Twin Cities campus

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Twin Cities Campus

Mathematics B.A.

School of Mathematics
College of Liberal Arts
  • Program Type: Baccalaureate
  • Requirements for this program are current for Fall 2015
  • Required credits to graduate with this degree: 120
  • Required credits within the major: 30 to 72
  • Degree: Bachelor of Arts
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 in the College of Liberal Arts leading to a bachelor of arts 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 may emphasize various fields of interest, such as preparation for secondary school teaching, actuarial science, or programs in applied mathematics. This includes 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 3 courses before admission to the program.
Successful completion of Calculus I (1271/1371/1571H) plus Calculus II (1272/1372/1572H) plus one 2xxx level Calculus course: (2243/2373/2574H/3592H) or (2263/2374/2573H/3593H). See equivalent course lists below.
For information about University of Minnesota admission requirements, visit the Office of Admissions website.
Required prerequisites
Required Calculus Courses
Both Calculus I & II plus one 2xxx (or 3xxx level Honors) Calculus course must be successfully completed in order to declare the Math major.
Calculus Sequence
Calculus I
MATH 1271 - Calculus I [MATH] (4.0 cr)
or MATH 1371 - CSE Calculus I [MATH] (4.0 cr)
or MATH 1571H - Honors Calculus I [MATH] (4.0 cr)
Calculus II
MATH 1272 - Calculus II (4.0 cr)
or MATH 1372 - CSE Calculus II (4.0 cr)
or MATH 1572H - Honors Calculus II (4.0 cr)
2xxx Level Calculus Course
MATH 2243 - Linear Algebra and Differential Equations (4.0 cr)
or MATH 2373 - CSE Linear Algebra and Differential Equations (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)
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 are required to complete 4 semester(s) of any second language. with a grade of C-, or better, or S, or demonstrate proficiency in the language(s) as defined by the department or college.
Students must complete a minimum of 6 upper division math courses at 4xxx or above and a senior project (4995 or 4997W). Please note that MATH 3113, 3116, 3118, 4116, 4118, 3283W, 4005, 4067W, 49xx and 59xx math courses do not satisfy upper division mathematics course requirements. The School of Mathematics will accept STAT 5101 and STAT 5102 as part of the upper division mathematics course requirements. 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 Mathematics Major course requirements. 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 adviser about appropriate course choices. Beginning fall 2012, all incoming CLA freshman must complete the appropriate First Year Experience course sequence. Specific information about this collegiate requirement can be found at: http://class.umn.edu/degree_requirements/index.html
Remaining Required Lower Division Calculus Courses
Multivariable Calculus
MATH 2263 - Multivariable Calculus (4.0 cr)
or MATH 2374 - CSE Multivariable Calculus and Vector Analysis (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, and Foundations
MATH 3283W - Sequences, Series, and Foundations: Writing Intensive [WI] (4.0 cr)
or MATH 2283 {Inactive} (3.0 cr)
Senior Project
Students should consult with a mathematics adviser prior to beginning the senior year to determine possible topic and possible faculty mentor for the senior project.
MATH 4997W - Senior project (Writing Intensive) [WI] (1.0 cr)
or MATH 4995 - Senior Project for CLA (1.0 cr)
Mathematics Options
Mathematics (No Specialization)
Students who do not choose one of the specializations must complete the basic Mathematics course requirements listed here.
Take 6 or more course(s) including 3 or more sub-requirements(s) from the following:
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)
· 4xxx/5xxx Level Mathematics Electives Requirement
Courses from the Algebra and Analysis lists which have not already taken to fulfill those requirements may be taken to fulfill the Electives requirement.
Take 2 or more course(s) from the following:
· MATH 4xxx
· MATH 5xxx
-OR-
Actuarial Science Specialization
Complete the requirements for the Actuarial Science subplan.
-OR-
Mathematics Education Specialization
Complete the requirements for the Mathematics Education subplan.
-OR-
Computer Applications Specialization
Complete the requirements for the Computer Applications subplan.
-OR-
Mathematical Biology: Genomics
Complete the requirements for the Genomics subplan.
-OR-
Mathematical Biology: Physiology
Complete the requirements for the Physiology subplan.
Program Sub-plans
A sub-plan is not required for this program.
Actuarial Science
The BA-Mathematics with Actuarial Specialization requires a minimum of 7 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 Mathematics course requirements. It is recommended that students in this specialization should plan for a summer internship after junior year.
Mathematics Courses for the Actuarial Specialization
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 for Actuarial Specialization
Probability and Statistics
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)
MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
Actuarial Mathematics Courses
MATH 4065 - Theory of Interest (4.0 cr)
MATH 5067 - Actuarial Mathematics I (4.0 cr)
MATH 5068 - Actuarial Mathematics II (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 Course Requirements
Introductory Economics
ECON 1101 - Principles of Microeconomics [SOCS, GP] (4.0 cr)
ECON 1102 - Principles of Macroeconomics (4.0 cr)
Economics and Finance
ACCT 2051 - 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 4105 - Corporate Risk Management (2.0 cr)
· INS 4101 - Employee Benefits (2.0 cr)
· INS 4205 - Insurance Theory and Practice (2.0 cr)
Computer Applications
A minimum of six upper division (4xxx level and above) Mathematics courses and a minimum of two upper division Computer Science courses (plus lower division prerequisites) from the courses indicated below are needed to fulfill the requirements for the Computer Applications Specialization. Students who complete the Computer Applications Specialization also meet requirements for a minor in Computer Science.
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)
or MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
or 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
MATH 4567 - Applied Fourier Analysis (4.0 cr)
or MATH 4603 - Advanced Calculus I (4.0 cr)
or MATH 4604 - Advanced Calculus II (4.0 cr)
or MATH 5535 - Dynamical Systems and Chaos (4.0 cr)
or MATH 5525 - Introduction to Ordinary Differential Equations (4.0 cr)
or MATH 5583 - Complex Analysis (4.0 cr)
or MATH 5587 - Elementary Partial Differential Equations I (4.0 cr)
or MATH 5588 - Elementary Partial Differential Equations II (4.0 cr)
or MATH 5615H - Honors: Introduction to Analysis I (4.0 cr)
or MATH 5616H - Honors: Introduction to Analysis II (4.0 cr)
or MATH 5651 - Basic Theory of Probability and Statistics (4.0 cr)
or MATH 5652 - Introduction to Stochastic Processes (4.0 cr)
or MATH 5654 - Prediction and Filtering (4.0 cr)
or STAT 5101 - Theory of Statistics I (4.0 cr)
Additional Computing-Related Mathematics
Mathematical Logic
MATH 5165 - Mathematical Logic I (4.0 cr)
Computer-Related Mathematics Electives
MATH 4242 - Applied Linear Algebra (4.0 cr)
or MATH 5166 {Inactive} (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)
or MATH 5286H - Honors: Fundamental Structures of Algebra II (4.0 cr)
or MATH 5385 - Introduction to Computational Algebraic Geometry (4.0 cr)
or MATH 5705 - Enumerative Combinatorics (4.0 cr)
or MATH 5707 - Graph Theory and Non-enumerative Combinatorics (4.0 cr)
or MATH 5711 - Linear Programming and Combinatorial Optimization (4.0 cr)
Computer Applications Prerequisite 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)
CSCI 2011 - Discrete Structures of Computer Science (4.0 cr)
Upper Division Computer Science Courses
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 - Machine Learning Fundamentals (3.0 cr)
Mathematics Education
Six upper division (4xxx level and above) Mathematics courses are required for the Mathematics Education Specialization. These courses prepare students to meet admission requirements for the Secondary Teaching Licensure Program in Mathematics. The topics covered by these courses include Theoretical and Applied Algebra-Combinatorics, Probability, Mathematical Analysis, and Geometry.
Mathematics Education Specialization 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 requirement 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 Elective
If a sixth Mathematics course is needed after requirements for this specialization have been met, a course from either the Algebra or Analysis lists or another standard 4xxx or 5xxx level course may be taken.
Take 0 or more course(s) from the following:
Mathematical Biology: Genomics
A minimum of six upper division (4xxx level and above) Mathematics courses and a minimum of three upper division courses in related areas (plus lower division prerequisites) are needed to fulfill the requirements for the specialization in Mathematical Biology: Genomics. Note that some Genomics Elective choices have additional prerequisite courses.
Mathematics Requirements for MathBio - Genomics
Mathematical Modeling
MATH 4428 - Mathematical Modeling (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
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 Elective
If MATH 5445 not is chosen as the Genomics Elective course, then a sixth upper division Mathematics course is needed for this specialization. A course from either the Algebra or Analysis lists or another standard 4xxx or 5xxx level course may be taken to fulfill this requirement for the major.
Take 0 or more course(s) from the following:
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
· MATH 4xxx
· MATH 5xxx
Genomics, Computer Science Requirements
Computer Science for Genomics
CSCI 1133, 1933, 2011 plus 4041 may serve as the substitute prerequisite for CSCI 5461.
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)
CSCI 1133 - Introduction to Computing and Programming Concepts (4.0 cr)
CSCI 1933 - Introduction to Algorithms and Data Structures (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) which will also fulfill the Physical Sciences Liberal education degree requirement.
1xxx Level Biology Requirement
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.
Take 1 or more course(s) from the following:
· EEB 5042 - Quantitative Genetics (3.0 cr)
· GCD 4143 - Human Genetics and Genomics (3.0 cr)
· MATH 5445 - Mathematical Analysis of Biological Networks (4.0 cr)
· Plant Genomics
PBIO 5301 has these additional prerequisite courses: CHEM 1061, CHEM 1065 (lab), CHEM 1062, CHEM 1066 (lab), CHEM 2301; BIOC 3021.
· PMB 5301 {Inactive} (3.0 cr)
· Molecular Biology of Cancer
GCD 4151 has these 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
A minimum of six upper division (4xxx level and above) Mathematics courses and a minimum of three upper division courses in related areas (plus lower division prerequisites) are needed to fulfill the requirements for the specialization in 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
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)
Physiology, Biology, Chemistry Requirements
1xxx Level Biology Requirement
BIOL 1009H may be substituted.
BIOL 1009 - General Biology [BIOL] (4.0 cr)
Physiology Requirement
PHSL 3061 - Principles of Physiology (4.0 cr)
Physics Prerequisites
1xxx Level Physics
Phys 1301W & 1302W may be substituted.
PHYS 1201W {Inactive} [PHYS, WI] (5.0 cr)
PHYS 1202W {Inactive} [PHYS, WI] (5.0 cr)
1xxx Level Chemistry Requirements
CHEM 1061 - Chemical Principles I [PHYS] (3.0 cr)
CHEM 1065 - Chemical Principles I Laboratory [PHYS] (1.0 cr)
CHEM 1062 - Chemical Principles II [PHYS] (3.0 cr)
CHEM 1066 - Chemical Principles 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 Elective requirement.
Take 1 or more course(s) from the following:
· PHSL 4702 - 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)
 
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MATH 1271 - Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: 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 1371 - CSE Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1271/Math 1281/Math 1371/
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 1571H - Honors Calculus I (MATH)
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1271/Math 1281/Math 1371/
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 1272 - Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
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 1372 - CSE Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
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 1572H - Honors Calculus II
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 1272/Math 1282/Math 1372/
Grading Basis: A-F only
Typically offered: Every Fall & Spring
Continuation of 1571. Infinite series, differential calculus of several variables, introduction to linear algebra. prereq: 1571H (or equivalent) honors student
MATH 2243 - Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/Math 2373/Math 2574H
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 2373 - CSE Linear Algebra and Differential Equations
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/Math 2373/Math 2574H
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 2574H - Honors Calculus IV
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2243/Math 2373/Math 2574H
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 two-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.
MATH 2263 - Multivariable Calculus
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/Math 2374/Math 2573H
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 2374 - CSE Multivariable Calculus and Vector Analysis
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/Math 2374/Math 2573H
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 2573H - Honors Calculus III
Credits: 4.0 [max 4.0]
Course Equivalencies: Math 2263/Math 2374/Math 2573H
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 equivalent), honors student
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 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 4995 - Senior Project for CLA
Credits: 1.0 [max 1.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
Directed study. May consist of paper on specialized area of math or original computer program or other approved project. Covers some math that is new to student. Scope/topic vary with instructor. prereq: 2 sem of 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: 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: 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: Math 4604/Math 5616
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/Math 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: 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]
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), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)
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: 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: 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]
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), (MATH 2142 or 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
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. The online modality for CSci 1113 will only be offered during the summer session. 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: 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 1101/1165 ApEc 1101/1101H
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: 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 2051 - Introduction to Financial Reporting
Credits: 4.0 [max 4.0]
Course Equivalencies: Acct 2050/ApEc 1251/Dbln 2051
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
This course introduces the topics of financial reporting and accounting. The purpose of financial accounting is to provide information to the entity owners and external parties to serve as the basis for making decisions about that entity. A student who successfully completes this class should be able to 1) understand the concepts and principles of accounting, 2) analyze, record and report the accounting treatment of business transactions, and 3) prepare, interpret, and analyze financial statements.
ECON 3101 - Intermediate Microeconomics
Credits: 4.0 [max 4.0]
Course Equivalencies: Econ 3101/Econ 3101H/ApEc 3001
Grading Basis: A-F or Aud
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. Students cannot take this course if they have taken ApEc 3001, as ApEc 3001 does not contain all material in Econ 3101. prereq: ECON 1101, 1102, and MATH 1271 or equivalent courses approved by the Economics Department.
ECON 4261 - Introduction to Econometrics
Credits: 4.0 [max 4.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall, Spring & Summer
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: (ECON 1101 or ECON 1165, APEC 1101), ECON 1102 (or APEC 1102), ECON 3101, MATH 1271, MATH 1272, MATH 2243, MATH 2263, STAT 4101 (or 5101), STAT 4102 (or 5102) or equivalent courses approved by the Economics Department.
FINA 3001 - Finance Fundamentals
Credits: 3.0 [max 3.0]
Course Equivalencies: ApEc 3501/Fina 3001/Fina 3001H
Grading Basis: A-F or Aud
Typically offered: Every Fall & Spring
How competition for capital in Capital Markets establishes metrics and measures used to understand financial performance of the firm. The course introduces the finance view of the firm and the application of value creation principles to firm decision making. Course presents the centrality of cash flows, the theoretical foundations for Time Value of Money, decision tools for investment of capital, basic valuation of stocks and bonds, and the theoretical foundations for the impact of risk on the required return on investor capital. prereq: ACCT 2050 or ACCT 2051, SCO 2550 or BA 2551 or equivalent statistics course
INS 4105 - Corporate Risk Management
Credits: 2.0 [max 2.0]
Course Equivalencies: Ins 6105/ Ins 4105
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]
Course Equivalencies: Ins 6101/ Ins 4101
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 4205 - 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: 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: Math 4604/Math 5616
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/Math 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: 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]
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), (MATH 2142 or 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: 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 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: 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: CSci 1902/CSci 1933/CSci 1933H
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. The online modality for CSci 1113 will only be offered during the summer session. 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: CSci 2011/CSci 2011H
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: CSci 4041/CSci 4041H
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: CSci 4511W/CSci 5511
Typically offered: Every Fall & 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: CSci 4511W/CSci 5511
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/CSci 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 - Machine Learning Fundamentals
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, and knowledge of partial derivatives
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: 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: Math 4604/Math 5616
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/Math 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: 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]
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), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)
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: 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: 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]
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), (MATH 2142 or 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 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]
Course Equivalencies: CSci 3003/CSci 5465
Typically offered: Fall Odd Year
This course builds computational skills needed to carry out basic data analysis tasks common in modern biology. Students will learn computing concepts (algorithm development, data structures, complexity analysis) along with practical programming skills in Python and R. No previous programming knowledge assumed. Prereq: introductory biology course.
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: CSci 4041/CSci 4041H
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: CSci 2011/CSci 2011H
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 1133 - Introduction to Computing and Programming Concepts
Credits: 4.0 [max 4.0]
Course Equivalencies: 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: CSci 1902/CSci 1933/CSci 1933H
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
BIOL 1009 - General Biology (BIOL)
Credits: 4.0 [max 4.0]
Course Equivalencies: Biol 1009/Biol 1009H
Typically offered: Every Fall, Spring & Summer
A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.
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: Introductory biology course such as 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 and Genomics
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
Human Genetics ? the science of how our genomes function, vary, and shape our unique, individual characteristics ? is a rapidly expanding field with major implications for medical and fundamental research, clinical practice, and many other areas. In this course, students will learn about the principles of human genetics & genomics at the levels of molecules, cells, individuals, and populations. Topics include patterns of inheritance; the molecular causes and biochemical basis of genetic disorders; disease gene identification; the origin and distribution of human genetic variation; genetic influences on common, complex diseases; epigenetics and regulation of gene expression; genomic technologies for understanding human genomes; cancer genetics; behavioral genetics; human ancestry and evolution; applications such as genetic screening, genetic counseling, and gene therapy; and ethical questions raised by emerging abilities to edit the human genome, modify the human germline, and many more. prereq: BIOL 4003 or instructor 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
GCD 4151 - Molecular Biology of Cancer
Credits: 3.0 [max 3.0]
Grading Basis: A-F or Aud
Typically offered: Every Fall
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: 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: 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]
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), (MATH 2142 or CSCI 2033 or MATH 2373 or MATH 2243)
BIOL 1009 - General Biology (BIOL)
Credits: 4.0 [max 4.0]
Course Equivalencies: Biol 1009/Biol 1009H
Typically offered: Every Fall, Spring & Summer
A comprehensive introduction to biology - includes molecular structure of living things, cell processes, energy utilization, genetic information and inheritance, mechanisms of evolution, biological diversity, and ecology. Includes lab. This comprehensive course serves as a prerequisite and requirement in many majors.
PHSL 3061 - Principles of Physiology
Credits: 4.0 [max 4.0]
Course Equivalencies: Phsl 3063/Phsl 3071
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
CHEM 1061 - Chemical Principles I (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: Chem 1061/Chem 1071H/Chem 1081
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: 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 1062 - Chemical Principles II (PHYS)
Credits: 3.0 [max 3.0]
Course Equivalencies: Chem 1062/1072H/1082
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: 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
PHSL 4702 - Cell Physiology
Credits: 3.0 [max 3.0]
Course Equivalencies: AnSc 5702/Phsl 4702/Phsl 5702
Grading Basis: A-F or Aud
Typically offered: Every Fall
Cell Physiology involves the study of control mechanisms involved in maintaining homeostasis with respect to a variety of parameters including regulation of pH, volume, nutrient content, intracellular electrolyte composition, membrane potential, receptor signaling and aspects of intercellular communication. The first half of this team-taught course is organized in a partially on-line format where students learn from on-line materials and then take an on-line quiz each week before meeting with the instructor to review key concepts in class. The second half of the course is presented in lecture format. Student evaluation is based on quiz scores, in-class exams and graded problem sets. 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 5444/ Phsl 5444
Typically offered: Every Spring
Muscle molecular structure/function and disease. Muscle regulation, ion transport, and force generation. Muscular dystrophy and heart disease. prereq: PHSL 3061 or PHSL 5061 or BioC 3021, BIOL 3021 or BIOL 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