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


Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 1142/1271/1281/1371/1571H 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00067  Math 1271/Math 1281/Math 1371/ 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00067  Math 1142/1271/1281/1371/1571H 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 1272/1282/1252/1372/1572 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 1272/1282/1252/1372/1572 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00068  Math 1272/1282/1252/1372/1572 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2243/2373/2573 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2243/2373/2573 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2263/2373/2573H/3251 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2263/2373/2573H/3251 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00561  Math 2243/Math 2373/Math 2573H 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  5.0 [max 5.0] 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00078 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00078 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00078  Phys 1201W/Phys1301W/Phys1401V 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00079 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00079 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00079  Phys 1202W/1302W/1402V 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2263/2373/2573H/3251 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2263/2373/2573H/3251 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00069  Math 2263/2374/3251 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  5.0 [max 5.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2283/3283W 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  Math 2283/3283W 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 2283/3283W 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  1.0 [max 2.0] 
Prerequisites:  2 sem upper div math, % 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01072  Math 4606/Math 5615/Math 5616 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01776 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 3574/5583 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503/2503H 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  Math 4152/5165 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 4152/5165 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 3574/5583 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01072  Math 4606/Math 5615/Math 5616 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01776 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF only 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  00117  Chem 3501/4501 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  00119  Chem 3502/4502 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02015 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Periodic Spring 
Credits:  3.0 [max 3.0] 
Prerequisites:  4041 or # 
Typically offered:  Periodic Fall & Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01666 
Prerequisites:  [2041 or #], grad student 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  CSci 5512W/5512 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00025  Econ 3101/Econ 3101H/ApEc 3001 
Grading Basis:  AF only 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00026  Econ 3102/ApEc 3006 
Grading Basis:  AF only 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  5.0 [max 5.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF only 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Econ 1101/1104/1111/ApEc 1101 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00020  ApEc 1102/Econ 1102/1105/1112 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00458  Acct 2050/ApEc 1251 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00025  Econ 3101/Econ 3101H/ApEc 3001 
Grading Basis:  AF only 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  00196 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall, Spring & Summer 
Credits:  2.0 [max 2.0] 
Typically offered:  Every Fall & Spring 
Credits:  2.0 [max 2.0] 
Typically offered:  Every Fall 
Credits:  2.0 [max 2.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01072  Math 4606/Math 5615/Math 5616 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01776 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 3574/5583 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 4152/5165 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00008 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02004 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02015 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01666  CSci 4511W/CSci 5511 
Prerequisites:  2041 or # 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Periodic Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall & Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01666 
Prerequisites:  [2041 or #], grad student 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  CSci 5512W/5512 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503/2503H 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01072  Math 4606/Math 5615/Math 5616 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01776 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  Math 3574/5583 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503/2503H 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00080  Phys 2303/2403H/2503 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00008 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02015 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02004 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01525  Biol 1009/Biol 1009H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  Biol 4003/GCD 3022 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Grading Basis:  AF or Aud 
Typically offered:  Periodic Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01212  Math 4242/Math 4457 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Typically offered:  Periodic Fall & Spring 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  MATH 4653/Math 5651/Stat 5101 
Typically offered:  Every Fall & Spring 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  00259  Math 5651/Stat 5101 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  02133  CSci 1133/CSci 1133H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01354 
Typically offered:  Every Fall 
Credits:  4.0 [max 4.0] 
Course Equivalencies:  01525  Biol 1009/Biol 1009H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01884  Chem 1061/Chem 1071H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  1.0 [max 1.0] 
Course Equivalencies:  01878  Chem 1065/Chem 1075H 
Grading Basis:  AF only 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01884  Chem 1061/Chem 1071H 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  1.0 [max 1.0] 
Course Equivalencies:  01878  Chem 1065/Chem 1075H 
Grading Basis:  AF only 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01885  Chem 1062/Chem 1072H 
Typically offered:  Every Fall, Spring & Summer 
Credits:  1.0 [max 1.0] 
Course Equivalencies:  01879  Chem 1066/Chem 1076H 
Grading Basis:  AF only 
Typically offered:  Every Fall, Spring & Summer 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  01885  Chem 1062/Chem 1072H 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  1.0 [max 1.0] 
Course Equivalencies:  01879  Chem 1066/Chem 1076H 
Grading Basis:  AF only 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Grading Basis:  AF or Aud 
Typically offered:  Every Fall 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  BioC/Phsl 5444 
Typically offered:  Every Spring 
Credits:  3.0 [max 3.0] 
Course Equivalencies:  NSc 5202/Phsl 5202 
Typically offered:  Every Spring 