160 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 0701Basic Mathematics for Today's World4
This course is typically offered in Fall, Spring, Summer I and Summer II.This course surveys a variety of mathematical topics. Topics include numeracy with an emphasis on estimation and fluency with large numbers, evaluating expressions and formulas, rates, ratios, proportions, and percentages, solving equations, linear models, data interpretations including graphs and tables, verbal, algebraic and graphical representations of functions, exponential models. The course will help students develop conceptual understanding and acquire multiple strategies for solving problems. It will prepare students for success in future quantitative courses and will help them develop skills for the workplace and for everyday life. Please note that MATH 0701 is no longer a prerequisite for MATH 1021, College Algebra, or STAT 1001, Quantitative Methods for Business I. Students whose program of studies requires one of these two courses must complete MATH 0702, Intermediate Algebra, instead.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is typically offered in Fall, Spring, Summer I, and Summer II.This course is designed as an intermediate algebra course that prepares students for the topics covered in MATH 1021. This course covers the real number system, basic properties of real numbers, operations with fractional expressions, simplifying complex fractions, powers and roots, operations with radicals, graphing linear equations and inequalities, and factoring of polynomials.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is not offered every year.This course is about becoming an "informed user" of quantitative information. Do numbers make us more or less rational? What does "free" really mean? What's the difference between "correlation" and "cause"? How can we be misled by numbers? How can we make better decisions and have more effective discussions by understanding mathematics? Does it make sense to play the lottery? What are your chances of drawing the card you in need in a poker game? How long will it take you to save a million dollars assuming interest is earned but you keep spending? How does math play into the digital world that surrounds us, whether it is email, online tools or the creation of passwords, IDs or serial numbers? These and many other questions will be explored and answered throughout the course. NOTE: (1) This course fulfills the Quantitative Literacy (GQ) requirement for students under GenEd and a Quantitative Reasoning (QA or QB) requirement for students under Core. (2) Duplicate Course: Students cannot receive credit for CIS 0823/0923 if they have successfully completed MATH 0823/0923.
This course is typically offered in Fall, Spring, Summer I and Summer II.This course will convey the essence of mathematics and its current breadth. It sets out to describe mathematics as a rich and living part of human culture, and is intended for the general student with minimal mathematical knowledge. Exposure to this subject matter will contribute to students' educational breadth and intellectual development by sharpening their problem-solving skills, enhancing their understanding of logical reasoning and analysis, and strengthening their ability to use language and symbolic expression in a disciplined manner. The course will consist of a series of vignettes. Topics may include problem solving, voting theory, graph theory, finance, mathematical models, cryptography, statistics and probability. NOTE: This course fulfills the Quantitative Literacy (GQ) requirement for students under GenEd and a Quantitative Reasoning (QA or QB) requirement for students under Core. Students cannot receive credit for MATH 0824 if they have successfully completed MATH 0924.
This course is not offered every year. This course is about becoming an "informed user" of quantitative information. Do numbers make us more or less rational? What does "free" really mean? What's the difference between "correlation" and "cause"? How can we be misled by numbers? How can we make better decisions and have more effective discussions by understanding mathematics? Does it make sense to play the lottery? What are your chances of drawing the card you in need in a poker game? How long will it take you to save a million dollars assuming interest is earned but you keep spending? How does math play into the digital world that surrounds us, whether it is email, online tools or the creation of passwords, IDs or serial numbers? These and many other questions will be explored and answered throughout the course. NOTE: (1) This course fulfills the Quantitative Literacy (GQ) requirement for students under GenEd and a Quantitative Reasoning (QA or QB) requirement for students under Core. (2) Duplicate Course: Students cannot receive credit for CIS 0823/0923 if they have successfully completed MATH 0823/0923.
This course is typically offered in Fall and Spring.This course will convey the essence of mathematics and its current breadth. It sets out to describe mathematics as a rich and living part of human culture, and is intended for the general student with minimal mathematical knowledge. Exposure to this subject matter will contribute to students' educational breadth and intellectual development by sharpening their problem-solving skills, enhancing their understanding of logical reasoning and analysis, and strengthening their ability to use language and symbolic expression in a disciplined manner. The course will consist of a series of vignettes. Topics may include problem solving, voting theory, graph theory, finance, mathematical models, cryptography, statistics and probability. (This is an Honors course.) NOTE: This course fulfills the Quantitative Literacy (GQ) requirement for students under GenEd and a Quantitative Reasoning (QA or QB) requirement for students under Core. Students cannot receive credit for MATH 0924 if they have successfully completed MATH 0824.
This course is typically offered in Spring.This course provides a firm foundation for the study of statistics in other fields. Although no one field is emphasized to the exclusion of others, applications are drawn from psychology, political science, exercise science, and other areas.
This course is typically offered in Fall.This is a course intended for students wishing to familiarize themselves with basic arithmetic and geometric concepts. Subjects include the real numbers, the decimal system, and fractions, elementary number theory (primes, gcd, lcm, rational and irrational numbers), and geometry (angles, triangles, polygons, polyhedra, circles, spheres, symmetry, congruence, and similarity).
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (any MATH course numbered 0701 to 0702, MATH 1021 (may be taken concurrently), 'Y' in MC3, 'Y' in MC4, 'Y'
This course is not offered every year.Fundamentals of finite mathematics necessary for a business student to pursue statistics and other quantitatively oriented business courses. Topics and illustrations are specifically directed to applications in business and economics. Topics include algebraic concepts; linear, quadratic, polynomial and rational functions; logarithm and exponential functions; elementary matrix manipulations. Fitting of curves, interest rate calculations, present and future values of annuities are some of the specific applications. Use of a graphing calculator. NOTE: (1) Duplicate Course: Students cannot receive credit for MATH 1018 if they have successfully completed Statistics 1001. (2) This course can be used to satisfy the university Core Quantitative Reasoning A (QA) requirement. Although it may be usable towards graduation as a major requirement or university elective, it cannot be used to satisfy any of the university GenEd requirements. See your advisor for further information.
This 2-credit course is intended as a supplement to MATH 1021 College Algebra for students with a Math GQ/1015 ALEKS math placement. The course will cover the particular intermediate algebra concepts that are necessary background for success in College Algebra.
Subject
MATH
Credits (min)
2
Credits (max)
2
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 0702, 'Y' in MC3, or 'Y' in MC4)
This course is typically offered in Fall, Spring, Summer I and Summer II.This course covers polynomial, rational and algebraic expressions, equations and inequalities. It also includes some topics in graphing, an introduction to the concept of a function, and a brief introduction to the exponential and logarithmic functions. NOTE: This course can be used to satisfy the university Core Quantitative Reasoning A (QA) requirement. Although it may be usable towards graduation as a major requirement or university elective, it cannot be used to satisfy any of the university GenEd requirements. See your advisor for further information.
This course is typically offered in Fall, Spring, Summer I and Summer II.This course is designed to prepare students for the calculus courses. Topics include functions and function operations, one-to-one and inverse functions, exponential and logarithmic functions, trigonometric functions, inverse trigonometric functions, basic trigonometric identities, polar coordinates, and an introduction to vectors. The course also contains a brief review of basic algebra. NOTE: This course can be used to satisfy the university Core Quantitative Reasoning A (QA) requirement. Although it may be usable towards graduation as a major requirement or university elective, it cannot be used to satisfy any of the university GenEd requirements. See your advisor for further information.
This is a 1-credit course to be taken as a supplement to MATH 1022: Precalculus for students with a C- in the prerequisite MATH 1021: College Algebra. The course supplements Precalculus by giving an in-depth review of the College Algebra concepts, in the context of Precalculus, that are necessary background for success in Precalculus.
Subject
MATH
Credits (min)
1
Credits (max)
1
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 1021, 'Y' in MC5, or 'Y' in MC6)
This course is typically offered in Fall and Spring.This is a calculus course in the reform style that will introduce students to the basic concepts of differential and integral calculus. The emphasis of the course will be on understanding the concepts (intuitively rather than rigorously). However, the course will also cover the basic techniques of differentiation and some techniques of integration. NOTE: This course may be used to satisfy the GenEd Quantitative Literacy (GQ) requirement.
This course is designed as an introduction to MATLAB and as preparation for computing in undergraduate applied mathematics courses. Topics include computer arithmetic, vectors and matrices, graphics, loops, functions, and conditional operators. No prior programming or MATLAB skills are required.
Subject
MATH
Credits (min)
1.5
Credits (max)
1.5
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 1022, MATH 1039 (may be taken concurrently), 'Y' in MC6, 'Y' in MA04, 'Y' in MC6A, 'Y' in CRMA05, 'Y'
This course is designed as a supplement to MATH 1033 Computing in MATLAB and will introduce students to some particular applications using MATLAB. Topics covered will require students to reinforce their programming skills while exposing them to a variety of problems where computation is useful and necessary. After completing the course, students will be better prepared for the use of computing in more advanced undergraduate courses, research projects, and future internships/employment.
Subject
MATH
Credits (min)
1.5
Credits (max)
1.5
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1022, MATH 1039 (may be taken concurrently), 'Y' in MC6, 'Y' in MA04, 'Y' in MC6
This course is typically offered in Fall and Spring.This is the lab component of MATH 1041, a first semester calculus course that involves both theory and applications. MATH 1039 is required for students who earned a grade of C- in MATH 1022 Precalculus. Students with no previous calculus experience or those needing extra review of algebra and precalculus topics are strongly encouraged to register for MATH 1039. Topics include algebra and precalculus in the context of the topics covered in MATH 1041.
Subject
MATH
Credits (min)
1
Credits (max)
1
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of D (except where noted) in (MATH 1022 (C- or higher), MATH 1041, MATH 1042, MATH 1044, MATH 1941, MATH 1942, MATH
This is a first semester calculus course primarily for students with some calculus background or strong precalculus skills. It involves both theory and applications. Students who earned a grade of C- in MATH 1022 must register for MATH 1039 simultaneously with MATH 1041. Students with no previous calculus experience or those needing extra review of precalculus topics are strongly encouraged to register for MATH 1039. Topics include functions, limits and continuity, differentiation of algebraic, trigonometric, exponential and logarithmic functions, curve sketching, optimization and L'Hospital's rule. NOTE: (1) Students may not get credit for more than one of MATH 1041 and MATH 1941. (2) This course can be used to satisfy the university Core Quantitative Reasoning B (QB) requirement or the GenEd Quantitative Literacy (GQ) requirement. However, this course is not appropriate for students whose sole purpose is to fulfill the quantitative core requirements. They should take MATH 1031 instead.
This course is typically offered in Fall, Spring, Summer I and Summer II.This is a second semester calculus course that involves both theory and applications. Topics include the definite integral and the Fundamental Theorem of Calculus, applications of the definite integral, techniques of integration, improper integrals and sequences and series, including power and Taylor series.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1041, MATH 1941, MATH 1038, MATH 2043 (D or higher), 'Y' in MA06, 'Y' in MATW, '
MATH 1044Introduction to Probability and Statistics for the Life Sciences4
A one-semester course at the freshman level to follow Calculus I for majors in Biology and Earth and Environmental Sciences (EES). Probabilistic and statistical methods needed for empirical modeling and associated data analysis, with examples primarily taken from the life sciences. This course does not serve as a prerequisite to Calculus III. Primarily for majors in Biology and EES.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 1041, MATH 1038, MATH 1941, MATH 1951, any MATH course numbered 2043 to 3080 (may be taken concurren
This course is typically offered in Fall and Spring.This is a first semester calculus course that involves both theory and applications. Topics include functions, limits and continuity, differentiation of algebraic, trigonometric, exponential and logarithmic functions, curve sketching, optimization and L'Hospital's Rule. NOTE: This course can be used to satisfy the university Core Quantitative Reasoning B (QB) requirement or the GenEd Quantitative Literacy (GQ) requirement. However, this course is not appropriate for students whose sole purpose is to fulfill the quantitative core requirements. They should take MATH 1031 instead.
This course is typically offered in Fall and Spring.This is a second semester calculus course that involves both theory and applications. Topics include the definite integral and the Fundamental Theorem of Calculus, applications of the definite integral, techniques of integration, improper integrals and sequences and series, including power and Taylor series.
This course is typically offered in Fall.This is a course for students who have had a year of calculus in high school. Its purpose is two-fold: to present a more theoretical treatment of calculus than is usually seen in an American high school and to prepare students for MATH 2043, Calculus III. Topics covered will include some or all of the following: limits and continuity, derivatives and rules of differentiation, the Mean Value Theorem, L'Hospital's rule, optimization, graphing, the definite integral and the Fundamental Theorem of Calculus, u-substitution and integration by parts, limits of sequences, infinite series, convergence tests, power series, and Taylor series. NOTE: Prior to summer 2010, the course title was "Honors Differential & Integral Calculus."
This course is typically offered in Spring.In this course, required for TUteach Mathematics with Teaching majors, students will give presentations and work in small groups to engage in explorations and lab activities designed to strengthen and expand their knowledge of the topics found in secondary mathematics; illuminate the connections between secondary and college mathematics and between various areas of mathematics; and illustrate productive uses of technology in teaching. Students will engage in non-routine problem solving, problem-based learning, and applications of mathematics. The course consists of four units: 1) Functions, 2) Modeling, 3) Overlooked Topics and Explorations, and 4) Geometry of Complex Numbers. Specific topics of investigation include function properties and patterns, complex numbers, parametric equations, polar equations, vectors, and exponential growth and decay. Explorations involve the use of multiple representations, transformations, data analysis techniques (such as curve fitting) and interconnections among topics in algebra, analytic geometry, statistics, trigonometry, and calculus. The lab investigations include use of various technologies including computers, calculators, and computer graphing software.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 1042, MATH 1951, or 'Y' in MATW) and (SCTC 1189, SCTC 1289, SCTC 1389, or MGRE 3111)
This course is typically offered in Fall and Spring.This course presents basic principles of statistical reasoning and the concepts from probability theory that give the student an understanding of the logic behind statistical techniques. Topics covered include rules of probability, discrete probability distributions, normal distribution, sampling distributions, the central limit theorem, point estimation, interval estimation, tests concerning means, tests based on count data, correlation and regression, and nonparametric statistics. NOTE: This course cannot be credited towards graduation if taken after MATH 3031.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 1031, MATH 1041, MATH 1042, MATH 1044, MATH 1942, any MATH course numbered 2043 to 3080 (may be take
This is a course in ordinary differential equations. Topics include first order ordinary differential equations, linear second order ordinary differential equations, systems of differential equations, numerical methods and the Laplace transform.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 1042, MATH 1942, 'Y' in MATW, 'Y' in MA07, 'Y' in CRMA09, or 'Y' in CRMA11)
Topics include complex numbers, vectors and geometry of space, partial derivatives, and multiple integrals. This course is offered as an alternative to MATH 2043. Students should check their major requirements to confirm if this course is an option in their degree program.
Subject
MATH
Credits (min)
2
Credits (max)
2
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 1042, MATH 1942, 'Y' in MA07, or 'Y' in MATW)
This course is typically offered in Fall, Spring, Summer I and Summer II.This is a third semester calculus course that involves both theory and applications. Topics include vectors in two or three dimensions, lines and planes in space, parametric equations, vector functions and their derivatives, functions of several variables, partial derivatives, multiple integrals, line integrals, and Green's, Divergence and Stokes' theorems.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 1042, MATH 1942, MATH 1951, 'Y' in MA07, 'Y' in MATW, 'Y' in CRMA09, or 'Y' in CRMA11)
MATH 2045Differential Equations with Linear Algebra4
This course is typically offered in Fall.This is a course in ordinary differential equations that emphasizes the use of linear algebra. It has two objectives: 1) to teach students how to solve linear differential equations and systems of linear differential equations, and 2) to introduce students to the linear algebra concepts such as vector spaces, dimension, basis, matrices, eigenvalues and eigenvectors, that play a key role in the theory of linear differential equations.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 2043 (may be taken concurrently), MATH 2943 (may be taken concurrently), 'Y' in MA08, 'Y' in CRMA12
This course is typically offered in Spring.This course provides a thorough coverage of Euclidean geometry from an advanced standpoint and with an emphasis on mathematical proofs and reasoning. Several topics from non-Euclidean geometry are also discussed. Note: Prior to Spring 2026, this course was titled "Euclidean Geometry."
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1042, MATH 1942, MATH 1951, MATH 2043 (may be taken concurrently), any MATH cour
This course is typically offered in Fall, Spring, Summer I, and Summer II.Intensive study in a specific area. This course does not count for a mathematics related major elective credit. Prerequisites are MATH 1042 and a GPA of 3.5 or higher.
Subject
MATH
Credits (min)
1
Credits (max)
4
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is typically offered in Fall, Spring, Summer I and Summer II.This course covers vectors and vector spaces, matrices, determinants, systems of linear equations, linear transformations, inner products and orthogonality, and eigenvectors and eigenvalues. NOTE: Only one course, MATH 2101 or MATH 2103, can be credited towards graduation.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 1042, MATH 1942, MATH 1951, 'Y' in MA07, 'Y' in MATW, 'Y' in CRMA09, or 'Y' in CRMA11)
This course is typically offered in Fall.Topics in this course include: systems of linear equations; matrix algebra; determinants; fundamental subspaces; linear transformations; eigenvalues and eigenvectors; inner products; orthogonality; and spectral theory. Included is a computational lab component that uses activities and applications designed to promote understanding of the basic concepts from algebraic, symbolic, and geometric viewpoints. NOTE: Only one course, MATH 2101 or MATH 2103, can be credited towards graduation.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 1042, MATH 1942, MATH 1951, 'Y' in MA07, 'Y' in MATW, 'Y' in CRMA09, or 'Y' in CRMA11) and MATH 1033.
This course is typically offered in Fall, Spring, and Summer I.This is a course designed to introduce students to mathematical abstraction and the language of mathematical proof. Topics include logic, sets, relations, integers, induction and modular arithmetic, functions, and cardinality. It will also cover inequalities and limits of sequences and functions. This course is highly recommended for students who have not been exposed to mathematical proof and intend to take advanced math courses.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1042, MATH 1942, MATH 1951, any MATH course numbered 2043 to 2110 (C- or higher;
This course exposes students to first-principles models of real-world processes, simulations on computers, and the proper interpretation of simulation results and data. The course focuses on applications in which first-principles modeling and simulation are not yet standard toolsets, such as: bacterial motion, disease spread, traffic flow, animal swarming/flocking/herding, crowd dynamics, ecology, economic markets, and social networks. However, the fundamental concepts and techniques apply equally to fields in which simulation is more commonplace, such as computational physics and engineering. In the course, students are provided with suitable software and high-level programming environments that enable them to engage right away in devising, modifying, and simulating models of interacting agents that describe real-world phenomena. In addition to homework problems that involve mathematical modeling and programming, the course also involves course projects, including final project reports and presentations.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (CIS 1051, CIS 1057, CIS 1068, CIS 1951, CIS 1968, 'Y' in CRCI01, 'Y' in CRCI04, 'Y' in CRCI05, 'Y' in CRCI
This course exposes students to first-principles models of real-world processes, simulations on computers, and the proper interpretation of simulation results and data. The course focuses on applications in which first-principles modeling and simulation are not yet standard toolsets, such as: bacterial motion, disease spread, traffic flow, animal swarming/flocking/herding, crowd dynamics, ecology, economic markets, and social networks. However, the fundamental concepts and techniques apply equally to fields in which simulation is more commonplace, such as computational physics and engineering. In the course, students are provided with suitable software and high-level programming environments that enable them to engage right away in devising, modifying, and simulating models of interacting agents that describe real-world phenomena. In addition to homework problems that involve mathematical modeling and programming, the course also involves course projects, including final project reports and presentations.
This course is typically offered in Fall and Spring.This is a course in ordinary differential equations. Topics include first order ordinary differential equations, linear second order ordinary differential equations, systems of differential equations, numerical methods and the Laplace transform. Additional topics may include series solutions to differential equations, the matrix exponential, and various applications.
This course is typically offered in Fall and Spring.This is a third semester calculus course that involves both theory and applications. Topics include vectors in two or three dimensions, lines and planes in space, parametric equations, vector functions and their derivatives, functions of several variables, partial derivatives, multiple integrals, line integrals, and Green's, Divergence and Stokes' theorems.
This course is typically offered in Fall.Divisibility properties of integers, prime factorization, distribution of primes, linear and quadratic congruences, primitive roots, quadratic residues, quadratic reciprocity, simple Diophantine equations, cryptology.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 2111.
This course is typically offered in Fall and Spring.Counting techniques, axiomatic definition of probability, independence, conditional probability, random variables, discrete and continuous probability distributions, expected values, moments and moment generating functions, joint probability distributions, covariance and correlation. NOTE: Prior to Spring 2026, the course title was "Probability Theory I."
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1042, MATH 1942, MATH 1951, MATH 2043 (C- or higher; may be taken concurrently)
This course is typically offered in Spring.Random sampling, sampling distributions, Student's t, chi-squared and F distributions, unbiasedness, minimum variance unbiased estimators, confidence intervals, tests of hypothesis, Neyman-Pearson Lemma, and uniformly most powerful tests. NOTE: Prior to summer 2010, the course title was "Introduction to Mathematical Statistics."
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3031 or AS 2101)
This course is typically offered in Fall, Spring, Summer I and Summer II.This is a course in ordinary differential equations. Topics include first order ordinary differential equations, linear second order ordinary differential equations, systems of differential equations, numerical methods and the Laplace transform.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 2043 (may be taken concurrently)
This course is not offered every year.This is a second course in differential equations. Topics include orthogonal polynomials, including Legendre and Chebyshev polynomials, Fourier series, partial differential equations, the boundary value problems and other topics of the instructor's choice. NOTE: This course is offered only in odd-numbered years.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3041 or MATH 3045)
This course is typically offered in Fall.Computer arithmetic, pitfalls of computation, iterative methods for the solution of a single nonlinear equation, interpolation, least squares, numerical differentiation, numerical integration, and solutions of linear systems by direct and iterative methods.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 2043, (MATH 2101, MATH 2103, or MATH 2045), and (CIS 1051, CIS 1951, CIS 1053, CIS 1057, CIS 1068, CI
This course is typically offered in Spring.Solution of systems of nonlinear equations, solution of initial value problems, matrix norms and the analysis of iterative solutions, numerical solution of boundary value problems and partial differential equations, and introduction to the finite element method. NOTE: Offered in even-numbered years only.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 3043.
MATH 3045Differential Equations with Linear Algebra4
This course is typically offered in Fall.This is a course in ordinary differential equations that emphasizes the use of linear algebra. It has two objectives: 1) to teach students how to solve linear differential equations and systems of linear differential equations, and 2) to introduce students to the linear algebra concepts such as vector spaces, dimension, basis, matrices, eigenvalues and eigenvectors, that play a key role in the theory of linear differential equations.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 2043 (may be taken concurrently), 'Y' in MA08, or 'Y' in CRMA12)
MATH 3046Differential Equations with Computer Lab4
This course is typically offered in Spring.This course combines traditional material with a modern systems approach. It presents a thorough introduction to differential equations, tempering a classic "pure math" approach with more practical applied aspects. The course covers key topics such as first order equations, matrix algebra, systems, and phase plane portraits. The focus is on interpreting and solving problems through the use of software support and technology projects. Using software tools graphics will be used to display the ideas in ODEs; modeling and applications; and projects. An objective is to provide students with the opportunity to bring together much of what they have learned, including analytical, computational, and interpretative skills.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 2043 (may be taken concurrently), 'Y' in MA08, or 'Y' in CRMA12) and MATH 1033.
MATH 3047Differential Equations for Science and Mathematics3
This course is typically offered in Spring.This is a course on ordinary differential equations. Topics include the Existence and Uniqueness Theorem and its consequences, first order ordinary differential equations, linear ordinary differential equations of second and higher orders, systems of ordinary differential equations, power series solutions of ordinary differential equations, numerical methods, and some applications.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2043 (may be taken concurrently) or MATH 2943 (may be taken concurrently)) and MATH 2101.
This course is typically offered in Spring.This is a course in linear algebra with a higher degree of abstraction than a traditional undergraduate linear algebra course. Topics include vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, canonical forms, inner product spaces, and bilinear forms.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- (except where noted) in (MATH 2111 (C or higher) or 'Y' in CRMA14) and (MATH 3045, MATH 2045, MATH 2101, or M
This course is typically offered in Fall.An introduction to Euclidean and Noneuclidean geometries with a particular emphasis on theory and proofs.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2061 or MATH 2111) and (MATH 2045, MATH 2101, MATH 2103, or MATH 3051)
This course is typically offered in Fall and Spring.This is a one-semester course in modern algebra that covers topics from group, ring, and field theory. Topics include groups and their basic properties, subgroups, normal subgroups and quotient groups, group homomorphisms, rings, rings of integers and polynomial rings, congruences in the rings of integers and polynomial rings, ideals and quotient rings, ring homomorphism, fields and field extensions, Galois theory.
This course is typically offered in Fall.This is the first semester in a year-long modern algebra sequence MATH 3098 - MATH 3101. It is a thorough introduction to the theory of groups and rings. NOTE: Students who have had limited exposure to proofs should consider taking MATH 2111 first.
This course is typically offered in Spring.This is the second semester of a year-long modern algebra course. Topics come from theory of rings, fields and modules and from Galois theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 3098.
This course is typically offered in the Fall.This is the first course in real analysis. Topics include the real number system, completeness, sequences and series and their limits, limits of real valued functions, continuity, differentiability, the Riemann integral, and power series.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2043 or MATH 2943) and MATH 2111.
This course is typically offered in Spring.This is the second course in real analysis. Topics include point-set topology of Euclidean spaces, differentiation and integration of functions of several variables, Fourier series, and the Lebesgue integral. Students cannot receive credits for both MATH 3142 and MATH 3132.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 3131 or MATH 3141) and (MATH 2101, MATH 2045, or 'Y' in MA09)
This course is typically offered in Fall.Real and complex number systems, completeness. Sequences and series and their limits. Continuity of real and complex functions. Derivative. Analytic functions. Power series.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 2043, 'Y' in MA08, or 'Y' in CRMA12) and MATH 2111 (C- or higher)
This course is typically offered in Spring.The Riemann-Stiltjes integral. Cauchy integral theorem. Cauchy integral formula and its consequences. The calculus of residues.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3137 or MATH 3141)
This course is typically offered in Fall.This is a first semester course in real analysis. Topics include the real number system and the completeness property, sequences and their limits, limits of real-valued functions and continuity and point-set topology of Euclidean spaces. NOTE: Students who have had limited exposure to proofs should consider taking MATH 2111 first.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (MATH 2043, 'Y' in CRMA12, or 'Y' in MA08), (MATH 2111, 'Y' in MA11, or 'Y' in CRMA14), and (MATH 2101, MAT
This course is typically offered in Spring.This is a second semester course in real analysis. Topics include the derivative and differentiable functions, the Riemann integral, infinite series and convergence tests, power and Taylor series and operations with them, and topics from calculus of several variables.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in MATH 3141.
Complex numbers, analytic functions, harmonic functions, power and Laurent series, Cauchy's theorem, calculus of residues, and conformal mappings. Students cannot earn credits for both MATH 4051 and MATH 3151.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3131 or MATH 3142)
This course provides an in depth exposure to selected topics in advanced mathematics.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.Pre-requisites: Minimum grade of C (except where noted) in (MATH 1042, MATH 1942, MATH 2043 (C- or higher; may be taken concurrently), MATH 2943 (C- o
This course is typically offered in Fall and Spring.This is a course in ordinary differential equations. Topics include first order ordinary differential equations, linear second order ordinary differential equations, systems of differential equations, numerical methods and the Laplace transform. Additional topics may include series solutions to differential equations, the matrix exponential, and various applications.
This course is not offered every year.The development of the major mathematical concepts from ancient times to the present, emphasizing topics in the standard undergraduate curriculum. Special attention will be paid to the history of mathematics and mathematics education in the United States. NOTE: Offered in even-numbered years only.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in (any MATH course numbered 3001 to 4999 or 'Y' in CRMA20)
This course is not offered every year.Basic theorems and applications of combinatorial analysis, including generating functions, difference equations, Polya's theory of counting, graph theory, matching, and block diagrams. NOTE: Offered in odd-numbered years only.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2111, MATH 2196, or MATH 3003)
This course is typically offered in Fall.Markov chains, exponential distribution, Poisson process, continuous time Markov chains, Brownian motion, stationary processes. NOTE: Prior to Spring 2026, the course was titled "Probability Theory II."
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3031 or AS 2101) and (MATH 2101, MATH 3045, or MATH 2045)
This course is typically offered in Spring.The solution and properties of first and second order equations; heat and wave equation. Elliptic boundary value problems and Green's functions. Hyperbolic problems and the theory of characteristics. Finite difference methods. The equations of mathematical physics.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2101, MATH 2045, or MATH 3051) and (MATH 2041, MATH 2045, or MATH 3047)
This course is typically offered in Fall.The construction and study of mathematical models for physical, economic, and social processes. NOTE: Offered in odd-numbered years only.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 2045, MATH 2101, or MATH 3051) and (MATH 2041, MATH 2045, or MATH 3047)
This course is typically offered in Fall.Complex numbers, analytic functions, harmonic functions, power and Laurent series, Cauchy's theorem, calculus of residues, and conformal mappings. NOTE: Prior to summer 2010, the course title was "Introduction to Functions of a Complex Variable."
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C (except where noted) in (MATH 3138, MATH 3142 (C- or higher), 'Y' in MA12, or 'Y' in CRMA17)
This course is typically offered in Spring of even years.This course is an introduction to differential geometry starting with concepts learned in Calculus III. A particular emphasis will be placed on the study of curves and surfaces in 3-space and their generalizations. The course will revolve around Riemannian geometry, but, time permitting, it will also include a brief introduction to one or more of the following: symplectic geometry and its relation to classical mechanics, general connections and their relation with field theory and pseudoriemannian manifolds, and general relativity.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- (except where noted) in (MATH 2043 (C or higher), 'Y' in MA08, or 'Y' in CRMA12) and (MATH 2045, MATH 2101, M
This course is typically offered in Spring of odd years.Topological and metric spaces. Continuity, compactness, connectedness, convergence. Introduction to algebraic and combinatorial topology. Classification of compact surfaces, fundamental groups and covering spaces.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C- in (MATH 3137, MATH 3141, or MATH 3131) and (MATH 3096 or MATH 3098)
This course is typically offered in Fall, Spring, Summer I and Summer II.Intensive individual study at a senior or graduate level. Arranged each semester. Please consult with the instructor. NOTE: Can be taken in either semester.
Subject
MATH
Credits (min)
1
Credits (max)
4
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course is typically offered in Fall, Spring, Summer I and Summer II.Intensive individual study at a senior or graduate level. Arranged each semester. Please consult with the instructor. NOTE: Can be taken in either semester.
Subject
MATH
Credits (min)
1
Credits (max)
4
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course is typically offered in Fall and Spring.This is a course in mathematical discovery through problem solving. Students will be expected to develop two or three areas of mathematics by solving problems, assigned by the instructor. Problems will be solved both individually and in groups. (Capstone writing course.)
Vector spaces and subspaces over the real and complex numbers; linear independence and bases; linear mappings; dual and quotient spaces; fields and general vector spaces; polynomials, ideals and factorization of polynomials; determinant; Jordan canonical form. Fundamentals of multilinear algebra.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This class advances intentional Professional Development by creating an online professional profile and portfolio that allows employers to determine the strength of a student's candidacy for a specific job. Students develop an online professional profile, attend a Professional Development Workshop and write a White paper which demonstrates analytical and technical writing skills on a topic of interest to the student. The White Paper proposes a change in any STEM area where a lack of efficiency in a process, or gap in knowledge, in an area of research, exists. Finally, students organize a networking event by inviting speakers, hiring managers and graduate students in CST.
Subject
MATH
Credits (min)
1
Credits (max)
1
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course will examine the social, legal, and privacy issues applying to scientific data. Students will be given the opportunity to discuss contemporary case studies, in addition to NIH-sanctioned online training modules (Responsible Conduct in Research). The case-study based approach used in class will expose students to ethics of database management and security, open-access and open-source philosophies, the ethics of collecting, storing, and disseminating data.
Subject
MATH
Credits (min)
2
Credits (max)
2
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
Basic theorems and applications of combinatorial analysis, including generating functions, difference equations, Polya's theory of counting, graph theory, matching, and block diagrams.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This class will broaden and deepen our understanding of algebra and functions and their many applications. We will begin with an examination of the concept of function generally and then look at examples. We will consider the usefulness of functions, both in modeling real phenomena and in solving equations. We will carefully develop more advanced concepts from basic principles and logic as we proceed from polynomial functions to rational, radical, exponential, logarithmic, and trigonometric functions. As we do this, we will explore non-traditional teaching techniques and tools such as the practice of inquiry-based learning and the appropriate use of technology. We will also utilize and discuss the eight Mathematical Practice Standards set forth in the Common Core State Standards.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 1042.
MATH 5012Introduction to Mathematical Modeling for Teaching3
In this course, mathematics will be discussed as the language of science. Many students do not have an adequate picture of mathematics: they see it either as a dry formal list of formulas or a dull study of numbers. Mathematics is in fact a network of intriguing and profound ideas that are deeply connected to reality. As a language, mathematics provides penetrating techniques of thought that allow us to analyze physical reality and to look for answers or solutions to some of the most intriguing real-life questions. Students will be asked to read the material in advance and come prepared for class discussion. The in-class activities will be conducted in an inquiry-minded fashion.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 1042.
This class will provide a deep and complete picture of the underlying concepts needed to teach high school geometry. We'll start by learning about the basic axiomatic method, which is fundamental to all of mathematics. We'll learn about the rigid transformations (reflections, rotations, and translations) and the important role that they can play in defining congruence more generally. We'll finish by looking at some important examples of non-Euclidean geometry, where Euclid's famous parallel postulate does not hold.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 1042.
MATH 5014Probability Theory and Applications for Teaching3
Probability is a fundamental topic with applications in nearly every aspect of life. The goal for this course is to equip the student with a large and diverse set of tools with which to tackle a wide variety of problems, both theory and application based. We will focus on the ideas behind the important topics e.g. conditioning, averages, binomial distribution, and explain their origins and applications. This will equip the student to teach their own students this material with an emphasis on the "why", which is essential to maintaining attentiveness.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 1042.
Students will understand the integers and polynomial rings over a field as being specific examples of rings. The idea of quotient spaces will be emphasized with the particular examples of the integers modulo n and factor rings of polynomial rings illustrating and introducing the concept. Moreover, the ability to read and to construct well-written and correct mathematical proofs on these topics is an overarching goal of the course. Written communication skills will also be emphasized.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 2111.
This course will start with a discussion of the basic topology of the real line and the creation of the basic tools using the completeness axiom. From there, the course will proceed to sequences and series, limits, continuity, differentiation, Riemann integration, and Taylor series representations of functions.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 2043.
In this course, we encounter and explore fundamental ideas in number theory. Basic properties of the integers and their two principal operations, addition and multiplication, will form the starting point of our study. Along the way, the course will introduce some basic logic and the rigorous notion of mathematical proof, including mathematical induction, in the context of number theory. Through this elementary foundation, students will experience the richness of mathematics: proof going back as far as Euclid, examples of elementary yet still unproven conjectures, and results that are easy to state and understand but require extremely complicated proofs.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of C in MATH 1042.
This course is an introduction to stochastic calculus based on Brownian motion and Gaussian processes, covering stochastic differential equations as well as applications to option pricing in finance. Concepts and results are illustrated with examples and numerical projects.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is an introduction to some of the basic models, concepts, results and techniques in the study of stochastic processes and touches upon applications along the way. It covers a large selection of the following topics: finite- and countable-state Markov chains, Poisson and birth-and-death processes, optimal stopping, martingales, renewal processes, Markov chain algorithms, and introduction to Brownian motion.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course provides a self-contained introduction to the area of high-dimensional probability and statistics from a non-asymptotic perspective, aimed at students across the mathematical sciences. It will include a focus on core methodology and theory (tail bounds, concentration of measure, random matrices, random graphs and networks) as well as in-depth exploration of various applications (to statistical learning theory, sparse linear and graphical models, community detection, as examples).
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This is a first semester course in basic real analysis. Topics include the real number system and the completeness property, ordered fields, topology of metric spaces, sequences and series, limits of functions and continuity, and differentiation.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This is a second semester course in real analysis, representing a continuation of MATH 5041. Topics include the Riemann integral, infinite series and convergence tests, sequences of functions, uniform convergence, power and Taylor series and operations with them, differentiability of vector valued functions, inverse and implicit function theorems, differential forms, vector analysis, and formula of change of variables in multiple integrals.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 5041.
This course provides a graduate level introduction to classical and modern methods for fundamental problems in computational science and engineering, including approximation and interpolation, numerical integration/quadrature, direct methods for systems of equations, and solution of systems of nonlinear equations. A rigorous mathematical approach to these topics is taken, including floating point arithmetic, error analysis, conditioning and stability, and convergence theorems. The course is accessible to graduate students from all areas of science and engineering interested in a mathematical foundation for the listed computational methods.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 5044Numerical Methods for Ordinary Differential Equations3
This course introduces numerical methods for ordinary differential equations, including explicit, implicit, and semi-implicit time stepping methods (such as Runge-Kutta, multistep, and Taylor series methods). A rigorous mathematical basis is established, including convergence, stability, and error estimators. Critical challenges commonplace in applications, like stiff problems, and specialized time stepping methods, are also presented.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
The course covers existence and uniqueness theorems for ordinary differential equations (ODEs), along with continuous and smooth dependence on initial conditions and parameters, assuming familiarity with the material of advanced calculus. Topics include linear differential equations, their qualitative and asymptotic behavior, and the analysis of isolated singularities. The course also introduces nonlinear equations and Sturm-Liouville problems, emphasizing both theoretical aspects and applications. Basic methods for the numerical solution of ODEs are presented, including stability and convergence considerations.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 5057Applied Partial Differential Equations and Optimization3
This course introduces and studies partial differential equations (PDEs) central to applied mathematics and related fields, arising from continuum mechanics and optimization. Material includes continuum mechanics, methods for linear PDEs, calculus of variations, as well as basic constrained optimization and control. Course topics have a wide applicability to the sciences and engineering.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course introduces fundamental principles of mathematical modeling. Basics of constructing and analyzing models, including scaling and asymptotics, are studied in large part through dynamical systems and their applications. Examples from many areas across the sciences and engineering disciplines are central to this course.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 5061Fundamentals of Computer Programming for Scientists and Engineers4
Scientists and engineers use computers for a multitude of purposes. Even with ready-to-use applications, some amount of computer programming is commonly required to adapt to changing technology while attaining the rigorous standards of each specific discipline. This course focuses on fundamental computer programming constructs, introducing the languages Python, C++ and Fortran. Through lectures and intensive exercises students will learn to implement fundamental mathematical constructs and solve basic programming problems relevant to scientific applications. The course briefly reviews also the Linux environment, its software development tools and language interoperability. For each programming language, the course focuses on constructs and syntax designed for performance and numerical accuracy, in connection with methods from applied science, mathematics and engineering. The students taking the course are expected to have sufficient mathematical maturity, as evidenced, for example, by having completed an undergraduate Calculus sequence. The majority of the grade is determined by a mid-term and a final exam, both including a combination of questionnaires and supervised programming assignments.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 5062High Performance Computer Programming for Scientific Modeling3
This course will provide theory and hands-on experience programming high performance computers for the solution of scientific modeling problems. This includes in particular problems arising from the discretizations of differential equations. Topics covered include domain decomposition and mesh partitioning, quantifying the computation and communication cost, communication avoidance methods, Monte Carlo methods, multithreading, benchmarking and optimization of the parallel computations.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 5061.
MATH 5063Introduction to High-Performance Computing Technology for Scientists4
This course is an introduction to the technology used in Linux clusters and supercomputers dedicated to calculations in applied science and engineering. The basic architecture of modern computers (processing units, memory, storage, operating system) is briefly reviewed, emphasizing the role and performance impact of each element in numerical computation. The core of the course focuses on setup and management of computer hardware specialized for scientific computing, and on its impact on commonly used strategies and methods for scientific computation. The material is organized in a combination of lectures and hands-on exercises, using computer hardware hosted at local facilities as well as virtualized resources. The majority of the grade is determined by a mid-term and a final exam, both including a combination of questionnaires and identification of the most efficient solution to common numerical problems.
Subject
MATH
Credits (min)
4
Credits (max)
4
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 5061 (may be taken concurrently)
This course covers the fundamentals of metric spaces and topological spaces. Core topics include continuity, compactness, connectedness, and convergence. Time permitting, the course will include the classification of compact surfaces and an introduction to algebraic topology, including fundamental groups and covering spaces.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 5066Mathematical Methods for High Performance Computing3
This course presents mathematical methods for the solution of a variety of discrete and algebraic problems which are at the core of many scientific and engineering applications. The methods covered are especially tailored for high performance computing. Topics include large matrix computations, graphs and networks, fast Fourier transforms, geometric and algebraic multi-grid methods, and constrained optimization.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 5061, MATH 5062, and MATH 5063.
This course on the mathematical aspects of cryptography proceeds in four parts. In Part 1, we go over groups, rings, and finite fields. Part 2 is devoted to symmetric key cryptosystems, including both classical cryptosystems (affine cipher, substitution cipher, Hill cipher) and modern cryptosystems, e.g., the Advanced Encryption Standard (AES, Rijndael). Part 3 is devoted to aspects of elementary number theory related to cryptography. Part 4 is devoted to public key cryptosystems. In this part, we learn the discrete logarithm problem, the Diffie-Hellman key exchange, the Pohlig-Hellman algorithm and the collision algorithm, the ElGamal public key cryptosystem, the Rivest-Shamir-Adleman (RSA) public key cryptosystem, and attacks on RSA. The course involves programming problems and a study project.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This is the first semester of a year-long sequence in Abstract Algebra. Topics in group theory include group actions, the Sylow theorems, nilpotent and solvable groups, and free groups. Topics in ring theory include structure results on factorization and polynomial rings. The structure theorem for finitely generated modules over principal ideal domains is proved. Throughout, the theme of universal properties and basic category theory is developed.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This is the second semester of a year-long sequence in Abstract Algebra. The course covers fields and Galois theory, module theory including canonical forms for matrices, and Noetherian rings and modules.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8011.
This course presents the fundamental numerical techniques for Linear Algebra, aimed at graduate students in mathematics and related areas who seek a mathematical introduction. Topics include orthogonalization and QR factorization in theory and practice, iterative methods for solving linear systems, Krylov subspace methods, variational formulations for symmetric and nonsymmetric problems, convergence estimates, relations to orthogonal polynomials, preconditioning techniques, incomplete factorizations, multigrid methods, domain decomposition, and basic methods for eigenvalue problems.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 8023Numerical Methods for Partial Differential Equations3
This course is designed for graduate students of all disciplines and areas who are interested in numerical methods for partial differential equations, focusing on a rigorous mathematical derivation and analysis. Topics include finite difference, finite element, Fourier, and spectral methods for boundary value problems, elliptic equations, transport, diffusion/heat equation, and wave propagation problems. Fundamental concepts like stability, convergence, and error analysis are a key focus.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 8024Numerical Methods for Nonlinear Partial Differential Equations3
This course is designed for graduate students of all disciplines and areas who are interested in numerical methods for partial differential equations, focusing on a rigorous mathematical derivation and analysis. Topics include finite difference, finite element, Fourier, and spectral methods for boundary value problems, elliptic equations, transport, diffusion/heat equation, and wave propagation problems. Fundamental concepts like stability, convergence, and error analysis are a key focus.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course provides a rigorous treatment of probability theory, covering the following: the axioms of probability, random variables and their distributions, expectation and variance, conditional probability and independence, Markov chains, random walks, laws of large numbers, weak convergence of measures, characteristic functions, the central limit theorem, and additional topics if time permits.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course provides a rigorous treatment of stochastic processes, focusing on the following: existence of stochastic processes, Poisson process, conditional expectation and martingales, continuous-time Markov processes, stationary processes, ergodicity and mixing, Brownian motion and its properties.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8031.
This course focuses on the development of the Lebesgue measure and integration theory. It covers core areas in analysis, including functions of bounded variation, Lebesgue measure and outer measure, measurable functions, Lebesgue integral, modes of convergence, and repeated integration. This course presumes knowledge of undergraduate Real Analysis.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is a continuation of MATH 8041. It covers core areas in analysis including Lebesgue differentiation theory, maximal functions, absolute continuity, approximation of identity, L^p spaces, Hilbert spaces, abstract measures and integration.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8041.
This course is an introduction to the theory of functions of one complex variable. Topics include holomorphic functions, derivatives and path integrals, power series, exponential and trigonometric functions, the Cauchy integral theorem and consequences (the maximum principle, Liouville's theorem, Morera's theorem, Schwarz' reflection principle, and Goursat's theorem), residue calculus, convergence in the space of holomorphic functions, Hurwitz' theorem, Montel's theorem, conformal maps and the Riemann mapping theorem. This course presumes knowledge of undergraduate Real Analysis.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
The topics and the textbook choice are at the instructor's discretion. Topics of focus include: Phragmen-Lindelof method, Runge's theorem, Weierstrass factorization theorem, Mittag-Leffler theorem, theory of entire functions, elements of theory of elliptic functions, several complex variables, theory of Riemann surfaces.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8051.
This is a standard introductory graduate course in differential topology. Topics include: smooth structures on manifolds; smooth functions and maps between manifolds; tangent and cotangent bundles; vector bundles; differential forms; tensors; integration and Stokes' theorem.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This is a standard introductory graduate course in algebraic topology. Topics include: the fundamental group; van Kampen's theorem; covering space theory; singular homology and cohomology; exact sequences; de Rham cohomology and de Rham's theorem; Poincare duality.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 8107Mathematical Modeling for Science, Engineering, and Industry3
In this course, students form research groups for projects provided by partners in industry, engineering, or in other disciplines of science. Throughout the semester, the teams are advised by the course instructors and the external partners. The problems themselves are formulated in non-mathematical language, so the students are required to translate these into mathematical language and develop solutions using methods of mathematical modeling. This means that the mathematical and computational methods must be selected or created by the students themselves. At the end, research findings and final results need to be formulated in a language accessible to the external partner. Students disseminate their progress and achievements in weekly presentations, a mid-term and a final project report, as well as a final presentation. Group work with and without the instructors' involvement is a crucial component in this course. Graduate students from disciplines other than mathematics, interested in collaborating in teams on mathematical modeling, and with a background in principles of modeling and computational methods, are welcome to this course.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course introduces fundamental concepts and results in the theory of elliptic, parabolic, and hyperbolic differential equations, preparing students for problem-solving in PDEs and their applications. Topics covered: Laplace's equation (maximum principles, Dirichlet problem, Green's function and Poisson kernel), Heat equation (initial boundary value problems, fundamental solution, mean value formula, maximum principle, uniqueness theorems, examples of non-uniqueness, backward heat equation, and energy methods), Wave equation (D'Alembert's formula, plane waves, solution by spherical means, Huygens' Principle, Energy methods: uniqueness, domain of dependence). Solution of the Cauchy problem for nonlinear first order PDEs. This course presupposes knowledge of undergraduate Real Analysis.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
MATH 8142Intermediate Partial Differential Equations3
This course builds on the foundations of graduate-level PDE theory. The choice of content is at the instructor's discretion. Topics to be covered include nonlinear PDEs, Fourier transform methods, dispersive equations, Sobolev spaces, energy methods, and the Fredholm alternative.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8141.
This course aims to familiarize first-year PhD students with the structure of a PhD in Mathematics. A significant focus of the course is professional development, wherein students learn about important milestones in the program and are trained in the related responsibilities. Students enrolled in this course must attend at least one seminar or colloquium per week, in order to be exposed to research-level mathematics and best practices for communicating mathematics. The seminar itself features a weekly discussion on a topic of interest, led by the Director of Graduate Studies and/or a senior TA. Topics covered in the seminar should include: Basics of departmental structure; effective study techniques for graduate courses and qualifying exams; best practices for professional conduct; creating a professional webpage; written and oral communication of research-level mathematics; research topics studied by faculty in the department; the process of finding a PhD advisor, e.g. through independent study courses; organizing PhD studies with perspective of post-PhD career goals; finding and applying for summer internships in industry and education; and applying for post-PhD employment, in and out of academia.
Subject
MATH
Credits (min)
1
Credits (max)
1
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
This course is required for any student seeking Temple's Teaching in Higher Education Certificate. The course focuses on the research on learning theory and the best teaching practices, with the aim of preparing students for effective higher education teaching. All educational topics will be considered through the lens of teaching mathematics and quantitative thinking.
Subject
MATH
Credits (min)
1
Credits (max)
3
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.
Analytic and algebraic number theory. Classical results and methods and special topics such as partition theory, asymptotic, Zeta functions, transcendence, modular functions.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course introduces students to the basic objects, tools, and questions of algebraic number theory. The focus is on number fields and their rings of integers, though some topics related to local fields or global function fields may be introduced. After covering the basics of Dedekind domains and the behavior of prime ideals in extension fields, the two major finiteness theorems -- Dirichlet's unit theorem and the finiteness of class groups -- are proved. Additional possible topics include the analytic class number formula, Dirichlet's Theorem for primes in arithmetic progressions, Chebotarev's Density Theorem, the Kronecker-Weber Theorem, and an introduction to class field theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
This course introduces students to elliptic curves. Basic experience with algebraic geometry will be helpful, but is not assumed. The course starts with an introduction to algebraic varieties, curves, and the geometry of elliptic curves over a general base field, assuming Riemann-Roch. After this, time is spent delving into the structure of elliptic curves over various fields, specifically the complex numbers, the rational numbers, and finite fields. The course culminates in a proof of the Mordell-Weil Theorem, which assumes the two major finiteness theorems from MATH 9001.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
This course introduces students to modular forms. Topics include Eisenstein series, finiteness of spaces of modular forms, Hecke operators, modular curves, L-functions of modular forms, and moduli descriptions of modular curves and modular forms. Additional possible topics include congruences between modular forms and an introduction to modularity.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8051.
The course is devoted to fundamental notions of homological algebra: chain complexes, abelian categories, derived functors, and spectral sequences. A portion of this course is also devoted to rudiments of category theory. Students will learn how to apply constructions of homological algebra and category theory to questions from abstract algebra, topology and deformation theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
This course primarily focuses on representations of finite groups over a field of characteristic zero. The bulk of the course covers the basics of subrepresentations, irreducibility, semisimplicity, character theory and orthogonality relations, induced representations, and Mackey theory. Additional possible topics include Schur indices, pseudorepresentations, representations of Lie algebras, and modular representation theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
This course focuses on the fundamental concepts of commutative algebra. Topics of the course include ideals of commutative rings, modules, Noetherian and Artinian rings, Noether normalization, Hilbert's Nullstellensatz, rings of fractions, primary decomposition, discrete valuation rings and the rudiments of dimension theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
This course introduces students to the vast subject of algebraic geometry. Topics of the course include affine and projective varieties, morphisms of algebraic varieties, birational equivalence, and basic intersection theory. Students will also learn about schemes, morphisms of schemes, coherent sheaves, and divisors.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8012.
The goal of this course is to provide a solid introduction to the two central concepts of Riemannian geometry, namely, geodesics and curvature. Topics include Riemannian metrics, Riemannian connections, geodesics, curvature (sectional, Ricci, and scalar), the Jacobi equation, the second fundamental form, and global results such as the Gauss-Bonnet theorem, Hopf-Rinow theorem, and Hadamard's theorem.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8061 and MATH 8062 (may be taken concurrently)
This course covers the theory of knots and links, with a focus on different flavors of invariants. The course covers a large selection of the following topics: polynomial invariants, connections to braid groups, Dehn surgery, geometric invariants, quantum invariants of 3-manifolds.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8062.
This course is a broad introduction to low-dimensional topology with an emphasis on 3-manifolds, especially their construction, classification results, and invariants. Potential topics include: gluing constructions, Dehn surgery, foliations and flows, geometric structures, and connections to group theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8062.
Functional Analysis provides the foundation for high-dimensional geometry, analysis, and probability. This course introduces the fundamental concepts and methods of functional analysis, with an emphasis on concrete examples. Topics include the Baire Category Theorem and its applications, particularly to Banach space theory principles such as the Uniform Boundedness Principle, the Open Mapping Theorem, and the Closed Graph Theorem. The course also explores different notions of convergence, weak topology, duality, and convexity. In addition, it introduces linear operator theory, including spectral theory for compact operators, self-adjoint operators, Fredholm theory, and their applications.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in (MATH 5042 or MATH 8042)
MATH 9042Fourier Analysis and Distribution Theory3
This course is a basic introduction to Fourier Analysis and Distribution Theory. Topics include Fourier series, the Fourier transform, Schwartz functions, tempered distributions, convolutions, and applications to partial differential equations. Knowledge of MATH 9041, Functional Analysis, is recommended but not required.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8042.
The course covers the first variation and Euler-Lagrange equations, including null Lagrangians and Caratheodory's "Royal Road". It introduces geodesic coverings, the eikonal equation, and the Hamilton-Jacobi equation. The second variation is explored through Jacobi's theory of conjugate points and Weierstrass's E-function. The Hamiltonian formalism, convex duality, and Hilbert's invariant integral are also discussed, highlighting connections between variational principles, geometry, and physics.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8042.
This course presents a rapid introduction to modern tools of Harmonic Analysis. These tools are relevant to problems in a very dynamic area of mathematics at the interface of several branches such as Fourier Analysis, Functional Analysis, Partial Differential Equations, Index Theory, and Geometric Measure Theory. Topics of focus include Hardy spaces, singular integrals, maximal operators, functions of bounded and vanishing mean oscillation, square functions, applications to elliptic partial differential equations in the upper half space.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8042.
This course develops Lie theory from the ground up. Starting with basic definitions of Lie groups and Lie algebras, the course develops structure theory, analytic and algebraic aspects, structure of nilpotent and solvable Lie groups, and the classification of semisimple Lie groups.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8062.
This course covers the analytic and geometric theory of Riemann surfaces. Topics include: uniformization, algebraic perspectives, calculus on Riemann surfaces, moduli space. Moduli and Teichmuller spaces for compact Riemann surfaces; introduction to modular forms; embedding of compact Riemann surfaces in complex projective spaces. Branched coverings and maps onto the Riemann sphere.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8051.
This is an introduction to hyperbolic manifolds, their structure, and their deformations. Potential topics include: thick-thin decomposition, rigidity results, hyperbolic Dehn filling, arithmetic manifolds, and the general theory of Kleinian groups.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8061 and MATH 8062 (may be taken concurrently)
This course surveys the rapidly expanding field of geometric group theory, focusing on the role played by negative curvature. The course begins with classical combinatorial techniques used to construct and study infinite discrete groups. After introducing basic concepts in coarse geometry, it turns attention to Gromov's notion of hyperbolic groups. In addition to studying geometric, algebraic, and algorithmic properties of these groups, the course keeps an eye towards several generalizations of hyperbolicity that have recently played a large role in understanding many geometrically significant groups. As examples, it also touches on the study of mapping class groups, outer automorphism groups of free groups, and cubical groups.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may not be repeated for additional credits.Pre-requisites: Minimum grade of B- in MATH 8062.
This course covers a variable set of timely topics in Numerical Analysis, including, but not limited to, numerical optimization, computational fluid dynamics, numerical methods for general flow problems, or advanced finite element methods.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course covers a variable set of timely topics in Applied Mathematics, including, but not limited to, mathematical biology, multiscale modeling and methods, material science, or control theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course presents research topics related to probability theory, depending on the interests of the students and the instructor. Potential topics include interacting particle systems, random matrix theory, probability models in mathematical physics, statistical mechanics, homogenization, stochastic optimal control, differential and mean-field games.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course focuses on advanced topics in Analysis and the theory of Partial Differential Equations with the goal of introducing students to open problems in the field. The focus changes with the instructor. Potential topics covered include non-linear PDEs, Monge-Ampere equations, elliptic PDE in irregular domains, spectral theory, singular integrals, optimal transport, regularity theory of solutions to elliptic PDEs, mathematical analysis of fluid equations, and analysis on quasi-metric spaces.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This is a year-long sequence. Topics covered may include the theory of elliptic partial differential equations in divergence form and non-divergence form, and nonlinear PDEs. These courses may also focus on pseudodifferential operators and Fourier integral operators.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
Variable topics in geometric topology and related areas. Possibilities include: Morse theory, surfaces and their diffeomorphisms, mapping class groups, Teichmuller theory, braids, dynamics of group actions, and homogeneous dynamics.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credit Hours
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.Pre-requisites: Minimum grade of B- in MATH 8062.
Short-term, limited research project or laboratory project in the field. This course is not the capstone project course, nor can it be used for thesis based research. The course is for master's students only, including PSM, MA or MS. This class will not confer full-time program status unless nine credits are taken.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
This course is required for students who are preparing for the preliminary or candidacy examination. Students should enroll after coursework is completed or when preparing for the candidacy exam until the time that the preliminary or candidacy examination is completed. This course will confer full-time status at the minimum credit hour registration limit of one credit. All students must complete a minimum of one credit of this course. Students must complete a total of 6 credit hours of 9994, 9998 and 9999.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
Capstone project for master's students including students in PSM, MA or MS. This class will provide full-time status. Students in PSM programs need to register for at least one credit of this course to fulfill program requirements. Additional credits may be required for specific programs. This course will confer full-time status at the minimum credit hour registration limit of one credit.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
Course for master's thesis research. Only intended for students in thesis bearing master's programs. A minimum of one credit is required. This course will confer full-time status at the minimum credit hour registration limit of one credit.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
MATH 9998Pre-Dissertation Research / Elevation to Candidacy1-6
This course is intended for students who are performing research prior to candidacy. Students can register for this course after required courses are completed. This course will confer full-time status at the minimum credit hour registration limit of one credit. Students must be registered for this course during the semester that they are to be elevated to candidacy examination. Students must complete a total of 6 credit hours of 9994, 9998 and 9999.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
The course is for Ph.D. students who have been elevated to candidacy. During the course of their candidacy students must complete a minimum of two credits of dissertation research. This course will confer full-time status at the minimum credit hour registration limit of one credit. Students must complete a total of 6 credit hours of 9994, 9998 and 9999.
Subject
MATH
Credits (min)
1
Credits (max)
6
Credit unit
Credit Hour
Type
course
Repeatable
Repeatability: This course may be repeated for additional credit.
