis lists not used to fulfill those requirements may also be taken to fulfill this math electives requirement.
Take 2 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
Computer Science Requirement
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
Third Semester Physics Requirement
Take one of the following physics courses in the third semester (fall semester of the second year).
PHYS 2303 - Physics III: Physics of Matter (4.0 cr)
or PHYS 2311 - Modern Physics (4.0 cr)
or PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity (4.0 cr)
Technical Electives
Students must complete 6 credits of courses at the 3xxx level or above which have Calculus I (1271, 1371, 1571H) as a prerequisite and which form a coherent part of student's program. technical electives are selected by consultation and approval of your math advisor. Earliest semester: Y3 fall; latest semester: Y4 spring.
Mathematical Biology: Genomics
Note that some Genomics Elective choices have additional prerequisite courses.
Mathematics Requirements for MathBio: Genomics
Mathematical Modeling Requirement
MATH 4428 - Mathematical Modeling (4.0 cr)
Algebra Requirements
Theoretical Algebra
Take 1 or more course(s) from the following:
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
Applied Algebra
MATH 4242 - Applied Linear Algebra (4.0 cr)
Analysis Requirements
Genomics Analysis Requirement
Take 1 or more course(s) from the following:
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
Theory of Probability & Statistics I
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Mathematics Electives
Mathematics courses from the algebra, analysis, and genomics electives lists which were not used to fulfill those requirements may be taken as mathematics electives to meet the 8 course requirement for the major.
Take 3 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
Computer Science Requirements for Genomics
Introduction to Computing and Programming Concepts
CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
CSCI 1933 - Introduction to Algorithms and Data Structures (4.0 cr)
or Introduction to Computer Programming
CSCI 1913 - Introduction to Algorithms, Data Structures, and Program Development (4.0 cr)
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
5xxx Level CSCI Course Requirements
CSCI 2011 & CSCI 4041 may together serve as the substitute prerequisite courses for CSCI 5461.
Functional Genomics, Systems Biol., Bioinformatics
CSCI 5461 - Functional Genomics, Systems Biology, and Bioinformatics (3.0 cr)
CSCI 3003 - Introduction to Computing in Biology (3.0 cr)
or Computational Techniques for Genomics
CSCI 5481 - Computational Techniques for Genomics (3.0 cr)
CSCI 4041 - Algorithms and Data Structures (4.0 cr)
CSCI 2011 - Discrete Structures of Computer Science (4.0 cr)
Genomics, Biology Requirements
If the genomics elective course chosen does not require a chemistry sequence, then it is still recommended that one semester of chemistry is taken (CHEM 1061 & CHEM 1065 Lab).
1xxx Level Biology
BIOL 1009H may be substituted.
BIOL 1009 - General Biology [BIOL] (4.0 cr)
Genetics Requirement
GCD 3022 - Genetics (3.0 cr)
Genomics Elective Requirement
The 5xxx level CSCI course which was not taken to fulfill the computer science requirement may (with its prerequisites) be used to fulfill the genomics elective requirement.
MATH 5445 may be used to fulfill this requirement.
Take 1 or more course(s) from the following:
· EEB 5042 - Quantitative Genetics (3.0 cr)
· GCD 4143 - Human Genetics (3.0 cr)
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
· Plant Genomics
PBIO 5301 has additional prerequisite courses: CHEM 1061, CHEM 1065 (lab), CHEM 1062, CHEM 1066 (lab), CHEM 2301, BIOC 3021.
· PBIO 5301 - Plant Genomics (3.0 cr)
· Molecular Biology of Cancer
GCD 4151 has additional prerequisite courses: CHEM 1061, CHEM 1065 (lab), CHEM 1062, CHEM 1066 (lab), CHEM 2301, BIOC 3021, BIOL 4003.
· GCD 4151 - Molecular Biology of Cancer (3.0 cr)
Mathematical Biology: Physiology
Note that some Physiology Elective choices have additional prerequisite courses.
Mathematics Requirements for MathBio: Physiology
Mathematical Modeling Requirement
MATH 4428 - Mathematical Modeling (4.0 cr)
Biological Networks or Neuroscience
MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
or MATH 5447 - Theoretical Neuroscience (4.0 cr)
Theoretical Algebra
Take 1 or more course(s) from the following:
· MATH 4281 - Introduction to Modern Algebra (4.0 cr)
· MATH 5248 - Cryptology and Number Theory (4.0 cr)
· MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves (4.0 cr)
· MATH 5285H - Honors: Fundamental Structures of Algebra I (4.0 cr)
· MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
· MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
Applied Algebra Requirement
MATH 4242 - Applied Linear Algebra (4.0 cr)
Analysis Requirements
Physiology Analysis Requirement
Take 1 or more course(s) from the following:
· MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
· MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
Theory of Probability & Statistics
MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Mathematics Electives
Mathematics courses from the algebra, analysis or required mathematics for physiology lists which were not used to fulfill those requirements may be used to fulfill this requirement.
Take 2 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
Lower Division Computer Science Requirement
CSCI 1103 - Introduction to Computer Programming in Java (4.0 cr)
or CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers (4.0 cr)
or CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
Physiology, Biology, Chemistry Requirements
Physiology Requirement
PHSL 3061 - Principles of Physiology (4.0 cr)
1xxx Level Biology Requirement
BIOL 1009H may be substituted.
BIOL 1009 - General Biology [BIOL] (4.0 cr)
1xxx Level Chemistry Requirements
CHEM 1061 - Chemical Principles I [PHYS] (3.0 cr)
CHEM 1065 - Chemical Principles I Laboratory [PHYS] (1.0 cr)
or CHEM 1071H - Honors Chemistry I [PHYS] (3.0 cr)
CHEM 1075H - Honors Chemistry I Laboratory [PHYS] (1.0 cr)
CHEM 1062 - Chemical Principles II [PHYS] (3.0 cr)
CHEM 1066 - Chemical Principles II Laboratory [PHYS] (1.0 cr)
or CHEM 1072H - Honors Chemistry II [PHYS] (3.0 cr)
CHEM 1076H - Honors Chemistry II Laboratory [PHYS] (1.0 cr)
Physiology Electives
Whichever course - Math 5445 or Math 5447 - was not taken to fulfill the mathematics requirement can be taken to fulfill this electives requirement.
Take 1 or more course(s) from the following:
· PHSL 4700 - Cell Physiology (3.0 cr)
· PHSL 5444 - Muscle (3.0 cr)
· NSC 5202 has additional prerequisite courses: CHEM 2301, BIOC 3021, NSCI 3101, NSCI 3102.
· NSC 5202 - Theoretical Neuroscience: Systems and Information Processing (3.0 cr)
 
More program views..
View college catalog(s):
· College of Science and Engineering

View sample plan(s):
· Mathematics
· Actuarial Science
· Computer Applications
· Mathematics Education
· Mathematical Biology: Genomics
· Mathematical Biology: Physiology

View checkpoint chart:
· Mathematics B.S.Math.
View PDF Version:
Search.
Search Programs

Search University Catalogs
Related links.

College of Science and Engineering

TC Undergraduate Admissions

TC Undergraduate Application

One Stop
for tuition, course registration, financial aid, academic calendars, and more
 
MATH 1371 - CSE Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1142/1271/1281/1371/1571H
Typically offered: Every Fall & Spring
Differentiation of single-variable functions, basics of integration of single-variable functions. Applications: max-min, related rates, area, curve-sketching. Use of calculator, cooperative learning. prereq: CSE or pre-bioprod concurrent registration is required (or allowed) in biosys engn (PRE), background in [precalculus, geometry, visualization of functions/graphs], instr consent; familiarity with graphing calculators recommended
MATH 1271 - Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00067 - Math 1271/Math 1281/Math 1371/
Typically offered: Every Fall, Spring & Summer
Differential calculus of functions of a single variable, including polynomial, rational, exponential, and trig functions. Applications, including optimization and related rates problems. Single variable integral calculus, using anti-derivatives and simple substitution. Applications may include area, volume, work problems. prereq: 4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]
MATH 1571H - Honors Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00067 - Math 1142/1271/1281/1371/1571H
Grading Basis: A-F only
Typically offered: Every Fall
Differential/integral calculus of functions of a single variable. Emphasizes hard problem-solving rather than theory. prereq: Honors student and permission of University Honors Program
MATH 1372 - CSE Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/1282/1252/1372/1572
Typically offered: Every Spring
Techniques of integration. Calculus involving transcendental functions, polar coordinates, Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. Use of calculators, cooperative learning. prereq: Grade of at least C- in [1371 or equiv], CSE or pre-Bioprod/Biosys Engr
MATH 1272 - Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/1282/1252/1372/1572
Typically offered: Every Fall, Spring & Summer
Techniques of integration. Calculus involving transcendental functions, polar coordinates. Taylor polynomials, vectors/curves in space, cylindrical/spherical coordinates. prereq: [1271 or equiv] with grade of at least C-
MATH 1572H - Honors Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: 00068 - Math 1272/1282/1252/1372/1572
Grading Basis: A-F only
Typically offered: Every Spring
Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra. prereq: 1571H, honors student, permission of University Honors Program
MATH 2373 - CSE Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/2373/2573
Typically offered: Every Fall & Spring
Linear algebra: basis, dimension, eigenvalues/eigenvectors. Differential equations: linear equations/systems, phase space, forcing/resonance, qualitative/numerical analysis of nonlinear systems, Laplace transforms. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bio Prod/Biosys Engr
MATH 2243 - Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/2373/2573
Typically offered: Every Fall, Spring & Summer
Linear algebra: basis, dimension, matrices, eigenvalues/eigenvectors. Differential equations: first-order linear, separable; second-order linear with constant coefficients; linear systems with constant coefficients. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-
MATH 2374 - CSE Multivariable Calculus and Vector Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/2373/2573H/3251
Typically offered: Every Fall & Spring
Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes theorems. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bioprod/Biosys Engr
MATH 2263 - Multivariable Calculus
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/2373/2573H/3251
Typically offered: Every Fall, Spring & Summer
Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes Theorems. prereq: [1272 or 1372 or 1572] w/grade of at least C-
MATH 2574H - Honors Calculus IV
Credits: 4.0 [max 4.0]
Course Equivalencies: 00561 - Math 2243/Math 2373/Math 2573H
Grading Basis: A-F only
Typically offered: Every Spring
Advanced linear algebra, differential equations. Additional topics as time permits. prereq: Math 1572H or Math 2573H, honors student and permission of University Honors Program
MATH 3592H - Honors Mathematics I
Credits: 5.0 [max 5.0]
Grading Basis: A-F only
Typically offered: Every Fall
First semester of three-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra. prereq: dept consent; for students with mathematical talent
PHYS 1301W - Introductory Physics for Science and Engineering I (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00078
Typically offered: Every Fall, Spring & Summer
Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, structure of matter. Applications to mechanical systems. prereq: concurrent registration is required (or allowed) in Math 1271 or concurrent registration is required (or allowed) in Math 1371 or concurrent registration is required (or allowed) in Math 1571
PHYS 1401V - Honors Physics I (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00078
Grading Basis: A-F only
Typically offered: Every Fall
Comprehensive, calculus-level general physics. Emphasizes use of fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles. Structure of matter, with applications to mechanical systems.
PHYS 1501V - Honors Introduction to Mechanics (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00078 - Phys 1201W/Phys1301W/Phys1401V
Grading Basis: A-F only
Typically offered: Every Fall
Principles of mechanics for those with full year of calculus/equivalent of one year of high-school physics. Introduction to kinematics, forces, momentum/energy, conservation laws, angular momentum, rigid body motion, gravity, simple harmonic motion, waves. prereq: One year of high school physics, one year of college-level calculus (or a grade of 5 on the BC-level AP calculus exam), Honors, permission of UHP
PHYS 1302W - Introductory Physics for Science and Engineering II (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00079
Typically offered: Every Fall & Spring
Use of fundamental principles to solve quantitative problems. Motion, forces, conservation principles, fields, structure of matter. Applications to electromagnetic phenomena. prereq: 1301W, concurrent registration is required (or allowed) in Math 1272 or Math 1372 or Math 1572
PHYS 1402V - Honors Physics II (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00079 - Phys 1202W/1302W/1402V
Grading Basis: A-F only
Typically offered: Every Spring
Fundamental principles to solve quantitative problems. Description of motion, forces, conservation principles, fields. Structure of matter, with applications to electro-magnetic phenomena. prereq: 1401V, honors student or permission of University Honors Program
PHYS 1502V - Honors Introduction to Electricity and Magnetism (PHYS, WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 00079 - Phys 1202W/1302W/1402V
Grading Basis: A-F only
Typically offered: Every Spring
Principles of electricity/magnetism for those with full year of calculus/equivalent of one year of high-school physics. Introduction to electrostatics, magnetostatics, electrodynamics, electric/magnetic properties of materials, circuits, Maxwell's equations, electromagnetic waves. prereq: 1501V, honors
MATH 2374 - CSE Multivariable Calculus and Vector Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/2373/2573H/3251
Typically offered: Every Fall & Spring
Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes theorems. Use of computer technology. prereq: [1272 or 1282 or 1372 or 1572] w/grade of at least C-, CSE or pre-Bioprod/Biosys Engr
MATH 2263 - Multivariable Calculus
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/2373/2573H/3251
Typically offered: Every Fall, Spring & Summer
Derivative as linear map. Differential/integral calculus of functions of several variables, including change of coordinates using Jacobians. Line/surface integrals. Gauss, Green, Stokes Theorems. prereq: [1272 or 1372 or 1572] w/grade of at least C-
MATH 2573H - Honors Calculus III
Credits: 4.0 [max 4.0]
Course Equivalencies: 00069 - Math 2263/2374/3251
Grading Basis: A-F only
Typically offered: Every Fall
Integral calculus of several variables. Vector analysis, including theorems of Gauss, Green, Stokes. prereq: Math 1572H or Math 2574H, honors student and permission of University Honors Program
MATH 3593H - Honors Mathematics II
Credits: 5.0 [max 5.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Second semester of three-semester sequence. Focuses on multivariable calculus at deeper level than regular calculus offerings. Rigorous introduction to sequences/series. Theoretical treatment of multivariable calculus. Strong introduction to linear algebra. prereq: 3592H or instr consent
MATH 3283W - Sequences, Series, and Foundations: Writing Intensive (WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2283/3283W
Typically offered: Every Fall & Spring
Introduction to reasoning used in advanced mathematics courses. Logic, mathematical induction, real number system, general/monotone/recursively defined sequences, convergence of infinite series/sequences, Taylor's series, power series with applications to differential equations, Newton's method. Writing-intensive component. prereq: [concurrent registration is required (or allowed) in 2243 or concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2373 or concurrent registration is required (or allowed) in 2374] w/grade of at least C-
MATH 2283 - Sequences, Series, and Foundations
Credits: 3.0 [max 3.0]
Course Equivalencies: Math 2283/3283W
Typically offered: Every Fall & Spring
Mathematical reasoning. Elements of logic. Mathematical induction. Real number system. General, monotone, recursively defined sequences. Convergence of infinite series/sequences. Taylor's series. Power series with applications to differential equations. Newton's method. prereq: [concurrent registration is required (or allowed) in 2243 or concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2373 or concurrent registration is required (or allowed) in 2374] w/grade of at least C-
MATH 3283W - Sequences, Series, and Foundations: Writing Intensive (WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2283/3283W
Typically offered: Every Fall & Spring
Introduction to reasoning used in advanced mathematics courses. Logic, mathematical induction, real number system, general/monotone/recursively defined sequences, convergence of infinite series/sequences, Taylor's series, power series with applications to differential equations, Newton's method. Writing-intensive component. prereq: [concurrent registration is required (or allowed) in 2243 or concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2373 or concurrent registration is required (or allowed) in 2374] w/grade of at least C-
MATH 4067W - Actuarial Mathematics in Practice (WI)
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Every Spring
Real world actuarial problems that require integration of mathematical skills with knowledge from other disciplines such as economics, statistics, and finance. Communication and interpersonal skills are enhanced by teamwork/presentations to the practitioner actuaries who co-instruct. prereq: 4065, ACCT 2050, ECON 1101, ECON 1102
MATH 4997W - Senior project (Writing Intensive) (WI)
Credits: 1.0 [max 2.0]
Prerequisites: 2 sem upper div math, %
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Directed study. A 10-15 page paper on a specialized area, including some math that is new to student. At least two drafts of paper given to instructor for feedback before final version. Student keeps journal of preliminary work on project. Scope/topic vary with instructor. prereq: 2 sem upper div math, dept consent
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5705 - Enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707
MATH 5711 - Linear Programming and Combinatorial Optimization
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 4567 - Applied Fourier Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573
MATH 4603 - Advanced Calculus I
Credits: 4.0 [max 4.0]
Course Equivalencies: 01072 - Math 4606/Math 5615/Math 5616
Typically offered: Every Fall, Spring & Summer
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent
MATH 4604 - Advanced Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: 01776
Typically offered: Every Spring
Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5583 - Complex Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 3574/5583
Typically offered: Every Fall, Spring & Summer
Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5588 - Elementary Partial Differential Equations II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent
MATH 5615H - Honors: Introduction to Analysis I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574
MATH 5616H - Honors: Introduction to Analysis II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 5654 - Prediction and Filtering
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
PHYS 2303 - Physics III: Physics of Matter
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503/2503H
Typically offered: Every Spring
Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student
PHYS 2311 - Modern Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Broad overview of physical concepts developed in twentieth century. Special relativity, wave-particle duality, Schrodinger equation, Bohr atom, hydrogen atom in wave mechanics, many-electron atoms, x-rays, nuclear structure, radioactivity, nuclear reactions, statistical physics. prereq: [1302 or 1402], Chem 1022, Math 2243
PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503
Typically offered: Every Fall
Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W, [MATH 1272 or MATH 1372 or MATH 1572H]
MATH 4152 - Elementary Mathematical Logic
Credits: 3.0 [max 3.0]
Course Equivalencies: Math 4152/5165
Typically offered: Every Spring
Propositional logic. Predicate logic: notion of a first order language, a deductive system for first order logic, first order structures, Godel's completeness theorem, axiom systems, models of formal theories. prereq: one soph math course or instr consent
MATH 5165 - Mathematical Logic I
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 4152/5165
Typically offered: Every Fall
Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic. prereq: 2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent
MATH 4567 - Applied Fourier Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573
MATH 5467 - Introduction to the Mathematics of Image and Data Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Background theory/experience in wavelets. Inner product spaces, operator theory, Fourier transforms applied to Gabor transforms, multi-scale analysis, discrete wavelets, self-similarity. Computing techniques. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283 or instr consent]; [[2263 or 2374], 4567] recommended
MATH 5345H - Honors: Introduction to Topology
Credits: 4.0 [max 4.0]
Grading Basis: A-F only
Typically offered: Every Fall
Rigorous introduction to general topology. Set theory, Euclidean/metric spaces, compactness/connectedness. May include Urysohn metrization, Tychonoff theorem or fundamental group/covering spaces. prereq: [2263 or 2374 or 2573], [concurrent registration is required (or allowed) in 2283 or concurrent registration is required (or allowed) in 2574 or concurrent registration is required (or allowed) in 3283]
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 5654 - Prediction and Filtering
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101
MATH 5615H - Honors: Introduction to Analysis I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574
MATH 5616H - Honors: Introduction to Analysis II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5588 - Elementary Partial Differential Equations II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent
MATH 5583 - Complex Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 3574/5583
Typically offered: Every Fall, Spring & Summer
Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 5445 - Mathematical Analysis of Biological Networks
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations
MATH 5447 - Theoretical Neuroscience
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574
MATH 5378 - Differential Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Basic geometry of curves in plane and in space, including Frenet formula, theory of surfaces, differential forms, Riemannian geometry. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]; [2283 or 3283] recommended]
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 5335 - Geometry I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Advanced two-dimensional Euclidean geometry from a vector viewpoint. Theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Hyperbolic geometry, how it compares with Euclidean geometry. prereq: [2243 or 2373 or 2573], [concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2374 or concurrent registration is required (or allowed) in 2574]
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 4653 - Elementary Probability
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Probability spaces, distributions of discrete/continuous random variables, conditioning. Basic theorems, calculational methodology. Examples of random sequences. Emphasizes problem-solving. prereq: [2263 or 2374 or 2573]; [2283 or 2574 or 3283] recommended
MATH 4707 - Introduction to Combinatorics and Graph Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Existence, enumeration, construction, algorithms, optimization. Pigeonhole principle, bijective combinatorics, inclusion-exclusion, recursions, graph modeling, isomorphism. Degree sequences and edge counting. Connectivity, Eulerian graphs, trees, Euler's formula, network flows, matching theory. Mathematical induction as proof technique. prereq: 2243, [2283 or 3283]
MATH 5705 - Enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707
MATH 5711 - Linear Programming and Combinatorial Optimization
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 4603 - Advanced Calculus I
Credits: 4.0 [max 4.0]
Course Equivalencies: 01072 - Math 4606/Math 5615/Math 5616
Typically offered: Every Fall, Spring & Summer
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent
MATH 4604 - Advanced Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: 01776
Typically offered: Every Spring
Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent
MATH 4512 - Differential Equations with Applications
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Laplace transforms, series solutions, systems, numerical methods, plane autonomous systems, stability. prereq: 2243 or 2373 or 2573
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 4428 - Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573
MATH 4065 - Theory of Interest
Credits: 4.0 [max 4.0]
Grading Basis: A-F only
Typically offered: Every Fall & Spring
Time value of money, compound interest and general annuities, loans, bonds, general cash flows, basic financial derivatives and their valuation. Primarily for students who are interested in actuarial mathematics. prereq: 1272 or 1372 or 1572
MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical background (e.g., partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods--including Monte Carlo simulation). Interest-rate derivative securities, exotic options, risk theory. First course of two-course sequence. prereq: Two yrs calculus, basic computer skills
MATH 5076 - Mathematics of Options, Futures, and Derivative Securities II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Mathematical background such as partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods (including Monte Carlo simulation), interest-rate derivative securities, exotic options, risk theory. prereq: 5075
MATH 5067 - Actuarial Mathematics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Future lifetime random variable, survival function. Insurance, life annuity, future loss random variables. Net single premium, actuarial present value, net premium, net reserves. prereq: 4065, [one sem [4xxx or 5xxx] [probability or statistics] course]
MATH 5068 - Actuarial Mathematics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Multiple decrement insurance, pension valuation. Expense analysis, gross premium, reserves. Problem of withdrawals. Regulatory reserving systems. Minimum cash values. Additional topics at instructor's discretion. prereq: 5067
CHEM 4501 - Introduction to Thermodynamics, Kinetics, and Statistical Mechanics
Credits: 3.0 [max 3.0]
Course Equivalencies: 00117 - Chem 3501/4501
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Physical chemistry as it relates to macroscopic descriptions of chemical systems. Chemical thermodynamics, phase equilibria, chemical equilibria. Statistical mechanics. Phenomenological reaction kinetics. Kinetic theory of gases. Collision, statistical theories of reaction rates. prereq: [1062/1066 or 1071H/1075H], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374], [PHYS 1302 or PHYS 1402V or PHYS 1502V]
CHEM 4502 - Introduction to Quantum Mechanics and Spectroscopy
Credits: 3.0 [max 3.0]
Course Equivalencies: 00119 - Chem 3502/4502
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
Microscopic descriptions of chemical systems. Quantum theory. Applications to atomic/molecular structure. Molecular spectroscopy. Quantum statistical mechanics. Discussion of solutions to several differential equations. prereq: [1062/1066 or 1072H/1076H], [MATH 2263 or concurrent registration is required (or allowed) in MATH 2263 or MATH 2374 or concurrent registration is required (or allowed) in MATH 2374 or MATH 2243 or concurrent registration is required (or allowed) in MATH 2243 or MATH 2373 or concurrent registration is required (or allowed) in MATH 2373], [PHYS 1302 or PHYS 1402V or PHYS 1502V]
CSCI 4011 - Formal Languages and Automata Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Logical/mathematical foundations of computer science. Formal languages, their correspondence to machine models. Lexical analysis, string matching, parsing. Decidability, undecidability, limits of computability. Computational complexity. prereq: 2041 or instr consent
CSCI 4041 - Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: 02015
Typically offered: Every Fall & Spring
Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr
CSCI 4061 - Introduction to Operating Systems
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Processes/threads, process coordination, interprocess communication, asynchronous events, memory management/file systems. Systems programming projects using operating system interfaces and program development tools. prereq: 2021 or EE 2361; CS upper div, CS minor, CompE upper div., EE upper div., EE grad, ITI upper div., Univ. honors student, or dept. permission; no cr for grads in CSci.
CSCI 4611 - Programming Interactive Computer Graphics and Games
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Tools/techniques for programming games/interactive computer graphics. Event loops, rendering/animation, polygonal models, texturing, physical simulation. Modern graphics toolkits. History/future of computer games technology. Social impact of interactive computer graphics. prereq: 2021 or instr consent
CSCI 5106 - Programming Languages
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Design and implementation of high-level languages. Course has two parts: (1) language design principles, concepts, constructs; (2) language paradigms, applications. Note: course does not teach how to program in specific languages. prereq: 4011 or instr consent
CSCI 5304 - Computational Aspects of Matrix Theory
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Perturbation theory for linear systems and eigenvalue problems. Direct/iterative solution of large linear systems. Matrix factorizations. Computation of eigenvalues/eigenvectors. Singular value decomposition. LAPACK/other software packages. Introduction to sparse matrix methods. prereq: 2031 or 2033 or instr consent
CSCI 5607 - Fundamentals of Computer Graphics 1
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081
CSCI 5608 - Fundamentals of Computer Graphics II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent
CSCI 5403 - Computational Complexity
Credits: 3.0 [max 3.0]
Prerequisites: 4041 or #
Typically offered: Periodic Fall & Spring
Computational models, complexity measures in each model, and related complexity classes. prereq: 4041 or instr consent
CSCI 5421 - Advanced Algorithms and Data Structures
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent
CSCI 5511 - Artificial Intelligence I
Credits: 3.0 [max 3.0]
Course Equivalencies: 01666
Prerequisites: [2041 or #], grad student
Typically offered: Every Fall
Introduction to AI. Problem solving, search, inference techniques. Logic/theorem proving. Knowledge representation, rules, frames, semantic networks. Planning/scheduling. Lisp programming language. prereq: [2041 or instr consent], grad student
CSCI 5512 - Artificial Intelligence II
Credits: 3.0 [max 3.0]
Course Equivalencies: CSci 5512W/5512
Typically offered: Every Spring
Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent
CSCI 5521 - Introduction to Machine Learning
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. prereq: [[2031 or 2033], STAT 3021] or instr consent
ECON 3101 - Intermediate Microeconomics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00025 - Econ 3101/Econ 3101H/ApEc 3001
Grading Basis: A-F only
Typically offered: Every Fall, Spring & Summer
Behavior of households, firms, and industries under competitive/monopolistic conditions. Factors influencing production, price, and other decisions. Applications of theory. Economic efficiency. Distribution of well-being. prereq: [[1101, 1102] or equiv], [MATH 1271 or equiv]
ECON 3102 - Intermediate Macroeconomics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00026 - Econ 3102/ApEc 3006
Grading Basis: A-F only
Typically offered: Every Fall, Spring & Summer
Determinants of national income, employment, and price level; effects of monetary and fiscal policies; emphasis on a general equilibrium approach. Applications of the theory, especially to current macroeconomic policy issues. Students cannot take this course if they have taken ApEc 3006, however, ApEc 3006 does not contain all material in Econ 3102. Econ majors are encouraged to take ECON 3102 instead of ApEc 3006 prereq: 3101 or equiv
ECON 4261 - Introduction to Econometrics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
For Econ B.S. majors only. Review of basic linear regression model, its variants. Time series/simultaneous equation models. Material may include panel data, censored/truncated regressions, discrete choice models. prereq: [3101 or equiv], [[Math 1271, Math 1272] or equiv], Math 2243, Math 2263, [[Stat 4101, Stat 4102] or [Stat 5101, Stat 5102]]; Math 4242 strongly recommended
PHYS 4001 - Analytical Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Analytic Newtonian mechanics. Mathematics beyond prerequisites developed as required. prereq: [2303 or 2601 or Chem 3501 or Chem 3502], two sems soph math
PHYS 4002 - Electricity and Magnetism
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Classical theory of electromagnetic fields using vector algebra and vector calculus. prereq: [2303 or 2601 or Chem 3501 or Chem 3502], two sems soph math
PHYS 4051 - Methods of Experimental Physics I
Credits: 5.0 [max 5.0]
Typically offered: Every Fall
Contemporary experimental techniques. Introduction to modern analog and digital electronics from an experimental viewpoint. Use of computers for data acquisition and experimental control. Statistics of data analysis. prereq: concurrent registration is required (or allowed) in 2605 or equiv lab experience or instr consent
PHYS 4101 - Quantum Mechanics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical techniques of quantum mechanics. Schrodinger Equation and simple applications. General structure of wave mechanics. Operator methods, perturbation theory, radiation from atoms. prereq: [2303 or 2601 or Chem 3502], two sems soph math
PHYS 4201 - Statistical and Thermal Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Principles of thermodynamics and statistical mechanics. Selected applications such as kinetic theory, transport theory, and phase transitions. prereq: 2601
PHYS 4511 - Introduction to Nuclear and Particle Physics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Fundamental particles and Standard Model. Symmetries/quarks, models of nuclei, interactions between particles/nuclei, tests of conservation laws, fission/fusion. prereq: 4101
PHYS 5001 - Quantum Mechanics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Schrodinger equation: bound state and scattering problems in one dimension. Spherically symmetric problems in three dimensions, angular momentum, and the hydrogen atom. Approximation methods for stationary states. Time-dependent perturbation theory. Operators and state vectors: general formalism of quantum theory. prereq: 4101 or equiv or instr consent
STAT 3021 - Introduction to Probability and Statistics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall, Spring & Summer
This is an introductory course in statistics whose primary objectives are to teach students the theory of elementary probability theory and an introduction to the elements of statistical inference, including testing, estimation, and confidence statements. prereq: Math 1272
STAT 3022 - Data Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Practical survey of applied statistical inference/computing covering widely used statistical tools. Multiple regression, variance analysis, experiment design, nonparametric methods, model checking/selection, variable transformation, categorical data analysis, logistic regression. prereq: 3011 or 3021 or SOC 3811
STAT 5021 - Statistical Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Intensive introduction to statistical methods for graduate students needing statistics as a research technique. prereq: Credit will not be granted if credit has been received for: : 3011; College algebra or instr consent; Stat course recommended
STAT 5031 - Statistical Methods for Quality Improvement
Credits: 4.0 [max 4.0]
Typically offered: Periodic Spring
Random variability/sampling. Controlling statistical process. Shewhart/accumulative charting. Analyzing plant data, trend surface, and variance/design of experiments. prereq: [3021 or 3022 or 4102 or 5021 or 5102 or 8102], Math 1272
STAT 5302 - Applied Regression Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Simple, multiple, and polynomial regression. Estimation, testing, prediction. Use of graphics in regression. Stepwise and other numerical methods. Weighted least squares, nonlinear models, response surfaces. Experimental research/applications. prereq: 3022 or 4102 or 5021 or 5102 or instr consent
STAT 5303 - Designing Experiments
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Analysis of variance. Multiple comparisons. Variance-stabilizing transformations. Contrasts. Construction/analysis of complete/incomplete block designs. Fractional factorial designs. Confounding split plots. Response surface design. prereq: 3022 or 4102 or 5021 or 5102 or instr consent
STAT 5421 - Analysis of Categorical Data
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Varieties of categorical data, cross-classifications, contingency tables. Tests for independence. Combining 2x2 tables. Multidimensional tables/loglinear models. Maximum-likelihood estimation. Tests for goodness of fit. Logistic regression. Generalized linear/multinomial-response models.
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 4065 - Theory of Interest
Credits: 4.0 [max 4.0]
Grading Basis: A-F only
Typically offered: Every Fall & Spring
Time value of money, compound interest and general annuities, loans, bonds, general cash flows, basic financial derivatives and their valuation. Primarily for students who are interested in actuarial mathematics. prereq: 1272 or 1372 or 1572
MATH 5067 - Actuarial Mathematics I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Future lifetime random variable, survival function. Insurance, life annuity, future loss random variables. Net single premium, actuarial present value, net premium, net reserves. prereq: 4065, [one sem [4xxx or 5xxx] [probability or statistics] course]
MATH 5068 - Actuarial Mathematics II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Multiple decrement insurance, pension valuation. Expense analysis, gross premium, reserves. Problem of withdrawals. Regulatory reserving systems. Minimum cash values. Additional topics at instructor's discretion. prereq: 5067
MATH 5075 - Mathematics of Options, Futures, and Derivative Securities I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Mathematical background (e.g., partial differential equations, Fourier series, computational methods, Black-Scholes theory, numerical methods--including Monte Carlo simulation). Interest-rate derivative securities, exotic options, risk theory. First course of two-course sequence. prereq: Two yrs calculus, basic computer skills
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 4428 - Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
ECON 1101 - Principles of Microeconomics (SOCS, GP)
Credits: 4.0 [max 4.0]
Course Equivalencies: Econ 1101/1104/1111/ApEc 1101
Typically offered: Every Fall, Spring & Summer
Microeconomic behavior of consumers, firms, and markets in domestic and world economy. Demand and supply. Competition and monopoly. Distribution of income. Economic interdependencies in the global economy. Effects of global linkages on individual decisions. prereq: knowledge of plane geometry and advanced algebra
ECON 1102 - Principles of Macroeconomics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00020 - ApEc 1102/Econ 1102/1105/1112
Typically offered: Every Fall, Spring & Summer
Aggregate consumption, saving, investment, and national income. Role of money, banking, and business cycles in domestic and world economy. International trade, growth, and development. U.S. economy and its role in the world economy. International interdependencies among nations. prereq: [1101 or equiv], knowledge of plane geometry and advanced algebra
ACCT 2050 - Introduction to Financial Reporting
Credits: 4.0 [max 4.0]
Course Equivalencies: 00458 - Acct 2050/ApEc 1251
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Introduction to financial accounting for U.S. organizations. Reading financial statements. prereq: Soph
ECON 3101 - Intermediate Microeconomics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00025 - Econ 3101/Econ 3101H/ApEc 3001
Grading Basis: A-F only
Typically offered: Every Fall, Spring & Summer
Behavior of households, firms, and industries under competitive/monopolistic conditions. Factors influencing production, price, and other decisions. Applications of theory. Economic efficiency. Distribution of well-being. prereq: [[1101, 1102] or equiv], [MATH 1271 or equiv]
ECON 4261 - Introduction to Econometrics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
For Econ B.S. majors only. Review of basic linear regression model, its variants. Time series/simultaneous equation models. Material may include panel data, censored/truncated regressions, discrete choice models. prereq: [3101 or equiv], [[Math 1271, Math 1272] or equiv], Math 2243, Math 2263, [[Stat 4101, Stat 4102] or [Stat 5101, Stat 5102]]; Math 4242 strongly recommended
FINA 3001 - Finance Fundamentals
Credits: 3.0 [max 3.0]
Course Equivalencies: 00196
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Financial management principles. Money/capital markets, risk/return/valuation triad, capital budgeting. Capital structure, financial leverage. Cost of capital, financial performance measures, dividend policy, working capital management, international financial management/derivatives. prereq: ACCT 2050, SCO 2550 or equivalent statistics course
INS 4100 - Corporate Risk Management
Credits: 2.0 [max 2.0]
Typically offered: Every Fall & Spring
Theory applied to corporate risk management and insurance practices. Identification, measurement, and treatment of an organization.s financial risks integrated with its property, liability, workers compensation, and human resource risks. Selection and application of risk control and risk financing tools: risk retention, reduction and transfer, including insurance.
INS 4101 - Employee Benefits
Credits: 2.0 [max 2.0]
Typically offered: Every Fall
Design/administration of employee benefit plans/pension. Health insurance, disability plans. Salary reduction/deferred compensation programs. Multiple employer trusts. Alternative funding methods, including self-insurance. Ethical issues, legal liability, compliance.
INS 4200 - Insurance Theory and Practice
Credits: 2.0 [max 2.0]
Typically offered: Every Spring
Risk theory is applied to practices in health, liability, life, property, and workers compensation insurance. Insurance marketing, pricing, underwriting, and claims administration, with adverse selection and moral hazard effects. Policy issues of tort versus no-fault compensation systems. Self-insurance and integrated risk financing methods.
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 5485 - Introduction to Numerical Methods I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Solution of nonlinear equations in one variable. Interpolation, polynomial approximation. Methods for solving linear systems, eigenvalue problems, systems of nonlinear equations. prereq: [2243 or 2373 or 2573], familiarity with some programming language
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 4567 - Applied Fourier Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573
MATH 4603 - Advanced Calculus I
Credits: 4.0 [max 4.0]
Course Equivalencies: 01072 - Math 4606/Math 5615/Math 5616
Typically offered: Every Fall, Spring & Summer
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent
MATH 4604 - Advanced Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: 01776
Typically offered: Every Spring
Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5583 - Complex Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 3574/5583
Typically offered: Every Fall, Spring & Summer
Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5588 - Elementary Partial Differential Equations II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent
MATH 5615H - Honors: Introduction to Analysis I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574
MATH 5616H - Honors: Introduction to Analysis II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 5654 - Prediction and Filtering
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
MATH 5165 - Mathematical Logic I
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 4152/5165
Typically offered: Every Fall
Theory of computability: notion of algorithm, Turing machines, primitive recursive functions, recursive functions, Kleene normal form, recursion theorem. Propositional logic. prereq: 2283 or 3283 or Phil 5201 or CSci course in theory of algorithms or instr consent
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5166 - Mathematical Logic II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
First-order logic: provability/truth in formal systems, models of axiom systems, Godel's completeness theorem. Godel's incompleteness theorem: decidable theories, representability of recursive functions in formal theories, undecidable theories, models of arithmetic. prereq: 5165
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 5705 - Enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707
MATH 5711 - Linear Programming and Combinatorial Optimization
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Simplex method, connections to geometry, duality theory, sensitivity analysis. Applications to cutting stock, allocation of resources, scheduling problems. Flows, matching/transportation problems, spanning trees, distance in graphs, integer programs, branch/bound, cutting planes, heuristics. Applications to traveling salesman, knapsack problems. prereq: 2 sems soph math [including 2243 or 2373 or 2573]
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
CSCI 1933 - Introduction to Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: 00008
Typically offered: Every Fall, Spring & Summer
Advanced object oriented programming to implement abstract data types (stacks, queues, linked lists, hash tables, binary trees) using Java language. Inheritance. Searching/sorting algorithms. Basic algorithmic analysis. Use of software development tools. Weekly lab. prereq: 1133 or instr consent
CSCI 1913 - Introduction to Algorithms, Data Structures, and Program Development
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Advanced object oriented programming to implement abstract data types(stacks, queues, linked lists, hash tables, binary trees) using Java language. Searching/sorting algorithms. Basic algorithmic analysis. Scripting languages using Python language. Substantial programming projects. Weekly lab. prereq: (EE major and EE 1301) or (CmpE major and EE 1301) or 1103 or 1113 or instr consent
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 2011 - Discrete Structures of Computer Science
Credits: 4.0 [max 4.0]
Course Equivalencies: 02004
Typically offered: Every Fall & Spring
Foundations of discrete mathematics. Sets, sequences, functions, big-O, propositional/predicate logic, proof methods, counting methods, recursion/recurrences, relations, trees/graph fundamentals. prereq: MATH 1271 or MATH 1371 or instr consent
CSCI 4011 - Formal Languages and Automata Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Logical/mathematical foundations of computer science. Formal languages, their correspondence to machine models. Lexical analysis, string matching, parsing. Decidability, undecidability, limits of computability. Computational complexity. prereq: 2041 or instr consent
CSCI 4041 - Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: 02015
Typically offered: Every Fall & Spring
Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr
CSCI 4511W - Introduction to Artificial Intelligence (WI)
Credits: 4.0 [max 4.0]
Course Equivalencies: 01666 - CSci 4511W/CSci 5511
Prerequisites: 2041 or #
Typically offered: Every Spring
Problem solving, search, inference techniques. Knowledge representation. Planning. Machine learning. Robotics. Lisp programming language. Cannot be taken for grad CSci credit. prereq: 2041 or instr consent
CSCI 5607 - Fundamentals of Computer Graphics 1
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Fundamental algorithms in computer graphics. Emphasizes programming projects in C/C++. Scan conversion, hidden surface removal, geometrical transformations, projection, illumination/shading, parametric cubic curves, texture mapping, antialising, ray tracing. Developing graphics software, graphics research. prereq: concurrent registration is required (or allowed) in 2033, concurrent registration is required (or allowed) in 3081
CSCI 5608 - Fundamentals of Computer Graphics II
Credits: 3.0 [max 3.0]
Typically offered: Periodic Spring
Advanced topics in image synthesis, modeling, rendering. Image processing, image warping, global illumination, non-photorealistic rendering, texture synthesis. Parametric cubic surfaces, subdivision surfaces, acceleration techniques, advanced texture mapping. Programming in C/C++. prereq: 5607 or instr consent
CSCI 5421 - Advanced Algorithms and Data Structures
Credits: 3.0 [max 3.0]
Typically offered: Every Fall & Spring
Fundamental paradigms of algorithm and data structure design. Divide-and-conquer, dynamic programming, greedy method, graph algorithms, amortization, priority queues and variants, search structures, disjoint-set structures. Theoretical underpinnings. Examples from various problem domains. prereq: 4041 or instr consent
CSCI 5451 - Introduction to Parallel Computing: Architectures, Algorithms, and Programming
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Parallel architectures design, embeddings, routing. Examples of parallel computers. Fundamental communication operations. Performance metrics. Parallel algorithms for sorting. Matrix problems, graph problems, dynamic load balancing, types of parallelisms. Parallel programming paradigms. Message passing programming in MPI. Shared-address space programming in openMP or threads. prereq: 4041 or instr consent
CSCI 5511 - Artificial Intelligence I
Credits: 3.0 [max 3.0]
Course Equivalencies: 01666
Prerequisites: [2041 or #], grad student
Typically offered: Every Fall
Introduction to AI. Problem solving, search, inference techniques. Logic/theorem proving. Knowledge representation, rules, frames, semantic networks. Planning/scheduling. Lisp programming language. prereq: [2041 or instr consent], grad student
CSCI 5512 - Artificial Intelligence II
Credits: 3.0 [max 3.0]
Course Equivalencies: CSci 5512W/5512
Typically offered: Every Spring
Uncertainty in artificial intelligence. Probability as a model of uncertainty, methods for reasoning/learning under uncertainty, utility theory, decision-theoretic methods. prereq: [STAT 3021, 4041] or instr consent
CSCI 5521 - Introduction to Machine Learning
Credits: 3.0 [max 3.0]
Typically offered: Periodic Fall
Problems of pattern recognition, feature selection, measurement techniques. Statistical decision theory, nonstatistical techniques. Automatic feature selection/data clustering. Syntactic pattern recognition. Mathematical pattern recognition/artificial intelligence. prereq: [[2031 or 2033], STAT 3021] or instr consent
PHYS 2303 - Physics III: Physics of Matter
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503/2503H
Typically offered: Every Spring
Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student
PHYS 2311 - Modern Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Broad overview of physical concepts developed in twentieth century. Special relativity, wave-particle duality, Schrodinger equation, Bohr atom, hydrogen atom in wave mechanics, many-electron atoms, x-rays, nuclear structure, radioactivity, nuclear reactions, statistical physics. prereq: [1302 or 1402], Chem 1022, Math 2243
PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503
Typically offered: Every Fall
Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W, [MATH 1272 or MATH 1372 or MATH 1572H]
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 4707 - Introduction to Combinatorics and Graph Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Existence, enumeration, construction, algorithms, optimization. Pigeonhole principle, bijective combinatorics, inclusion-exclusion, recursions, graph modeling, isomorphism. Degree sequences and edge counting. Connectivity, Eulerian graphs, trees, Euler's formula, network flows, matching theory. Mathematical induction as proof technique. prereq: 2243, [2283 or 3283]
MATH 5705 - Enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic enumeration, bijections, inclusion-exclusion, recurrence relations, ordinary/exponential generating functions, partitions, Polya theory. Optional topics include trees, asymptotics, listing algorithms, rook theory, involutions, tableaux, permutation statistics. prereq: [2243 or 2373 or 2573], [2263 or 2283 or 2374 or 2574 or 3283]
MATH 5707 - Graph Theory and Non-enumerative Combinatorics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Basic topics in graph theory: connectedness, Eulerian/Hamiltonian properties, trees, colorings, planar graphs, matchings, flows in networks. Optional topics include graph algorithms, Latin squares, block designs, Ramsey theory. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]; [2283 or 3283 or experience in writing proofs] highly recommended; Credit will not be granted if credit has been received for: 4707
MATH 5335 - Geometry I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Advanced two-dimensional Euclidean geometry from a vector viewpoint. Theorems/problems about triangles/circles, isometries, connections with Euclid's axioms. Hyperbolic geometry, how it compares with Euclidean geometry. prereq: [2243 or 2373 or 2573], [concurrent registration is required (or allowed) in 2263 or concurrent registration is required (or allowed) in 2374 or concurrent registration is required (or allowed) in 2574]
MATH 4653 - Elementary Probability
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Probability spaces, distributions of discrete/continuous random variables, conditioning. Basic theorems, calculational methodology. Examples of random sequences. Emphasizes problem-solving. prereq: [2263 or 2374 or 2573]; [2283 or 2574 or 3283] recommended
MATH 4567 - Applied Fourier Analysis
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Fourier series, integral/transform. Convergence. Fourier series, transform in complex form. Solution of wave, heat, Laplace equations by separation of variables. Sturm-Liouville systems, finite Fourier, fast Fourier transform. Applications. Other topics as time permits. prereq: 2243 or 2373 or 2573
MATH 4603 - Advanced Calculus I
Credits: 4.0 [max 4.0]
Course Equivalencies: 01072 - Math 4606/Math 5615/Math 5616
Typically offered: Every Fall, Spring & Summer
Axioms for the real numbers. Techniques of proof for limits, continuity, uniform convergence. Rigorous treatment of differential/integral calculus for single-variable functions. prereq: [[2243 or 2373], [2263 or 2374]] or 2574 or instr consent
MATH 4604 - Advanced Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: 01776
Typically offered: Every Spring
Sequel to MATH 4603. Topology of n-dimensional Euclidean space. Rigorous treatment of multivariable differentiation and integration, including chain rule, Taylor's Theorem, implicit function theorem, Fubini's Theorem, change of variables, Stokes' Theorem. prereq: 4603 or 5615 or instr consent
MATH 5486 - Introduction To Numerical Methods II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations. prereq: 5485
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5583 - Complex Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 3574/5583
Typically offered: Every Fall, Spring & Summer
Algebra, geometry of complex numbers. Linear fractional transformations. Conformal mappings. Holomorphic functions. Theorems of Abel/Cauchy, power series. Schwarz' lemma. Complex exponential, trig functions. Entire functions, theorems of Liouville/Morera. Reflection principle. Singularities, Laurent series. Residues. prereq: 2 sems soph math [including [2263 or 2374 or 2573], [2283 or 3283]] recommended
MATH 5587 - Elementary Partial Differential Equations I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Emphasizes partial differential equations w/physical applications, including heat, wave, Laplace's equations. Interpretations of boundary conditions. Characteristics, Fourier series, transforms, Green's functions, images, computational methods. Applications include wave propagation, diffusions, electrostatics, shocks. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5588 - Elementary Partial Differential Equations II
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Spring
Heat, wave, Laplace's equations in higher dimensions. Green's functions, Fourier series, transforms. Asymptotic methods, boundary layer theory, bifurcation theory for linear/nonlinear PDEs. Variational methods. Free boundary problems. Additional topics as time permits. prereq: [[2243 or 2373 or 2573], [2263 or 2374 or 2574], 5587] or instr consent
MATH 5615H - Honors: Introduction to Analysis I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Axiomatic treatment of real/complex number systems. Introduction to metric spaces: convergence, connectedness, compactness. Convergence of sequences/series of real/complex numbers, Cauchy criterion, root/ratio tests. Continuity in metric spaces. Rigorous treatment of differentiation of single-variable functions, Taylor's Theorem. prereq: [[2243 or 2373], [2263 or 2374], [2283 or 3283]] or 2574
MATH 5616H - Honors: Introduction to Analysis II
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Rigorous treatment of Riemann-Stieltjes integration. Sequences/series of functions, uniform convergence, equicontinuous families, Stone-Weierstrass Theorem, power series. Rigorous treatment of differentiation/integration of multivariable functions, Implicit Function Theorem, Stokes' Theorem. Additional topics as time permits. prereq: 5615
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
MATH 5652 - Introduction to Stochastic Processes
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Random walks, Markov chains, branching processes, martingales, queuing theory, Brownian motion. prereq: 5651 or Stat 5101
MATH 5654 - Prediction and Filtering
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Markov chains, Wiener process, stationary sequences, Ornstein-Uhlenbeck process. Partially observable Markov processes (hidden Markov models), stationary processes. Equations for general filters, Kalman filter. Prediction of future values of partially observable processes. prereq: 5651 or Stat 5101
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
PHYS 2303 - Physics III: Physics of Matter
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503/2503H
Typically offered: Every Spring
Thermodynamics, mechanical/electromagnetic waves, optics, quantum theory. Applications of quantum nature of solids. prereq: 1302, [MATH 1272 or MATH 1372 or MATH 1572H], [MatSci or EE] student
PHYS 2311 - Modern Physics
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Broad overview of physical concepts developed in twentieth century. Special relativity, wave-particle duality, Schrodinger equation, Bohr atom, hydrogen atom in wave mechanics, many-electron atoms, x-rays, nuclear structure, radioactivity, nuclear reactions, statistical physics. prereq: [1302 or 1402], Chem 1022, Math 2243
PHYS 2503 - Physics III: Intro to Waves, Optics, and Special Relativity
Credits: 4.0 [max 4.0]
Course Equivalencies: 00080 - Phys 2303/2403H/2503
Typically offered: Every Fall
Third semester of introductory physics. Mechanical/electromagnetic waves, optics, special relativity. prereq: 1302W, [MATH 1272 or MATH 1372 or MATH 1572H]
MATH 4428 - Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
MATH 5445 - Mathematical Analysis of Biological Networks
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
CSCI 1933 - Introduction to Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: 00008
Typically offered: Every Fall, Spring & Summer
Advanced object oriented programming to implement abstract data types (stacks, queues, linked lists, hash tables, binary trees) using Java language. Inheritance. Searching/sorting algorithms. Basic algorithmic analysis. Use of software development tools. Weekly lab. prereq: 1133 or instr consent
CSCI 1913 - Introduction to Algorithms, Data Structures, and Program Development
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Advanced object oriented programming to implement abstract data types(stacks, queues, linked lists, hash tables, binary trees) using Java language. Searching/sorting algorithms. Basic algorithmic analysis. Scripting languages using Python language. Substantial programming projects. Weekly lab. prereq: (EE major and EE 1301) or (CmpE major and EE 1301) or 1103 or 1113 or instr consent
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 5461 - Functional Genomics, Systems Biology, and Bioinformatics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Computational methods for analyzing, integrating, and deriving predictions from genomic/proteomic data. Analyzing gene expression, proteomic data, and protein-protein interaction networks. Protein/gene function prediction, Integrating diverse data, visualizing genomic datasets. prereq: 3003 or 4041 or instr consent
CSCI 3003 - Introduction to Computing in Biology
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Emphasizes computing tasks common in biology. Programming techniques: variables, flow control, input/output, strings, pattern matching, arrays, hash tables, functions, subroutines. Concepts in computing: algorithms, complexity, documentation, regular expressions/grammars, local variables, encapsulation. Students complete lab projects in Perl language. prereq: 1002H or Biol 1002 or 1009H or Biol 1009 or equiv or instr consent
CSCI 5481 - Computational Techniques for Genomics
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
Techniques to analyze biological data generated by genome sequencing, proteomics, cell-wide measurements of gene expression changes. Algorithms for single/multiple sequence alignments/assembly. Search algorithms for sequence databases, phylogenetic tree construction algorithms. Algorithms for gene/promoter and protein structure prediction. Data mining for micro array expression analysis. Reverse engineering of regulatory networks. prereq: 4041 or instr consent
CSCI 4041 - Algorithms and Data Structures
Credits: 4.0 [max 4.0]
Course Equivalencies: 02015
Typically offered: Every Fall & Spring
Rigorous analysis of algorithms/implementation. Algorithm analysis, sorting algorithms, binary trees, heaps, priority queues, heapsort, balanced binary search trees, AVL trees, hash tables and hashing, graphs, graph traversal, single source shortest path, minimum cost spanning trees. prereq: [(1913 or 1933) and 2011] or instr consent; cannot be taken for grad CSci cr
CSCI 2011 - Discrete Structures of Computer Science
Credits: 4.0 [max 4.0]
Course Equivalencies: 02004
Typically offered: Every Fall & Spring
Foundations of discrete mathematics. Sets, sequences, functions, big-O, propositional/predicate logic, proof methods, counting methods, recursion/recurrences, relations, trees/graph fundamentals. prereq: MATH 1271 or MATH 1371 or instr consent
BIOL 1009 - General Biology (BIOL)
Credits: 4.0 [max 4.0]
Course Equivalencies: 01525
Typically offered: Every Fall, Spring & Summer
Major concepts of modern biology. Molecular structure of living things, energy recruitment/utilization, flow of genetic information through organisms/populations. Principles of inheritance, ecology, and evolution. Includes lab. prereq: high school chemistry; 1 term college chemistry recommended
GCD 3022 - Genetics
Credits: 3.0 [max 3.0]
Course Equivalencies: Biol 4003/GCD 3022
Typically offered: Every Fall, Spring & Summer
Mechanisms of heredity, implications for biological populations. Applications to practical problems. prereq: BIOL 2002 or BIOL 1009
EEB 5042 - Quantitative Genetics
Credits: 3.0 [max 3.0]
Grading Basis: A-F only
Typically offered: Every Fall
Fundamentals of quantitative genetics. Genetic/environmental influences on expression of quantitative traits. Approaches to characterizing genetic basis of trait variation. Processes that lead to change in quantitative traits. Applied/evolutionary aspects of quantitative genetic variation. prereq: [BIOL 4003 or GCD 3022] or instr consent; a course in statistics is recommended
GCD 4143 - Human Genetics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Principles of human genetics at the molecular, cellular, individual, and populations levels. Chromosomal and biochemical disorders; gene mapping; mutation and natural selection; variation in intelligence and behavior; genetic screening, counseling and therapy. prereq: 3022 or Biol 4003 or instr consent
MATH 5445 - Mathematical Analysis of Biological Networks
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations
PBIO 5301 - Plant Genomics
Credits: 3.0 [max 3.0]
Course Equivalencies: 01050 - PBio 5301/PlPa 5301
Typically offered: Every Fall
Introduction to genomics. Emphasizes plants and relevant model organisms. DNA marker/sequencing technology, comparative genomics, whole genome sequencing, DNA chips/microarrays, EST libraries and SAGE analysis, gene-knockout systems, genome databases, sequence comparison/clustering algorithms, visualization tools. prereq: [Intro course in genetics, intro course in biochemistry] or instr consent
GCD 4151 - Molecular Biology of Cancer
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Periodic Spring
Regulatory pathways involved in directing normal development of complex eukaryotic organisms, how disruptions of these pathways can lead to abnormal cell growth/cancer. Causes, detection, treatment, prevention of cancer. prereq: Biol 4003
MATH 4428 - Mathematical Modeling
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Modeling techniques for analysis/decision-making in industry. Optimization (sensitivity analysis, Lagrange multipliers, linear programming). Dynamical modeling (steady-states, stability analysis, eigenvalue methods, phase portraits, simulation). Probabilistic methods (probability/statistical models, Markov chains, linear regression, simulation). prereq: 2243 or 2373 or 2573
MATH 5445 - Mathematical Analysis of Biological Networks
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Development/analysis of models for complex biological networks. Examples taken from signal transduction networks, metabolic networks, gene control networks, and ecological networks. prereq: Linear algebra, differential equations
MATH 5447 - Theoretical Neuroscience
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Nonlinear dynamical system models of neurons and neuronal networks. Computation by excitatory/inhibitory networks. Neural oscillations, adaptation, bursting, synchrony. Memory systems. prereq: 2243 or 2373 or 2574
MATH 4281 - Introduction to Modern Algebra
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall
Equivalence relations, greatest common divisor, prime decomposition, modular arithmetic, groups, rings, fields, Chinese remainder theorem, matrices over commutative rings, polynomials over fields. prereq: 2283 or 3283 or instr consent
MATH 5248 - Cryptology and Number Theory
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Classical cryptosystems. One-time pads, perfect secrecy. Public key ciphers: RSA, discrete log. Euclidean algorithm, finite fields, quadratic reciprocity. Message digest, hash functions. Protocols: key exchange, secret sharing, zero-knowledge proofs. Probablistic algorithms: pseudoprimes, prime factorization. Pseudo-random numbers. Elliptic curves. prereq: 2 sems soph math
MATH 5251 - Error-Correcting Codes, Finite Fields, Algebraic Curves
Credits: 4.0 [max 4.0]
Typically offered: Every Spring
Information theory: channel models, transmission errors. Hamming weight/distance. Linear codes/fields, check bits. Error processing: linear codes, Hamming codes, binary Golay codes. Euclidean algorithm. Finite fields, Bose-Chaudhuri-Hocquenghem codes, polynomial codes, Goppa codes, codes from algebraic curves. prereq: 2 sems soph math
MATH 5285H - Honors: Fundamental Structures of Algebra I
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Review of matrix theory, linear algebra. Vector spaces, linear transformations over abstract fields. Group theory, including normal subgroups, quotient groups, homomorphisms, class equation, Sylow's theorems. Specific examples: permutation groups, symmetry groups of geometric figures, matrix groups. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5286H - Honors: Fundamental Structures of Algebra II
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Ring/module theory, including ideals, quotients, homomorphisms, domains (unique factorization, euclidean, principal ideal), fundamental theorem for finitely generated modules over euclidean domains, Jordan canonical form. Introduction to field theory, including finite fields, algebraic/transcendental extensions, Galois theory. prereq: 5285
MATH 5385 - Introduction to Computational Algebraic Geometry
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Geometry of curves/surfaces defined by polynomial equations. Emphasizes concrete computations with polynomials using computer packages, interplay between algebra and geometry. Abstract algebra presented as needed. prereq: [2263 or 2374 or 2573], [2243 or 2373 or 2574]
MATH 4242 - Applied Linear Algebra
Credits: 4.0 [max 4.0]
Course Equivalencies: 01212 - Math 4242/Math 4457
Typically offered: Every Fall, Spring & Summer
Systems of linear equations, vector spaces, subspaces, bases, linear transformations, matrices, determinants, eigenvalues, canonical forms, quadratic forms, applications. prereq: 2243 or 2373 or 2573
MATH 5525 - Introduction to Ordinary Differential Equations
Credits: 4.0 [max 4.0]
Typically offered: Periodic Fall & Spring
Ordinary differential equations, solution of linear systems, qualitative/numerical methods for nonlinear systems. Linear algebra background, fundamental matrix solutions, variation of parameters, existence/uniqueness theorems, phase space. Rest points, their stability. Periodic orbits, Poincare-Bendixson theory, strange attractors. prereq: [2243 or 2373 or 2573], [2283 or 2574 or 3283]
MATH 5535 - Dynamical Systems and Chaos
Credits: 4.0 [max 4.0]
Typically offered: Every Fall & Spring
Dynamical systems theory. Emphasizes iteration of one-dimensional mappings. Fixed points, periodic points, stability, bifurcations, symbolic dynamics, chaos, fractals, Julia/Mandelbrot sets. prereq: [2243 or 2373 or 2573], [2263 or 2374 or 2574]
MATH 5651 - Basic Theory of Probability and Statistics
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - MATH 4653/Math 5651/Stat 5101
Typically offered: Every Fall & Spring
Logical development of probability, basic issues in statistics. Probability spaces, random variables, their distributions/expected values. Law of large numbers, central limit theorem, generating functions, sampling, sufficiency, estimation. prereq: [2263 or 2374 or 2573], [2243 or 2373]; [2283 or 2574 or 3283] recommended.
STAT 5101 - Theory of Statistics I
Credits: 4.0 [max 4.0]
Course Equivalencies: 00259 - Math 5651/Stat 5101
Typically offered: Every Fall
Logical development of probability, basic issues in statistics. Probability spaces. Random variables, their distributions and expected values. Law of large numbers, central limit theorem, generating functions, multivariate normal distribution. prereq: [Math 2263 or Math 2374 or Math 2573H], [CSCI 2033 or Math 2373 or Math 2243]
CSCI 1103 - Introduction to Computer Programming in Java
Credits: 4.0 [max 4.0]
Typically offered: Every Fall
Fundamental programming concepts/software development using Java language. Problem solving skills. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Substantial programming projects. Weekly lab.
CSCI 1113 - Introduction to C/C++ Programming for Scientists and Engineers
Credits: 4.0 [max 4.0]
Typically offered: Every Fall, Spring & Summer
Programming for scientists/engineers. C/C++ programming constructs, object-oriented programming, software development, fundamental numerical techniques. Exercises/examples from various scientific fields. prereq: Math 1271 or Math 1371 or Math 1571H or instr consent
CSCI 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 02133 - CSci 1133/CSci 1133H
Typically offered: Every Fall, Spring & Summer
Fundamental programming concepts using Python language. Problem solving skills, recursion, object-oriented programming. Algorithm development techniques. Use of abstractions/modularity. Data structures/abstract data types. Develop programs to solve real-world problems. prereq: concurrent registration is required (or allowed) in MATH 1271 or concurrent registration is required (or allowed) in MATH 1371 or concurrent registration is required (or allowed) in MATH 1571H or instr consent
PHSL 3061 - Principles of Physiology
Credits: 4.0 [max 4.0]
Course Equivalencies: 01354
Typically offered: Every Fall
Human physiology with emphasis on quantitative aspects. Organ systems (circulation, respiration, gastrointestinal, renal, endocrine, muscle, peripheral and central nervous systems), cellular transport processes, and scaling in biology. prereq: 1 year college chem and physics and math through integral calculus
BIOL 1009 - General Biology (BIOL)
Credits: 4.0 [max 4.0]
Course Equivalencies: 01525
Typically offered: Every Fall, Spring & Summer
Major concepts of modern biology. Molecular structure of living things, energy recruitment/utilization, flow of genetic information through organisms/populations. Principles of inheritance, ecology, and evolution. Includes lab. prereq: high school chemistry; 1 term college chemistry recommended
CHEM 1061 - Chemical Principles I (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: 01884 - Chem 1061/Chem 1071H
Typically offered: Every Fall, Spring & Summer
Atomic theory, periodic properties of elements. Thermochemistry, reaction stoichiometry. Behavior of gases, liquids, and solids. Molecular/ionic structure/bonding. Organic chemistry and polymers. energy sources, environmental issues related to energy use. Prereq-Grade of at least C- in [1011 or 1015] or [passing placement exam, concurrent registration is required (or allowed) in 1065]; intended for science or engineering majors; concurrent registration is required (or allowed) in 1065; registration for 1065 must precede registration for 1061
CHEM 1065 - Chemical Principles I Laboratory (PHYS)
Credits: 1.0 [max 1.0]
Course Equivalencies: 01878 - Chem 1065/Chem 1075H
Grading Basis: A-F only
Typically offered: Every Fall, Spring & Summer
Basic laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and proper treatment of hazardous wastes. prereq: concurrent registration is required (or allowed) in 1061
CHEM 1071H - Honors Chemistry I (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: 01884 - Chem 1061/Chem 1071H
Grading Basis: A-F only
Typically offered: Every Fall
Advanced introduction to atomic theory. Periodic properties of elements. Behavior of gases, liquids, and solids. Molecular/ionic structure, bonding. Aspects of organic chemistry, spectroscopy, and polymers. Mathematically demanding quantitative problems. Writing for scientific journals. prereq: Honors student, permission of University Honors Program, concurrent registration is required (or allowed) in 1075H; registration for 1075H must precede registration for 1071H
CHEM 1075H - Honors Chemistry I Laboratory (PHYS)
Credits: 1.0 [max 1.0]
Course Equivalencies: 01878 - Chem 1065/Chem 1075H
Grading Basis: A-F only
Typically offered: Every Fall
Develop laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and the proper treatment of hazardous wastes. Prereq-&1071H, honors student, permission of University Honors Program.
CHEM 1062 - Chemical Principles II (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: 01885 - Chem 1062/Chem 1072H
Typically offered: Every Fall, Spring & Summer
Chemical kinetics. Radioactive decay. Chemical equilibrium. Solutions. Acids/bases. Solubility. Second law of thermodynamics. Electrochemistry/corrosion. Descriptive chemistry of elements. Coordination chemistry. Biochemistry. prereq: Grade of at least C- in 1061 or equiv, concurrent registration is required (or allowed) in 1066; registration for 1066 must precede registration for 1062
CHEM 1066 - Chemical Principles II Laboratory (PHYS)
Credits: 1.0 [max 1.0]
Course Equivalencies: 01879 - Chem 1066/Chem 1076H
Grading Basis: A-F only
Typically offered: Every Fall, Spring & Summer
Basic laboratory skills while investigating physical and chemical phenomena closely linked to lecture material. Experimental design, data collection and treatment, discussion of errors, and proper treatment of hazardous wastes. prereq: concurrent registration is required (or allowed) in 1062
CHEM 1072H - Honors Chemistry II (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: 01885 - Chem 1062/Chem 1072H
Grading Basis: A-F only
Typically offered: Every Spring
Advanced introduction. Chemical kinetics/reaction mechanisms, chemical/physical equilibria, acids/bases, entropy/second law of thermodynamics, electrochemistry/corrosion; descriptive chemistry of elements; coordination chemistry; biochemistry. prereq: 1071H, concurrent registration is required (or allowed) in 1076H, honors student, registration for 1076H must precede registration for 1072H
CHEM 1076H - Honors Chemistry II Laboratory (PHYS)
Credits: 1.0 [max 1.0]
Course Equivalencies: 01879 - Chem 1066/Chem 1076H
Grading Basis: A-F only
Typically offered: Every Spring
Develop laboratory skills as experiments become increasingly complex. Data collection/treatment, discussion of errors, proper treatment of hazardous wastes, experiment design. prereq: concurrent registration is required (or allowed) in 1072H
PHSL 4700 - Cell Physiology
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
Critical cell functions. Regulation of pH, volume, intracellular electrolyte composition, calcium signaling, membrane potential dynamics, motility, aspects of intercellular communication. prereq: [3051 or 3061 or BIOL 3211], [CHEM 1022 or equiv], [MATH 1272 or equiv]
PHSL 5444 - Muscle
Credits: 3.0 [max 3.0]
Course Equivalencies: BioC/Phsl 5444
Typically offered: Every Spring
Muscle membranes: structures, mechanisms, and physiological roles of channels/pumps. Muscle contraction: force generation by actin/myosin. prereq: 3061 or 3071 or 5061 or BioC 3021 or BioC 4331 or instr consent
NSC 5202 - Theoretical Neuroscience: Systems and Information Processing
Credits: 3.0 [max 3.0]
Course Equivalencies: NSc 5202/Phsl 5202
Typically offered: Every Spring
Concepts of computational/theoretical neuroscience. Distributed representations and information theory. Methods for single-cell modeling, including compartmental/integrate-and-fire models. Learning rules, including supervised, unsupervised, and reinforcement learning models. Specific systems models from current theoretical neuroscience literature. Lecture/discussion. Readings from current scientific literature. prereq: [3101, 3102W] recommended