Mathematics (MAT)

MAT 106 Intermediate Algebra. (3) F, S, SS
Topics from basic algebra such as linear equations, polynomials, factoring, exponents, roots, and radicals. Prerequisite: 1 year of high school algebra.

MAT 114 College Mathematics. (3) F, S, SS
Applications of basic college-level mathematics to real-life problems. Appropriate for students whose major does not require MAT 117 or 170. Prerequisite: MAT 106 or 2 years of high school algebra. General Studies: N1.

MAT 117 College Algebra. (3) F, S, SS
Linear and quadratic functions, systems of linear equations, logarithmic and exponential functions, sequences, series, and combinatorics. Prerequisite: MAT 106 or 2 years of high school algebra. General Studies: N1.

MAT 119 Finite Mathematics. (3) F, S, SS
Topics from linear algebra, linear programming, combinatorics, probability, and mathematics of finance. Prerequisite: MAT 117 or equivalent. General Studies: N1.

MAT 170 Precalculus. (3) F, S, SS
Intensive preparation for calculus (MAT 260, 270 and 290). Topics include functions (including trigonometric), matrices, polar coordinates, vectors, complex numbers, and mathematical induction. Prerequisite: a grade of "B" in MAT 106 or "C" in MAT 117 or two years of high school algebra. General Studies: N1.

MAT 210 Brief Calculus. (3) F, S, SS
Differential and integral calculus of elementary functions with applications. Not open to students with credit in MAT 260, 270, or 290. Prerequisite: MAT 117 or equivalent. General Studies: N1.

MAT 242 Elementary Linear Algebra. (2) F, S, SS
Introduction to matrices, systems of linear equations, determinants, vector spaces, linear transformations, and eigenvalues. Emphasizes development of computational skills. Prerequisite: 1 semester of calculus or instructor approval. General Studies: N1.

MAT 243 Discrete Mathematical Structures. (3) F, S, SS
Introduction to lattices, graphs, Boolean algebra, and groups, with emphasis on topics relevant to computer science. Prerequisite: 1 semester of calculus.

MAT 260 Technical Calculus I. (3) F, S, SS
Analytic geometry, differential, and integral calculus of elementary functions, emphasizing physical interpretation and problem solving. Not open to students with credit in MAT 210, 270, or 290. Prerequisite: MAT 170 or equivalent. General Studies: N1.

MAT 261 Technical Calculus II. (3) F, S, SS
Continuation of MAT 260. Prerequisite: MAT 260 or instructor approval.

MAT 262 Technical Calculus III. (3) F, S
Infinite series, an introduction to differential equations and elementary linear algebra. Prerequisite: MAT 261 or equivalent.

MAT 270 Calculus with Analytic Geometry I. (4) F, S, SS
Real numbers, limits and continuity, and differential and integral calculus of functions of 1 variable. Not open to students with credit in MAT 290. The sequence MAT 270 and 271 may be substituted for MAT 290 to satisfy requirements of any curriculum. Prerequisite: Grade of "C" or better in MAT 170 or equivalent. General Studies: N1.

MAT 271 Calculus with Analytic Geometry II. (4) F, S, SS
Methods of integration, applications of calculus, elements of analytic geometry, improper integrals, sequences, and series. Not open to students with credit in MAT 291. The sequence MAT 270 and 271 and 272 may be substituted to satisfy requirements for MAT 290 and 291. Prerequisites: Grade of "C" or better in MAT 270 or equivalent.

MAT 272 Calculus with Analytic Geometry III. (4) F, S, SS
Vector-valued functions of several variables, multiple integration, and introduction to vector analysis. The sequence MAT 270 and 271 and 272 may be substituted to satisfy requirements for MAT 290 and 291. Prerequisites: Grade of "C" or better in MAT 271 or equivalent.

MAT 274 Elementary Differential Equations. (3) F, S, SS
Introduction to ordinary differential equations, adapted to the needs of students in engineering and the sciences. MAT 272 or equivalent is recommended. Prerequisite: MAT 271 or equivalent.

MAT 290 Calculus I. (5) F, S
Differential and integral calculus of elementary functions; topics from analytic geometry essential to the study of calculus. Prerequisite: MAT 170 or equivalent. General Studies: N1.

MAT 291 Calculus II. (5) F, S
Further applications of calculus, partial differentiation, multiple integrals, and infinite series. Prerequisite: MAT 290 or equivalent.

MAT 300 Mathematical Structures. (3) F, S
Introduction to rigor and proof in mathematics. Basic logic, set theory, mathematical induction, combinatorics, functions, relations, and probability. Prerequisite: 1 semester of calculus or instructor approval. General Studies: L2.

MAT 310 Introduction to Geometry. (3) S
Congruence, area, parallelism, similarity and volume, and Euclidean and non-Euclidean geometry. Prerequisite: MAT 272 or equivalent.

MAT 342 Linear Algebra. (3) F, S, SS
Linear equations, matrices, determinants, vector spaces, bases, linear transformations and similarity, inner product spaces, eigenvectors, orthonormal bases, diagonalization, and principal axes. Pre- or corequisite: MAT 272 or equivalent.

MAT 362 Advanced Mathematics for Engineers and Scientists I. (3) F, S, SS
Vector analysis, Fourier analysis, and partial differential equations. Prerequisites: MAT 272 and 274 or equivalents.

MAT 370 Intermediate Calculus. (3) F, S
Theory behind basic 1-variable calculus: continuity, derivative, Riemann integral, sequences, and series. Not open to students with credit in MAT 371. Prerequisites: MAT 272, 300.

MAT 371 Advanced Calculus I. (3) F, S
Real numbers, completeness, sequences/series, continuity, uniform theorems, derivative, Riemann integral, pointwise/uniform convergence, Taylor's theorem. Not open to students with credit in MAT 370. Prerequisite: MAT 272 or 300 or instructor approval.

MAT 372 Advanced Calculus II. (3) F, S
Open, closed, compact sets in Rn continuity, differentiation, partial differentiation, integration in Rn. Inverse/implicit function theorems. Not open to students with credit in MAT 460. Prerequisite: MAT 371. Pre- or corequisite: MAT 342.

MAT 410 Introduction to General Topology. (3) A
Topological spaces, metric spaces, compactness, connectedness, and product spaces. Prerequisite: MAT 300 or 371 or instructor approval.

MAT 415 Combinatorial Mathematics I. (3) F
Permutations and combinations, recurrence relations, generating functions, graph theory, and combinatorial proof techniques. Prerequisites: MAT 300 and 342 or instructor approval.

MAT 416 Combinatorial Mathematics II. (3) S
Continuation of MAT 415 considering some advanced aspects of the theory as well as applications. Topics chosen from transport networks, matching theory, block designs, coding theory, Polya's counting theory, and applications to the physical and life sciences. MAT 443 is recommended. Prerequisite: MAT 415 or instructor approval.

MAT 419 Linear Programming. (3) S
Linear programming and the simplex algorithm, network problems, quadratic, and nonlinear programming. Prerequisites: MAT 242 or 342; 1 semester of college calculus. General Studies: N2.

MAT 431 Foundations of Mathematics. (3) N
Topics from mathematical logic and set theory. May be repeated for credit with instructor approval. Prerequisites: MAT 300 and 342 or instructor approval.

MAT 442 Advanced Linear Algebra. (3) F
Fundamentals of linear algebra, dual spaces, invariant subspaces, canonical forms, bilinear and quadratic forms, and multilinear algebra. Prerequisites: MAT 300 and 342 or instructor approval.

MAT 443 Introduction to Abstract Algebra. (3) F
Introduction to concepts of abstract algebra. Not open to students with credit in MAT 444. Prerequisites: MAT 300 and 342 or instructor approval.

MAT 444 Intermediate Abstract Algebra. (3) S
Basic theory of groups, rings, and fields, including an introduction to Galois theory. Appropriate as preparation for MAT 543. Prerequisites: MAT 300 and 342.

MAT 445 Theory of Numbers. (3) S
Prime numbers, unique factorization theorem, congruences, Diophantine equations, primitive roots, and quadratic reciprocity theorem. Prerequisites: MAT 300 and 342 or instructor approval.

MAT 451 Mathematical Modeling. (3) S
A detailed study of 1 or more mathematical models that occur in the physical or biological sciences. May be repeated for credit with instructor approval. Prrequisites: MAT 242 (or 342) and 274 or instructor approval. General Studies: N2.

MAT 460 Applied Real Analysis. (3) S
Vectors, curvilinear coordinates, Jacobians, implicit function theorem, line and surface integrals, Green's, Stokes', and divergence theorems. Not open to students with credit in MAT 372. Prerequisites: MAT 242 (or 342), 272, 274.

MAT 461 Applied Complex Analysis. (3) F, SS
Analytic functions, complex integration, Taylor and Laurent series, residue theorem, conformal mapping, and harmonic functions. Prerequisite: MAT 272 or equivalent.

MAT 462 Partial Differential Equations. (3) F, S, SS
Second order partial differential equations, emphasizing Laplace, wave, and diffusion equations. Solutions by the methods of characteristics, separation of variables, and integral transforms. Prerequisites: MAT 242 (or 342), 274.

MAT 464 Numerical Analysis I. (3) F, S
Theory and methods for numerical solution of algebraic and transcendental equations; iteration methods; eigenvalues and eigenvectors; interpolation; introductory computer arithmetic. Prerequisites: MAT 342 and 371 and fluency in computer programming or instructor approval. General Studies: N3.

MAT 465 Numerical Analysis II. (3) F, S
Theory and methods for numerical solution of analysis problems; differentiation; quadrature; solution of differential equations. Prerequisite: MAT 342 and 371 and fluency in computer programming or instructor approval. General Studies: N3.

MAT 466 Applied Computational Methods. (3) F, S
Numerical methods for quadrature, differential equations, roots of nonlinear equations, interpolation, approximation, linear equations, floating-point arith metic, and roundoff error. Prerequisites: MAT 271 (or equivalent) and fluency in computer programming (preferably FORTRAN) or instructor approval. General Studies: N3.

MAT 467 Computer Arithmetic. (3) S
Number systems, hardware/software arithmetic, overflow, significance, rounding, multiple precision, and automatic error control; impact on languages, architectures, robust programming, and software development. Prerequisite: CSE 200 or 210 or MAT 464 or 466 or instructor approval. General Studies: N3.

MAT 472 Intermediate Real Analysis. (3) F
Introduction to analysis in metric spaces with emphasis on the real line. Appropriate as preparation for MAT 570. Prerequisites: MAT 300, 342.

MAT 475 Differential Equations. (3) S
Asymptotic behavior of solutions of linear and nonlinear ordinary differential equations, stability, Sturm-Liouville problems, boundary value problems, and singular point behavior of autonomous systems. Prerequisites: MAT 242 (or 342), 274.

MAT 485 History of Mathematics. (3) N
Topics from the history of the origin and development of mathematical ideas. Prerequisite: MAT 272 or equivalent.

MAT 510 Point Set Topology. (3) F
Topological spaces, metric spaces, compactness, connectedness, local properties, product and decomposition spaces, mappings, covering properties, and separation properties. Prerequisite: MAT 371 or 410 or instructor approval.

MAT 511 Point Set Topology. (3) S
Continuation of MAT 510. Prerequisite: MAT 510 or instructor approval.

MAT 520 Numerical Linear Algebra. (3) A
Direct solution of linear systems, iterative methods, eigenvalues and eigenvectors, singular value decomposition, the QR algorithm, error propagation, arithmetic, and stability. Prerequisites: MAT 342 and 464 (or 466) or instructor approval.

MAT 521 Iterative Methods. (3) N
Numerical methods for solving linear/nonlinear systems of equations (symmetric, nonsymmetric). Iterative methods for linear systems, conjugate gradients, multigrid methods, preconditioning, Krylov methods. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 523 Numerical Optimization. (3) N
Linear programming, unconstrained nonlinear minimization, line search algorithms, conjugate gradients, quasi-Newton methods, constrained nonlinear optimization, gradient projection, and penalty methods. Prerequisite: MAT 342 or 371 or 460 or 520 or equivalent or instructor approval.

MAT 524 Parallel Numerical Algorithms. (3) N
Algorithms for massively parallel, hypercube architectures; "parallel" FORTRAN; solution of linear, nonlinear systems; partial differential equations; iterative methods; multigrid; domain decomposition. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 526 Numerical Solution of Bifurcation Problems. (3) N
Nonlinear parameter-dependent differential, algebraic equations, numerical solutions; bifurcation, turning points; continuation methods, branch switching; steady-state, time-dependent cases; Hopf Bifurcation. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 528 Advanced Numerical Analysis. (3) N
Finite difference equations, orthogonal polynomials, quadrature, approximation and integration theory, numerical solution of differential equations, and numerical linear algebra. May be repeated for credit with instructor approval. Prerequisite: MAT 464 or instructor approval.

MAT 529 Advanced Numerical Analysis. (3) N
Continuation of MAT 528. Prerequisite: MAT 528 or instructor approval.

MAT 530 Numerical Solution of Ordinary Differential Equations. (3) N
One step, linear multistep methods; consistency, order, stability, convergence; discretization, round-off errors, error estimation, adaptive strategy; implementation, software for nonstiff equations. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 531 Numerical Solution of Stiff Differential Systems. (3) N
Runge-Kutta methods, order conditions, construction of highly stable methods, order stars, error estimation, stepsize selection, contractivity properties, linear multistep methods. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 533 Computational Elliptic and Parabolic Partial Differential Equations. (3) N
Parabolic and elliptic equations, finite difference, finite element methods, stability, consistency, convergence, practical aspects, applications, software. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 534 Computational Hyperbolic Partial Differential Equations. (3) N
Numerical solutions of hyperbolic PDEs, finite difference methods, well-posedness, stability, consistency, convergence, adaptive grids; Maxwell's equations, elastic wave propagation; Navier-Stokes. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 535 Spectral Methods for Partial Differential Equations. (3) N
Spectral, pseudo-spectral theory; Galerkin, collocation methods; Tau-methods, global approximation properties, stability; convergence; solutions for linear, nonlinear systems. Prerequisites: MAT 371 and 464 (or 466) or instructor approval.

MAT 536 Numerical Solution of Boundary Value Problems. (3) N
Difference methods, finite element methods, defect correction, irregular meshes, nonlinear problems, bifurcation, boundary layers, and sparse systems. May be repeated for credit with instructor approval. Prerequisites: MAT 371 (or 460 or 462) and 464 (or 466) or instructor approval.

MAT 543 Abstract Algebra. (3) F
Groups, modules, rings and fields, Galois theory, homological algebra, and the representation theory. Prerequisite: MAT 443 or instructor approval.

MAT 544 Abstract Algebra. (3) S
Continuation of MAT 543. Prerequisite: MAT 543 or instructor approval.

MAT 550 Variational Methods. (3) F
Calculus of variations and its applications to extremal problems, classical mechanics, and partial differential equations. Prerequisites: MAT 274 and 462 or equivalents.

MAT 551 Linear Operators and Integral Equations. (3) S
Bounded linear and compact operators on Hilbert spaces. Linear integral equations, Fredholm and Hilbert-Schmidt theory, and approximate methods. Distributions. Prerequisites: MAT 242 and 462 or equivalents.

MAT 570 Real Analysis. (3) S
Lebesgue integration, selected function spaces, differentiation, abstract measure theory, and elements of functional analysis. Prerequisite: MAT 372 or instructor approval.

MAT 571 Real Analysis. (3) F
Continuation of MAT 570. Prerequisite: MAT 570 or instructor approval.

MAT 572 Complex Analysis. (3) F
Analytic functions, series and product representations, entire and meromorphic functions, normal families, Riemann mapping theorem, harmonic functions, and Riemann surfaces. Prerequisite: MAT 371 or instructor approval.

MAT 573 Complex Analysis. (3) S
Continuation of MAT 572. Prerequisite: MAT 572 or instructor approval.

MAT 574 Theory of Ordinary Differential Equations. (3) N
Systems, existence proofs, singularities, asymptotic behavior of solutions, boundedness of solutions, eigenvalues and eigenfunctions, and perturbation theory. Prerequisite: MAT 372 or instructor approval.

MAT 575 Theory of Ordinary Differential Equations. (3) N
Continuation of MAT 574. Prerequisite: MAT 574 or instructor approval.

MAT 576 Theory of Partial Differential Equations. (3) N
Existence and uniqueness theorems, boundary value and initial value problems, characteristics, Green's functions, maximum principle, distributions, and weak solutions. Prerequisite: knowledge of Lebesgue integration or instructor approval.

MAT 577 Theory of Partial Differential Equations. (3) N
Continuation of MAT 576. Prerequisite: MAT 576 or instructor approval.

MAT 578 Functional Analysis. (3) N
Locally convex, normed, and Hilbert spaces. Linear operators, spectral theory, and application to classical analysis. Prerequisite: MAT 472 or 571 or instructor approval.

MAT 579 Functional Analysis. (3) N
Continuation of MAT 578. Prerequisite: MAT 578 or instructor approval.

MAT 591 Seminar. (1–3) N
Topics may be selected from the following:
 (a) Algebra (b) Analysis (c) Applied Mathematics (d) Combinatorial Mathematics (e) Mathematical Logic (f) Numerical Analysis (g) Topology

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