Mathematics Courses | 2026-2027 Graduate Catalog | SIU

This course examines financial mathematics and actuarial models for investments including interest, annuities, stocks, bonds, and mutual funds. There is an introduction to financial derivatives, options, and futures. Preparation for Exam FM/2. Prerequisite: MATH 250 with a grade of C or better. Credit Hours: 4.

Credit Hours: 4

This course is an introduction to measure theory and the Lebesgue integral. Its purpose is to develop many of the advanced mathematical tools that are necessary for the understanding of all other advanced courses in analysis. Topics will include: measures and measurable functions, Egoroff's theorem, the Lebesgue integral, Fatou's lemma, the monotone and dominated convergence theorems, functions of bounded variation and absolutely continuous functions, Lp-spaces, the Radon-Nikodm theorem, product measures, and Tonelli's and Fubini's theorems. Prerequisite: MATH 452.

Credit Hours: 3

This course is an introduction to infinite-dimensional spaces and their analysis. Topics include Hilbert and Banach spaces, separable and reflexive spaces, operators and their adjoints, and major theorems such as the Banach-Steinhaus, Open-Mapping, Closed Graph, Hahn-Banach, Riesz and matrix representation, Lax-Milgram, Arzela-Ascoli, Katos theorems. Spectral theory and applications to such areas as differential equations, Block iterations, quantum probability, fixed point theory or other areas are covered as time permits. Prerequisite: MATH 501 with a grade of B or better.

Credit Hours: 3

This course examines loss models including severity models, aggregate loss, estimation, ratemaking and reserving, and estimation from a sophisticated mathematical perspective. This course prepares students for Exam FAM-S. Prerequisite: MATH 483 or MATH 583A with C or better. Credit Hours: 3.

Credit Hours: 3

This course continues the examination of short-term loss models begun in MATH 403, including estimation, credibility, and extremal value theory. This course prepares students for Exam ASTAM. Prerequisite: MATH 403 or MATH 503A with C or better. Credit Hours: 3.

Credit Hours: 3

Existence and uniqueness theorems; general properties of solutions; linear systems; geometric theory of nonlinear equations; stability; self-adjoin boundary value problems; oscillation theorems. Theory will be illustrated with computer simulation of several real-world problems. Prerequisite: MATH 452 and MATH 421 or consent of instructor.

Credit Hours: 3

Selected advanced topics in ordinary differential equations chosen from such areas as: stability, oscillations, functional differential equations, perturbations, boundary value problems. Special approval needed from the instructor.

Credit Hours: 1-12

This course introduces the student to the mathematical techniques that are used to analyze qualitative properties of solutions to partial differential equations that arise in engineering and the sciences. Topics studied will include: function spaces including Sobolev spaces; weak derivatives; the Sobolev and Poincare inequalities; existence, uniqueness, and continuous dependence for model equations. Prerequisite: MATH 407 and MATH 501.

Credit Hours: 3

(Same as CI 529) Selected advanced topics in the teaching of mathematics chosen from such areas as: pedagogical theories; instructional strategies; applications of mathematics; problem solving. This course is counted by the Mathematics department only as part of an approved minor. Special approval needed from the instructor.

Credit Hours: 3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

This course is counted by the Mathematics department only as part of an approved minor.

Credit Hours: 1-3

Knowing mathematics is an insufficient qualification for teaching mathematics, and this course seeks to close that gap. In this course, we will explore the best practices in the teaching of mathematics to undergraduate students and apply this knowledge to particular problems of teaching mathematics at a mid-sized public university in the US.

Credit Hours: 1

Descriptive statistics; graphic display of data; concepts of probability; statistical estimation, and hypothesis testing. Applications to social science data. This course does not give credit toward a mathematics major. Prerequisite: one year of high school algebra or equivalent.

Credit Hours: 4

Matrix algebra; general linear model; multivariate statistics, ordinal and nominal measures of associations and causal modeling. Applications to social science data. This course does not give credit toward a mathematics major. Prerequisite: one year of high school algebra or equivalent.

Credit Hours: 4

Introduction to the basic techniques in the classification of finite groups, including homomorphism theorems, classification of finitely generated abelian groups, Sylow's theorems and classification of small groups, divisibility theory in rings, especially polynomial rings. Prerequisite: MATH 419 or consent of instructor.

Credit Hours: 3

This course offers a rigorous exploration of polynomial equations in one variable through the lens of modern algebra. Following a detailed study of polynomial rings and irreducibility criteria, the course develops the theory of field extensions and solvable groups. Students will investigate the interplay between field theory and group theory, culminating in a deep understanding of the Fundamental Theorem of Galois Theory. Applications include solving polynomials by radicals, classical geometric impossibility results, and the construction and classification of finite fields. Prerequisite: MATH 319 with C or better. Credit Hours: 3.

Credit Hours: 3

Free modules, torsion modules, tensor products of modules, finitely generated modules over principal ideal domains, application of abelian groups, algebraic geometry, homological algebra and group cohomology. Prerequisite: MATH 519.

Credit Hours: 3

Study the extension of basic linear algebra to arbitrary scalars. Key topics include vector spaces, linear independence, bases, matrices, eigenvalues, eigenvectors, diagonalization, inner product spaces, orthogonality, the Gram Schmidt process, adjoint operators, Jordan canonical forms, quadratic forms, Sylvester?s law of inertia. Prerequisite: MATH 221 with C or better. Credit Hours: 3.

Credit Hours: 3

Selected topics in modern algebra and number theory chosen from such areas as: group theory, commutative algebra, non-commutative algebra, field theory, representation theory, analytical number theory, algebraic number theory, additive number theory. Diophantine approximations, Dirichlet series and automorphic form. Special approval needed from the instructor.

Credit Hours: 1-12

Introduction to modern analytic techniques used in the study of quadratic forms, the distribution of prime numbers, Diophantine approximations and other topics of classical number theory. Prerequisites: MATH 425 and MATH 455 with grades of C or better.

Credit Hours: 3

Introduction to the modern algebraic techniques used in the study of number theory. Advanced Galois Theory, algebraic integers, prime factorization of ideals, Dirichlet unit theorem, ramification theory, local fields, and other topics. Prerequisites: MATH 425 and MATH 419 with grades of C or better.

Credit Hours: 3

This course covers the basics of point-set topology, Urysohn's lemma, Tychonoff's theorem, the Barie category theorem, manifolds and the fundamental group. Prerequisite: MATH 430 or MATH 452 with a C or better.

Credit Hours: 3

Study of the real line and the plane, metric spaces, topological spaces, compactness, connectedness, continuity, products, quotients and fixed-point theorems. This course will be particularly useful to students who intend to study analysis or applied mathematics. The course will prepare students for advanced study in differential equations, algebraic topology, computing theory and theoretical physics. Prerequisite: MATH 352 with C or better. Credit Hours: 3.

Credit Hours: 3

This course covers homotopy and homology groups, exact sequences, CW complexes, axioms of homology, and beginnings of cohomology. Prerequisite: MATH 530 with a C or better.

Credit Hours: 3

Topics may include dynamical systems, topological groups, knot theory, complexity theory, uniform spaces and frames, differential and Riemannian geometry, voting theory and mathematical physics. Special approval needed from the instructor.

Credit Hours: 1-12

This course covers differential forms, curvature, connections, integration on manifolds and may include Riemannian geometry or Lie groups. Prerequisite: MATH 530 with a C or better.

Credit Hours: 3

The course develops the basic results on convex sets and functions which are extensively used in several areas of applied mathematics and in business and engineering. Both finite and infinite dimensional spaces will be discussed. Topics covered include separation theorems, extreme points and the Krein-Milman Theorem. For infinite dimensional spaces elementary aspects of locally convex spaces will be covered. Applications include inequalities, constrained optimization and minimax theory. Prerequisite: MATH 452 or consent of instructor.

Credit Hours: 3

Graph theory is an area of mathematics which is fundamental to future problems such as computer security, parallel processing, the structure of the World Wide Web, traffic flow and scheduling problems. It also plays an increasingly important role within computer science. Topics include: trees, coverings, planarity, colorability, digraphs, depth-first and breadth-first searches, and advanced topics such as random graphs or the probabilistic method. Prerequisite: MATH 349 with C or better.

Credit Hours: 3

This course will introduce the student to various advanced topics in Combinatorial theory that are basic to modern methods in applicable mathematics. Possible topics include: Enumeration, Polya-Burnside theory, DeBruijn sequences, Graph theory, Cayley's Theorem, Ramsey's Theorem, Hall's Theorem, Design Theory, Distinct representatives, Latin squares and Finite geometries. Prerequisite: MATH 449 or consent of instructor.

Credit Hours: 3

This course will introduce the student to various basic topics in combinatorics that are widely used throughout applicable mathematics. Possible topics include elementary counting techniques, pigeonhole principle, multinomial principle, inclusion and exclusion, recurrence relations, generating functions, partitions, designs, graphs, finite geometry, codes and cryptography. Proofs of major theorems. Prerequisite: MATH 349 with C or better. Credit Hours: 3.

Credit Hours: 3

A rigorous development of single-variable calculus providing the tools necessary for understanding more advanced topics in analysis. Topics include: the Cauchy completion of the real numbers; metric space topology including limits, compactness and continuity; development of calculus on the real line (review); The Heine-Borel Theorem and compactness in Euclidean space; basic concepts related to function spaces; sequences and series of functions; the Arzela-Ascoli Theorem and compactness in function spaces. Prerequisite: MATH 352 with C or better. Credit Hours: 3.

Credit Hours: 3

Advanced topics in analysis and functional analysis from such areas as: harmonic analysis, approximation theory, integration theory, advanced complex variables, topological vector spaces, operator theory, Banach algebras, distribution theory. Special approval needed from the instructor.

Credit Hours: 1-12

We review the field of complex numbers, differentiability, series convergence and the Cauchy integral formula for functions of a single complex variable. We go on to study the properties analytic, entire, meromorphic, and harmonic functions. We develop rigorous proofs of the Maximum modulus theorem, the Riemann mapping theorem, the residue theorem, and the Weierstrass factorization theorem and related results. If time permits the gamma and Riemann zeta functions are presented. Prerequisite: MATH 455.

Credit Hours: 3

Analysis of differentiable functions of a single complex variable. Introduces mathematical techniques used to analyze problems in the sciences and engineering that are inherently two dimensional. Topics include: the complex plane, analytic functions, the Cauchy-Riemann equations, line integrals, the Cauchy integral formula, Taylor and Laurent series, the residue theorem, conformal mappings, applications. Proofs of major theorems. Prerequisite: MATH 251 with C or better. Credit Hours: 3.

Credit Hours: 3

Selected advanced topics in combinatorics chosen from such areas as: graph theory; combinatorial designs; enumeration; random graphs; finite geometry; coding theory; cryptography; combinational algorithms. Special approval needed from the instructor.

Credit Hours: 1-12

The theory of stochastic processes, including integration, martingales, Brownian motion, difference equations and Ito's lemma, is developed and applied to problems in mathematical finance, such as dynamic asset and option pricing, modeling of financial derivatives and interest rates. The binomial tree method of Cox-Ingersoll-Rubinstein, and the models of Vasicek, Dothan, and others are developed. Stochastic numerical methods and related statistical procedures as used in computational finance are covered if time permits. Since this is an interdisciplinary course, students should contact the instructor about prerequisite knowledge. Special approval needed from the instructor.

Credit Hours: 3

This course will provide a rigorous development of the mechanics of solids and fluids. Topics will include: elements of tensor analysis; kinematics; balance of mass, linear momentum and angular momentum; the concept of stress; constitutive equations for fluid and solid bodies; and invariance of constitutive equations under a change in observer. Applications of continuum mechanics to the solution of problems in materials science will be included as time permits. Prerequisite: MATH 450 or MATH 452.

Credit Hours: 3

Selected advanced topics in applied mathematics chosen from such areas as: continuum mechanics; electromagnetic theory; control theory; mathematical physics. Special approval needed from the instructor.

Credit Hours: 1-12

Selected advanced topics in optimization and operations research chosen from such areas as: calculus of variations, optimal control theory, nonlinear programming, convex analysis, non-smooth analysis, new flows, advanced computer simulation, large scale linear programming. Special approval needed from the instructor.

Credit Hours: 1-12

(Same as CS 572) Selected advanced topics in numerical analysis chosen from such areas as: approximation theory, spline theory; special functions; wavelets; numerical solution of initial value problems; numerical solution of boundary value problems; numerical linear algebra; numerical methods of optimization; and functional analytic methods. Special approval needed from the instructor.

Credit Hours: 1-12

A study of techniques for approximating functions by polynomials, trigonometric polynomials, polynomial splines, wavelets, etc. Topics include: existence, uniqueness and characterization of best approximations in normed linear spaces; projection methods for good approximation; the Weierstrass, Muntz-Szasz, and Stone-Weierstrass theorems; degree of approximation and the Jackson theorems; construction of optimal min-max and least squares approximation using rational functions, splines, wavelets. Students will use MATLAB to study the quality of various approximations developed in the course. Prerequisite: MATH 452, MATH 475, and MATH 421.

Credit Hours: 3

A practical introduction to modern numerical linear algebra. Topics include: vector and matrix norms; Householder, Givens and Gauss transforms; factorization methods for solving systems of linear equations with roundoff error analysis; QR and SVD methods for solving linear least squares problems; the QR algorithm for computing the eigenvalues of a matrix. Students will use MATLAB to study the algorithms developed in the course. Prerequisite: MATH 475 and one of MATH 406, MATH 421.

Credit Hours: 3

The course gives a rigorous introduction to statistical inference. Topics covered include statistical models; sufficiency and completeness; Cram?Rao bound; Rao-Blackwell theorem; best estimators; most powerful tests; likelihood ratio tests; elements of Bayes and minimax procedures. Prerequisite: MATH 483, or consent of instructor.

Credit Hours: 3

A rigorous, measure-theoretic introduction to probability theory. Principal topics include general probability spaces, product spaces and product measures, random variables as measurable functions, distribution functions, conditional expectation, types of convergence, characteristic functions and the Central Limit theorem, tail events and 0-1 laws, the Borel-Cantelli lemma, and the weak and strong law of large numbers. Prerequisite: MATH 501, or consent of instructor.

Credit Hours: 3

Selected advanced topics in probability chosen from such areas as: martingales, Markov processes, Brownian motion, infinitely divisible laws. Special approval needed from the instructor.

Credit Hours: 1-6

Selected advanced topics in statistics chosen from such areas as: advanced linear models, advanced experimental design, multivariate statistical analysis, decision theory, advanced nonparametric theory. Prerequisite: MATH 483.

Credit Hours: 1-12

Develops statistical techniques used in applied fields like engineering, and the physical and natural sciences. Principal topics include probability; random variables; expectations; moment generating functions; transformations of random variables; point and interval estimation; tests of hypotheses. Applications include one-way classification data and chi-square tests for cross classified data. Addresses more advanced topics compared to MATH 483. Prerequisite: MATH 250 with C or better.

Credit Hours: 4

This course examines the theory of linear models with applications to the analysis of variance and regression and to the design of experiments. Least squares estimation, and testing for full rank and less than full rank models are covered. Prerequisites: MATH 221 and MATH 484 with grades of C or better.

Credit Hours: 3

This course examines the multivariate normal and elliptically contoured distributions, estimators of multivariate location and dispersion, Hotelling's T^2 test, MANOVA, multivariate regression, principal component analysis, factor analysis, canonical correlation analysis, discriminant analysis, and clustering. Prerequisites: MATH 483 and MATH 221 with grades of C or better.

Credit Hours: 3

This course covers Statistical Computing and Learning, including supervised and unsupervised learning, statistical computations in software packages such as R and SAS, loops, approximation of distribution functions, computation of maximum likelihood estimations, random number generation, bootstrap, Monte Carlo, permutation tests, and Bayesian techniques. Prerequisites: MATH 483 and MATH 221 with grades of C or better.

Credit Hours: 3

Lectures on various mathematical topics of current research interest by members of the department and by distinguished visitors. Special approval needed from the graduate adviser.

Credit Hours: 1-6

Active participation in a seminar run by the School. Student is encouraged to present their research to the seminar at least once per semester. Graded S/U only. Special approval needed from the seminar organizer and the director of graduate studies.

Credit Hours: 1-2

Individual study supervised by a member of the continuing faculty. Graded S/U only. Special approval needed from the instructor.

Credit Hours: 1-12

Minimum of three hours to be counted toward the Master of Arts or Science in Mathematics degree. Graded S/U only. Special approval needed from the instructor.

Credit Hours: 1-6

Minimum of three hours to be counted toward the Master of Arts or Science in Mathematics degree. Graded S/U only. Special approval needed from the instructor.

Credit Hours: 1-6

Minimum of 24 hours to be earned for the Doctor of Philosophy degree in Mathematics. Special approval needed from the instructor.

Credit Hours: 1-30

For those graduate students who have not finished their degree programs and who are in the process of working on their dissertation, thesis, or research paper. The student must have completed a minimum of 24 hours of dissertation research, or the minimum thesis, or research hours before being eligible to register for this course. Concurrent enrollment in any other course is not permitted. Graded S/U or DEF only.

Credit Hours: 1

Must be a Postdoctoral Fellow. Concurrent enrollment in any other course is not permitted.

Credit Hours: 1