## Mathematics (MATH)

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#### Developmental Courses

**0301. Essential Mathematics (3). **A developmental course for students with weak preparation in fundamental mathematics, high school algebra, and geometry. MATH 0301 counts in the student’s semester load and is recorded on the transcript, but the hours do not count as part of the minimum number of hours required for graduation in any degree program of the university. Grades are awarded for the semester, but they are not computed in the student’s grade point average. This course counts for TSI math skills development provided the student has met with an advisor in the TSI Developmental Education Office in 78 Holden Hall.

**0302. Intermediate Algebra (3).** Prerequisite: Code 2 or higher on MPE or a score of at least 610 on the SATM or a score of at least 26 on the ACTM or a grade of A or B in MATH 0301 or a grade of A or B in TSI 0202 or a grade of D or better in a college level mathematics course. A developmental course for students with weak preparation in algebra or who need a review of high school algebra before enrolling in MATH 1320 or higher. MATH 0302 counts in the student’s semester load and is recorded on the transcript, but the hours do not count as part of the minimum number of hours required for graduation in any degree program of the university. Grades are awarded for the semester, but they are not computed in the student’s grade point average. This course counts for TSI math skills development provided the student has met with an advisor in the TSI Developmental Education Office in 78 Holden Hall.

#### 1000 Level Courses

**1300. [MATH 1332] Contemporary Mathematics (3). **Prerequisites: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302. Quantitative literacy and problem solving with applications to finance, population dynamics, politics, and business. Partially fulfills core Mathematics requirement.

**1320. [MATH 1314] College Algebra (3). **Prerequisites: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302. Inequalities, determinants, theory of equations, binomial theorem, progressions, mathematical induction. Partially fulfills core Mathematics requirement. Cannot receive credit for both MATH 1320 and 1420.

**1321. [MATH 1316] Trigonometry (3).**Prerequisite: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302.Trigonometric functions, radians, logarithms, solutions of triangles, identities, trigonometric equations, complex numbers, De Moivre’s Theorem. Partially fulfills core Mathematics requirement.

**1330. [MATH 1324] Introductory Mathematical Analysis I (3).** Prerequisites: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302. Pre-calculus topics of interest to students of business and the social sciences. These include mathematics of finance, probability and statistics, and Markov processes. Cannot receive credit for both MATH 1330 and 1430. Partially fulfills core Mathematics requirement.

**1331. [MATH 1325, 1425] Introductory Mathematical Analysis II (3).** Prerequisite: a grade of C or better in MATH 1330 or MATH 1430 or a test score of at least 610 on SATM or 26 on ACTM or Code 4 or higher on MPE. Contains an introduction to regression analysis and topics from differential and integral calculus that are of interest to students of business and the social sciences. Partially fulfills core Mathematics requirement.

**1350. [MATH 1348, 2312, 2412] Analytical Geometry (3). **Prerequisite: MATH 1321 or Code 6 or higher on MPE or a score of at least 660 on the SATM or a score of at least 29 on the ACTM. Fundamental concepts of analytical geometry. Partially fulfills core Mathematics requirement.

**1420. [MATH 1414] College Algebra With Review (4). **Prerequisites: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302. Review of topics from high school algebra, inequalities, functions and graphs, linear systems, sequences, mathematics induction. Partially fulfills core Mathematics requirement. Cannot receive credit for both MATH 1320 and 1420.

**1430. Introductory Mathematical Analysis With Review (4). **Prerequisites: Code 2 or higher on MPE or a score of at least 610 on the SATM or a score of at least 26 on the ACTM or a grade of A or B in MATH 0301 or a grade of A or B in TSI 0202 or a grade of D or better in a college level mathematics course. Review of topics from high school algebra, pre-calculus topics of interest to students of business and the social sciences. These include mathematics of finance, probability and statistics, and Markov processes. Partially fulfills core Mathematics requirement. Cannot receive credit for both MATH 1330 and 1430.

**1451. [MATH 2413, 2417, 2513] Calculus I With Applications (4)**. Prerequisite: MATH 1350 or 1550 with a grade of C or better, or MATH 1321 with a grade of C and Code 5 on MPE, or MATH 1321 with a grade of B or better, or Code 7 on MPE, or a score of at least 660 on the SATM, or a score of at least 29 on the ACTM, or a score of at least 3 on AP AB Calculus and Code 5 on MPE. Differentiation of algebraic and transcendental functions, differentials, indefinite integrals, definite integrals. Applications and problem-solving are strongly emphasized. Partially fulfills core Mathematics requirement. (Honors section offered.)

**1452. [MATH 2414, 2419] Calculus II With Applications (4).** Prerequisite: MATH 1451 or departmental consent. Methods of integration, parametric equations, polar coordinates, hyperbolic functions, infinite series. Applications and problem-solving are strongly emphasized. Partially fulfills core Mathematics requirement. (Honors section offered).

**1550. Precalculus (5). **Prerequisite: Code 3 or higher on MPE or a score of at least 610 on the SATM or a score of at least 26 on the ACTM or a grade of A in MATH 0302 or a grade of A in TSI 0302 or a grade of C or better in a college level mathematics course. Topics from college algebra, trigonometry, and analytical geometry that are necessary prerequisites for Calculus I. Partially fulfills core Mathematics requirement.Back to Top

#### 2000 Level Courses

**2300. [MATH 1342, 1442, 2342, 2442] Statistical Methods (3). **Prerequisite: A score of at least 500 on the SATM and composite score of 1070 or a score of at least 19 on the ACTM and composite score of 23 or a grade of C or better in MATH 0302 or a grade of C or better in TSI 0302. Methods of analyzing data, statistical concepts and models, estimation, tests of significance, introduction to analysis of variance, linear regression, and correlation. Partially fulfills core Mathematics requirement.

**2345. Introduction to Statistics with Application to Business (3). **Prerequisite: Code 4 or higher on MPE or a score of at least 610 on the SATM or a score of at least 26 on the ACTM or MATH 1330 or 1430 with a grade of C or better.. Statistics and probability for business. Data collection, description, interpretation, prediction, inference, and computer software. Partially fulfills core Mathematics requirement.

**2356. Quantitative Theory of Interest (3).** Prerequisite: MATH 1331 or 1451. Mathematical theory of compound interest, annuities, yield rates, amortization, funds, bonds, and depreciation.

**2360. [MATH 2318, 2418] Linear Algebra (3).** Prerequisite: MATH 2450 or concurrent with 2450 or consent of department. Finite-dimensional vector spaces, linear transformations and matrices, eigenvalues and eigenvectors.

**2370. [MATH 1350] Elementary Analysis I (3). **Prerequisite: MATH 1320 and major of EC or MDS or consent of department. Analytic geometry and the real number system with applications. Not for engineering, science, or mathematics majors. Partially fulfills core Mathematics requirement.

**2371. Elementary Analysis II (3). **Prerequisite: ** ** MATH 1320 and major of EC or MDS or consent of department.. Elementary differential and integral calculus with application. Not for engineering, science, or mathematics majors. Partially fulfills core Mathematics requirement.

**2450. [MATH 2415] Calculus III With Applications (4)**. Prerequisite: MATH 1452 or departmental consent. Partial differentiation, functions of several variables, multiple integrals, line integrals, surface integrals, Stokes Theorem. Applications and problem-solving are strongly emphasized. (Honors section offered).Back to Top

#### 3000 Level Courses

**3310. Introduction to Mathematical Reasoning and Proof (3). **Prerequisite: MATH 2450 or concurrent with 2450 or consent of department. Logic, techniques of proof, induction, writing proofs involving sets, relations, functions, graphs, number theory, and construction of real numbers. (Writing Intensive)

**3322. Higher Mathematics for Engineering Technology (3). **Prerequisite: MATH 1452 or consent of department. Topics include differential equations, Laplace transform, Fourier series, and vector and matrix algebra.

**3342. Mathematical Statistics for Engineers and Scientists (3). **Prerequisite: MATH 2450 or consent of department. Descriptive statistics, elementary probability, random variables and distributions, mean, variance, parameter estimation, hypothesis testing, regression, analysis of variance. MATH 3342 and 4342 cannot both be counted toward a mathematics major or minor.

**3350. Higher Mathematics for Engineers and Scientists I (3). **Prerequisite: C or better in MATH 1452 (cannot be taken concurrenlty) or consent of department. Ordinary differential equations. Laplace transforms. Other selected topics. MATH 3350 and 3354 may not both be counted toward a mathematics major or minor. Mathematics majors should take MATH 3354 and have the consent of the department to take MATH 3350.

**3351. Higher Mathematics for Engineers and Scientists II (3). **Prerequisites: C or better in MATH 2450 and in MATH 3350 or 3354 or consent of department. Partial differential equations and numerical methods. MATH 3351 and 4354 cannot both be counted toward a mathematics major or minor.

**3354. Differential Equations I (3).** Prerequisite: MATH 2450 and 2360 or consent of department. Solutions of ordinary differential equations, geometric and physical applications. MATH 3350 and 3354 may not both be counted toward a mathematics major or minor.

**3360. Foundations of Algebra I (3). **Prerequisite: MATH 2360 and 3310 or consent of department. Fundamental concepts of abstract algebra. Primarily group theory. (Writing Intensive)

**3370. Elementary Geometry (3). **Prerequisite: MATH 2370 or consent of department. Congruence and measures of plane and solid figures, similarity, areas, volumes, and a brief introduction to concepts in probability and statistics.

**3371. Elements of Finite Mathematics (3).** Prerequisite: MATH 1550 or 2370 or consent of department. Combinatorics, probability theory. Bayes’ Theorem, Bernoulli Trials. Probability distributions and statistics. Not for engineering, science, or mathematics majors.

**3372. Math Modeling for Teachers (3).** Prerequisite: MATH 2371. Not for engineering, math or science majors. Calculus and non-calculus based models in science and engineering. Appropriate technology for simulation. Computer algebra systems.

**3430. Computational Techniques for Science and Mathematics (4).** Prerequisite: MATH 2450 and 2360 or consent of department. Emphasis on scientific computing and problem solving techniques using state-of-the-art mathematics software packages. Restricted to mathematics majors or students enrolled in a secondary mathematics teacher program. Fulfills core Technology and Applied Science requirement.Back to Top

#### 4000 Level Courses

**4000. Selected Topics (V1-3). **Prerequisite: Consent of undergraduate program director. Selected topics in upper division mathematics. May be repeated for credit.

**4202. Preparation for Mathematics Competitions (Putnam Competition) (2)**. Prerequisite: Consent of instructor. Prepares students for the Putnam Competition. Only 2 hours of this course can be applied toward the major.

**4310. Introduction to Numerical Analysis I (3). **Prerequisite: MATH 3350 or 3354, or consent of instructor. Interpolation, approximations, numerical integration, and differentiation.

**4312. Introduction to Numerical Analysis II (3). **Prerequisite: MATH 2360 or consent of instructor. Numerical techniques in linear algebra.

**4324. Introduction to Topology (3)**. Prerequisite: MATH 3310. Euclidean spaces; metric, open, and closed sets; neighborhood; topology; Euler characteristic; triangulation; orientability classification of surfaces.

**4330. Mathematical Computing (3). **Prerequisite: Consent of undergraduate program director. Topics from computational mathematics and programming.

**4331. Advanced Geometry (3). **Prerequisite: MATH 2450 and 3310 or consent of department. Euclidean and non-Euclidean geometries.

**4342. Mathematical Statistics (3).** Prerequisite: MATH 2450 or consent of department. Frequency functions, moments, probability, correlation and regression, testing hypotheses, small sample distributions, analysis of variance, nonparametric methods, sequential analysis. MATH 3342 and 4342 cannot both be counted toward a mathematics major or minor.

**4343. Mathematical Statistics (3).** Prerequisite: MATH 4342 or consent of department. Frequency functions, moments, probability, correlation and regression, testing hypotheses, small sample distributions, analysis of variance, nonparametric methods, sequential analysis.

**4350. Advanced Calculus (3)**. Prerequisite: MATH 2450, 2360, and 3310 or consent of department. Sets, functions, vector fields, partial derivatives, power series, theory of integration, line, surface, and multiple integrals. (Writing Intensive)

**4351. Advanced Calculus (3)**. Prerequisite: MATH 4350 or consent of department. Sets, functions, vector fields, partial derivatives, power series, theory of integration, line, surface, and multiple integrals.

**4354. Differential Equations II (3) .**Prerequisite: MATH 3350 or 3354, or consent of department Partial differential equations and boundary value problems. MATH 4354 and 3351 may not both be counted toward a mathematics major or minor.

**4356. Elementary Functions of Complex Variables (3). **Prerequisite: MATH 4350 (concurrent) or consent of department. The complex number system, functions of a complex variable, differentiation, elementary functions, and contour integration.

**4360. Foundations of Algebra II (3). **Prerequisite: MATH 3360 or consent of department. Continuation of MATH 3360. Rings, fields, and applications.

**4362. Theory of Numbers (3). **Prerequisite: MATH 3310 or consent of department. Prime numbers, congruences, theorems of Fermat, Euler, and Wilson, residues, reciprocity law, Diophantine Equations.

**4363. Introduction to Combinatorics (3).** Prerequisite: MATH 3310. Basic counting techniques, pigeonhole principle, partitions, permutations, recurrence relations, coloring problems.

**4370. Elementary Problem Solving (3). **Prerequisite: MATH 3370 or consent of department. Techniques of problem solving using elementary number theory.

**4371. Basic Computer Literacy and Programming (3).** Prerequisite: MATH 3372 and 4370 or consent of department. Computer literacy, structured programming, and problem solving using modern mathematical computing technology. (For students seeking elementary school certification as mathematics specialists).Back to Top

#### 5000 Level Courses

**5099. Individual Study (V1-6)**. Prerequisite: Consent of instructor. A structural independent study course in mathematics or statistics under the guidance of a faculty member. May be repeated for credit.

**5101. Seminar in Mathematics (1). **Discussion of current research and topics of interest in mathematics. Must be taken pass/fail. May be repeated for credit.

**5104. Seminar in Statistics (1). **Discussion of current research and topics of interest in statistics. Must be taken pass-fail. May be repeated for credit.

**5310. Principles of Classical Applied Analysis I (3)**. Fourier series and integrals, discrete Fourier series, Laplace transforms, calculus of variations, Sturm-Louiville problems, integral equations, equations of fluids and solids, and ordinary and partial differential equations.

**5311. Principles of Classical Applied Analysis II (3)**. Fourier series and integrals, discrete Fourier series, Laplace transforms, calculus of variations, Sturm-Louiville problems, integral equations, equations of fluids and solids, and ordinary and partial differential equations.

**5312. Control Theory I (3). **Prerequisite: MATH 2360, 3354, 4351, or consent of instructor. Linear dynamical systems, stability, frequency response and Laplace transform, feedback, state-space description, and geometric theory of linear systems. (M E 5312)

**5313. Control Theory II (3). **Prerequisite: MATH 5312, 5316, 5318, or consent of instructor. Quadratic regulator for linear systems, Kalman filtering, non-linear systems, stability, local controllability, and geometric theory of non-linear systems. (M E 5313)

**5315. Introduction to Set Theory (3).** Zemelo-Fraenkel axioms set theory, axiom of choice and its equivalents, cardinal and ordinal numbers, cardinal and ordinal arithmetic.

**5316. Applied Linear Algebra (3). **Prerequisite: Consent of instructor. Solution of linear systems, matrix inversion, vector spaces, projections, determinants, eigenvalues and eigenvectors, Jordan form, computational methods, and applications.

**5317. Introduction to Modern Algebra (3).** Prerequisites: MATH 2360 and 3310, or similar courses on linear algebra and introduction to proof. Graduate-level introduction to the theory of groups and ring.

**5318 Intermediate Analysis I (3).** The real number system, introduction to metric spaces, sequences, continuity, differentiation, Riemann integration, power series, functions of several variables, and differential forms.

**5319. Intermediate Analysis II (3)**. The real number system, introduction to metric spaces, sequences, continuity, differentiation, Riemann integration, power series, functions of several variables, and differential forms.

**5320. Functions of a Complex Variable I (3)**. Prerequisite: MATH 4350 or 4356. Analytic functions as mappings, Cauchy theorems, Laurent series, maximum modulus theorems and ramifications, normal families, Riemann mapping theorem, Weierstrass factorization theorem, Mittag-Leffler theory, analytic continuation, and harmonic functions.

**5321. Functions of a Complex Variable II (3)**. Prerequisite: MATH 4350 or 4356. Analytic functions as mappings, Cauchy theorems, Laurent series, maximum modulus theorems and ramifications, normal families, Riemann mapping theorem, Weierstrass factorization theorem, Mittag-Leffler theory, analytic continuation, and harmonic functions.

**5322. Functions of a Real Variable I (3)**. Prerequisite: MATH 5319 or equivalent. General measure and integration theory, Lp theory, differentiation theory, and basic functional analysis.

**5323. Functions of a Real Variable II (3)**. Prerequisite: MATH 5319 or equivalent. General measure and integration theory, Lp theory, differentiation theory, and basic functional analysis.

**5324. Topology I (3)**. Prerequisite: MATH 4350 or consent of instructor. Point set theory, introduction to combinatorial topology and homology theory.

**5325. Topology II (3)**. Prerequisite: MATH 4350 or consent of instructor. Point set theory, introduction to combinatorial topology and homology theory.

**5326. Modern Algebra I (3)**. Prerequisite: MATH 3360 or consent of instructor. Groups, rings, fields, linear algebra, Galois theory.

**5327. Modern Algebra II (3)**. Prerequisite: MATH 3360 or consent of instructor. Groups, rings, fields, linear algebra, Galois theory.

**5330. Theory of Ordinary Differential Equations I, II (3).** Prerequisite: MATH 4351, 4354, or consent of instructor. Existence and uniqueness results, continuation of solutions, continuous dependence on data, linear equations, oscillation and comparison theorems, boundary value problems, and stability analysis.

**5331. Theory of Ordinary Differential Equations II (3). **Prerequisite: MATH 5330 or consent of instructor. Advanced existence, uniqueness, continuation, and continuity results; symmetry and variance; center manifold theorem.

**5332. Partial Differential Equations I (3**). Prerequisite: MATH 4351, 4354, or consent of instructor. Topics include first order equations, method of characteristics, parabolic, hyperbolic and elliptic equations, variational and Hilbert space methods.

**5333. Partial Differential Equations II (3)**. Prerequisite: MATH 4351, 4354, or consent of instructor. Topics include first order equations, method of characteristics, parabolic, hyperbolic and elliptic equations, variational and Hilbert space methods.

**5334. Numerical Analysis I (3)**. Prerequisite: MATH 5316 or equivalent. Stability and error analysis, numerical solution of ordinary and partial differential equations, integral equations.

**5335. Numerical Analysis II (3)**. Prerequisite: MATH 5316 or equivalent. Stability and error analysis, numerical solution of ordinary and partial differential equations, integral equations.

**5340. Functional Analysis I (3)**. Prerequisite: MATH 5322. Hilbert and Banach space theory, linear operator theory, the closed graph theorem, the open mapping theorem, the principle of uniform boundedness, linear functionals, dual spaces and weak topologies, distribution theory, topological vector spaces, spectral theory of compact and unbounded self-adjoint and unitary operators, and semigroup theory.

**5341. Functional Analysis II (3)**. Prerequisite: MATH 5322. Hilbert and Banach space theory, linear operator theory, the closed graph theorem, the open mapping theorem, the principle of uniform boundedness, linear functionals, dual spaces and weak topologies, distribution theory, topological vector spaces, spectral theory of compact and unbounded self-adjoint and unitary operators, and semigroup theory.

**5342. Advanced Topics in Analysis I (3)**. Prerequisite: Consent of instructor. Current topics in analysis. May be repeated for credit.

**5343. Advanced Topics in Analysis II (3)**. Prerequisite: Consent of instructor. Current topics in analysis. May be repeated for credit.

**5344. Topics in Numerical Analysis I (3)**. Prerequisite: MATH 5335. Current advanced topics in numerical analysis, research work using computers. May be repeated for credit.

**5345. Topics in Numerical Analysis II (3).** Prerequisite: MATH 5335. Current advanced topics in numerical analysis, research work using computers. May be repeated for credit.

**5346. Advanced Topics in Applied Mathematics I (3). **Prerequisite: Consent of instructor. Current topics in applied mathematics. May be repeated for credit.

**5354. Biomathematics I (3).** Prerequisite: Differential equations and linear algebra or consent of instructor. Qualitative and quantitative behavior of deterministic biological models are studied.

**5355. Biomathematics II (3). **Prerequisite: Statistics, differential equations, and linear algebra or consent of instructor. Qualitative and quantitative behavior of stochastic biological models are studied.

**5356. Topics in Biomathematics (3).** Prerequisite: Biomathematics II or consent of instructor. Current topics in biomathematics are studied such as biomechanics, mathematical epidemiology, mathematical neurology, mathematical opthalmology, and image processing. May be repeated for credit.

**5360. Advanced Mathematics for Teachers I (3)**. Prerequisite: Consent of instructor. Selected topics in mathematics. May be repeated for credit.

**5361. Advanced Mathematics for Teachers II (3)**. Prerequisite: Consent of instructor. Selected topics in mathematics. May be repeated for credit.

**5362. Theory of Numbers (3). **Prerequisite: MATH 4362. Diophantine equations, binary quadratic forms, algebraic numbers, theory of number-theoretic functions, partitions, the prime number theorem.

**5364. Computer Literacy and Programming I (3)**. Development of computer literacy and programming ability, algorithms and data structures, and recursion.

**5365. Computer Literacy and Programming II (3)**. Development of computer literacy and programming ability, algorithms and data structures, and recursion.

**5366. Introduction to Analysis I (3)**. Introduction to logic, proofs, sets functions, real numbers, and sequences. Not for M.S./Ph.D. in Math/Stat. Online.

**5367. Introduction to Analysis II (3)**. Prerequisite: MATH 5366. A formal introduction to differentiation and Riemann Integration. Not for M.S./Ph.D. in Math/Stat. Online.

**5368. Abstract Algebra Applied I (3).** An example-intensive introduction to fields and vector spaces. Not for M.S./Ph.D. in Math/Stat. Online.

**5369. Abstract Algebra Applied II (3)**. Prerequisite: MATH 5368. An example-intensive introduction to Galois Theory and unsolvability of the general quintic. Not for M.S./Ph.D. in Math/Stat. Online.

**5370. History of Mathematics (3)**. A history of mathematics with an emphasis on the development of commercial arithmetic, geometry, algebra, and calculus. Not for M.S./Ph.D. in Math/Stat. Online.

**5371. Topology of the Real Line I (3)**. An introduction to topology via linearly ordered sets. Emphasis is on creating and criticizing proofs and counter examples. Not for M.S./Ph.D. in Math/Stat. Online.

**5372. Topology of the Real Line II (3)**. Prerequisite: MATH 5371. Covers concepts of connectedness, separability, and characterization of the real line. Not for M.S./Ph.D. in Math/Stat. Online.

**5375. Modern Geometry I (3)**. A modern introduction to Euclidean geometry using metric and synthetic approaches. Uses dynamic geometry software. Not for M.S./Ph.D. in Math/Stat. Online.

**5376. Modern Geometry II (3)**. Prerequisite: MATH 5375. Advanced topics in Euclidean geometry and an introduction to hyperbolic geometry. Uses dynamic geometry software. Not for M.S./Ph.D. in Math/Stat. Online.

**5377. Applied Mathematics I (3)**. An introduction to mathematical applications. Explores handling of data, voting, golden ratio, modular arithmetic, and encryption. Not for M.S./Ph.D. in Math/Stat. Online.

**5378. Applied Mathematics II (3).** Explores mathematical ideas and applications, including infinity, surfaces, modeling of populations, and fractals and chaos. Not for M.S./Ph.D. in Math/Stat. Online

**5382. Advanced Probability I (3)**. Prerequisite: MATH 5319 or consent of instructor. Measure and integration, axiomatic foundations of probability theory, random variables, distributions and their characteristic functions, stable and infinitely divisible laws, limit theorems for sums of independent random variables, conditioning, Martingales.

**5383. Advanced Probability II (3)**. Prerequisite: MATH 5319 or consent of instructor. Measure and integration, axiomatic foundations of probability theory, random variables, distributions and their characteristic functions, stable and infinitely divisible laws, limit theorems for sums of independent random variables, conditioning, Martingales.

**5399. Advanced Problems (3). **Prerequisite: Graduate standing in mathematics. May be repeated for credit.Back to Top

#### 6000 Level Courses

**6000. Master's Thesis (V1-6).**

**6310. Master's Report (3).**

**6320. Representation Theory (3)**. Prerequisites: MATH 5326 and 5327. An introduction to basic methods and results of representation theory focusing on linear representations of finite groups.

**6321. Homological Algebra I: Introduction (3)**. Prerequisite: MATH 5326. Categories, functions, simplicial and singular homology, category of modules over a ring, resolutions, and derived categories.

**6322. Homological Algebra II: Applications (3)**. Prerequisite: MATH 6321. Homological dimensions, Koszul homology, local cohomology, duality theories, global dimension and regular rings, Cohen-Macaulay rings.

**6323. Algebraic Geometry I (3)**. Prerequisite: MATH 5326 or consent of instructor. Covers the basic theory of affine and projective varieties.

**6324. Algebraic Geometry II (3)**. Prerequisite: MATH 6323 or equivalent. Covers the theory of schemes and the scheme-theoretic concept of a variety.

**6325. Category Theory (3**). Prerequisites: MATH 5326 and 5327 or consent of instructor. Covers the basic theory of categories and functors.

**6330. Manifold Theory (3).** Prerequisites: MATH 5316 and 5318 or permission of instructor. Differentiable manifolds theory: smooth structures, tangent spaces, implicit mapping theorem, embeddings, immersions and submersions, vector fields, tensor analysis, Stokes theorem.

**6331. Riemannian Geometry (3)**. Prerequisite: MATH 5330 or consent of instructor. Affine connections, Riemannian connections, geodesics and geodesic flow, curvatures (Ricci, sectional), spaces of constant curvature. Applications to computer modeling and visualization.

**6332. Geometric Mechanics (3).** Prerequisite: MATH 5330 or consent of instructor. Geometric concepts in classical mechanics; Euler-Language equations, Legendre transform and Hamilton’s equations; symplectic manifolds; group actions; momentum maps; Hamiltonian and Langrangian reduction.

**6333. Introduction to Lie Groups and Their Representation (3).** Prerequisite: MATH 5330 or consent of instructor. Lie groups, Lie algebras, exponential map, Lie brackets, representation theory with examples, Peter-Weyl theorem, homogenous and symmetric spaces, applications to ODEs/PDEs arising in physics.Back to Top

#### 7000 Level Course

**7000. Research (V1-12).** Back to Top

#### 8000 Level Course

**8000. Doctor's Dissertation (V1-12).**