MATH 097 : Intermediate Algebra.
(0:2:1)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | High school algebra. |
| DESCRIPTION: | Elementary logic, real number system, equations and inequalities (linear, polynomial, rational, and radical expressions), graphing, function notation, inverse function, exponential functions, systems of equations, variations. |
| NOTE: | Fee. |
100-Level Courses
MATH 102 : Quantitative Reasoning.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| DESCRIPTION: | Practicing and applying quantitative reasoning: personal finance, consumer statistics, etc. |
| NOTE: | For students who do not need developmental algebra for subsequent courses. |
MATH 110 : College Algebra.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 97 or equivalent. |
| DESCRIPTION: | Functions, polynomials, theory of equations, exponential and logarithmic functions, matrices, determinants, systems of linear equations, permutations, combinations, binomial theorem. |
MATH 111 : Trigonometry.
(2:2:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 110 or equivalent. |
| DESCRIPTION: | Circular functions, triangle relationships, identities, inverse trig functions, trigonometric equations, vectors, complex numbers, DeMoivre's theorem. |
MATH 112 : Calculus 1.
(4:5:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 110 and 111 or equivalent. |
| DESCRIPTION: | Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule. |
| NOTE: | Honors also. |
| : Honors Calculus 1. | |
MATH 113 : Calculus 2.
(4:5:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 112 or equivalent. |
| DESCRIPTION: | Techniques and applications of integration; sequences, series, convergence tests, power series; parametric equations; polar coordinates. |
| NOTE: | Honors also. |
| : Honors Calculus 2. | |
MATH 119 : Introduction to Calculus.
(4:4:1)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 110 or equivalent. |
| DESCRIPTION: | Introduction to plane analytic geometry and calculus. |
| NOTE: | For students in the College of Life Sciences and the Marriott School of Management. |
MATH 190 : Fundamentals of Mathematics.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| PREREQUISITE: | Math 112 or concurrent enrollment with instructor's consent. |
| DESCRIPTION: | Achieving maturity in mathematical communication. Introduction to mathematical proof; methods of proof; analysis of proof; induction; logical reasoning. |
200-Level Courses
MATH 214 : Calculus of Several Variables.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 113; 343 or concurrent enrollment. |
| DESCRIPTION: | Partial differentiation, the Jacobian matrix, and integral theorems of vector calculus. |
300-Level Courses
MATH 300 : (Math-MthEd) History and Philosophy of Mathematics.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp |
| PREREQUISITE: | Math 113. |
| DESCRIPTION: | Historical development of important mathematical ideas and philosophies; implications for the mathematical curriculum. |
MATH 302 : Mathematics for Engineering 1.
(4:4:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| PREREQUISITE: | Math 113 and passing grade on required preparatory exam taken during first week of class. (Practice exams available on class Website). |
| DESCRIPTION: | Multivariable calculus, linear algebra, and numerical methods. |
MATH 315 : Theory of Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| PREREQUISITE: | Math 113, 190, 343. |
| DESCRIPTION: | Rigorous treatment of calculus of single and several variables. Topics include uniform continuity, metric spaces, Riemann integral, implicit function theorem, and integral theorems of vector calculus. |
MATH 316 : Theory of Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| PREREQUISITE: | Math 315. |
| DESCRIPTION: | Rigorous treatment of calculus of single and several variables. Topics include uniform continuity, metric spaces, Riemann integral, implicit function theorem, and integral theorems of vector calculus. |
MATH 331 : (Math - EC En 370) Probability Theory.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 343. |
| DESCRIPTION: | Axiomatic probability theory, conditional probability, discrete / continuous random variables, expectation, conditional expectation, moments, functions of random variables, multivariate distributions, laws of large numbers, central limit theorem. |
MATH 332 : Introduction to Complex Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| PREREQUISITE: | Math 214 or 316. |
| DESCRIPTION: | Complex algebra, analytic functions, integration in the complex plane, infinite series, theory of residues, conformal mapping. |
MATH 343 : Elementary Linear Algebra.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp, Su |
| PREREQUISITE: | Math 112 or 119. |
| DESCRIPTION: | Linear systems, matrices, vectors and vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and eigenvectors. |
| : Honors Elementary Linear Algebra. | |
MATH 347 : Introduction to Partial Differential Equations.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W, Su |
| PREREQUISITE: | Math 303 or 334. |
| DESCRIPTION: | Boundary value problems; transform methods; Fourier series; Bessel functions; Legendre polynomials. |
MATH 362 : (Math-MthEd) Survey of Geometry.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Su |
| PREREQUISITE: | Math 112, 190. |
| DESCRIPTION: | Logical and historical development of Euclidean and non-Euclidean geometry, transformations and symmetry; relationships among axiomatic systems; use of software and other geometric models; proofs and Van Hiele levels. |
MATH 371 : Abstract Algebra.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W, Sp |
| PREREQUISITE: | Math 190, 343. |
| DESCRIPTION: | Groups, rings, fields, vector spaces, linear transformations, matrices, field extensions, etc. |
MATH 387 : Number Theory.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, Sp |
| PREREQUISITE: | Math 343, 371. |
| DESCRIPTION: | Foundations; congruences; quadratic reciprocity; unique factorization, prime distribution or Diophantine equations. |
MATH 391R : Seminar in Mathematics.
(1:1:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F, W |
| DESCRIPTION: | Topics from classical problems of antiquity, combinatorial mathematics, graph theory, real functions, number theory, functional equations. |
400-Level Courses
MATH 410 : Introduction to Numerical Methods.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 214, 343. |
| DESCRIPTION: | Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. |
MATH 411 : Numerical Methods.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 334, 410. |
| DESCRIPTION: | Iterative solvers for linear systems, eigenvalue, eigenvector approximations, numerical solutions to nonlinear systems, numerical techniques for initial and boundary value problems, elementary solvers for PDEs. |
MATH 435 : Mathematical Finance.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 331. |
| DESCRIPTION: | The binomial asset pricing model (discrete probability). Martingales, pricing of derivative securities, random walk in financial models, random interest rates. |
MATH 451 : Introduction to Topology.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 315. |
| DESCRIPTION: | Developing topological concepts, beginning from a linear setting. Developing proofs or counterexamples from axioms to a structured sequence of topological propositions using only notes provided. |
MATH 460R : Topics in Geometry.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | On demand |
| PREREQUISITE: | Math 343, 362, or equivalent. |
| DESCRIPTION: | Topics selected from the various aspects of synthetic, analytic, algebraic, and differential geometry. |
MATH 465 : Differential Geometry.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| PREREQUISITE: | Math 214; 315 or equivalent. |
| RECOMMENDED: | Math 316 or equivalent. |
| DESCRIPTION: | Geometry of smooth curves and surfaces. Topics include the first and second fundamental forms, the Gauss map, orientability of surfaces, Gaussian and mean curvature, geodesics, minimal surfaces and the Gauss-Bonnet Theorem. |
MATH 480 : Mathematical Models.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | On demand |
| PREREQUISITE: | Math 214, 334, 343, 410. |
| DESCRIPTION: | Construction, solution, and interpretation of discrete and continuous models applied to problems in the physical, natural, and social sciences. |
500-Level Graduate Courses (available to advanced undergraduates)
MATH 510 : Numerical Methods for Linear Algebra.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 343, 410; or equivalents. |
| DESCRIPTION: | Numerical matrix algebra, orthogonalization and least squares methods, unsymmetric and symmetric eigenvalue problems, iterative methods, advanced solvers for partial differential equations. |
MATH 511 : Numerical Methods for Partial Differential Equations.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 303 or 347; 410; or equivalents. |
| DESCRIPTION: | Finite difference and finite volume methods for partial differential equations. Stability, consistency, and convergence theory. |
MATH 521 : Methods of Applied Mathematics 1.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | Sp |
| PREREQUISITE: | Math 334, 343; or equivalents. |
| DESCRIPTION: | Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics. |
MATH 522 : Methods of Applied Mathematics 2.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | On demand. |
| PREREQUISITE: | Math 334, 343; or equivalents. |
| DESCRIPTION: | Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics. |
MATH 532 : Complex Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | Su |
| PREREQUISITE: | Math 332 or instructor`s consent. |
| DESCRIPTION: | Introduction to theory of complex analysis at beginning graduate level. Topics: Cauchy integral equations, Riemann surfaces, Picard's theorem, etc. |
MATH 534 : Introduction to Dynamical Systems 1.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 315, 334; or equivalents. |
| DESCRIPTION: | Discrete dynamical systems; iterations of maps on the line and the plane; bifurcation theory; chaos, Julia sets, and fractals. Computational experimentation. |
MATH 541 : Real Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 315, 343; 214 or 316. |
| DESCRIPTION: | Rigorous treatment of differentiation and integration theory; Lebesque measure; Banach spaces. |
MATH 542 : Real Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 315, 343; 214 or 316. |
| DESCRIPTION: | Rigorous treatment of differentiation and integration theory; Lebesque measure; Banach spaces. |
MATH 543 : Advanced Probability 1.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 214 or equivalent. |
| RECOMMENDED: | Math 314, 315, Stat 441; or equivalents. |
| DESCRIPTION: | Probability theory and its applications. Topics include random variables, independence and conditioning, laws of large numbers, random walks, martingales, Markov chains, renewal processes, ergodic theorems, Brownian motion, and stochastic integration. |
MATH 544 : Advanced Probability 2.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 214 or equivalent. |
| RECOMMENDED: | Math 315, 316, Stat 441; or equivalents. |
| DESCRIPTION: | Probability theory and its applications. Topics include random variables, independence and conditioning, laws of large numbers, random walks, martingales, Markov chains, renewal processes, ergodic theorems, Brownian motion, and stochastic integration. |
MATH 547 : Partial Differential Equations 1.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | On demand |
| PREREQUISITE: | Math 214, 334; or equivalents. |
| RECOMMENDED: | Math 314, 315; or equivalents. |
| DESCRIPTION: | Topics include the method of characteristics, elliptic equations, potential theory, parabolic equations and systems, maximum principles, linear and nonlinear waves, Hamilton-Jacobi equations, Fourier transforms, Green's functions, distributions, and energy methods. |
MATH 548 : Partial Differential Equations 2.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | On demand |
| PREREQUISITE: | Math 214, 334; or equivalents. |
| RECOMMENDED: | Math 315, 316; or equivalents. |
| DESCRIPTION: | Topics include the method of characteristics, elliptic equations, potential theory, parabolic equations and systems, maximum principles, linear and nonlinear waves, Hamilton-Jacobi equations, Fourier transforms, Green's functions, distributions, and energy methods. |
MATH 553 : Foundations of Topology 1.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 451 or instructor's consent. |
| DESCRIPTION: | Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, complete metric spaces, function spaces, and Baire spaces. |
MATH 554 : Foundations of Topology 2.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 553 or instructor's consent. |
| DESCRIPTION: | Fundamental group, retractions and fixed points, homotopy types, separation theorems, classification of surfaces, Seifert-van Kampen Theorem, classification of covering spaces, and applications to group theory. |
MATH 561 : Introduction to Algebraic Geometry.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 671 or concurrent enrollment. |
| DESCRIPTION: | Projective varieties, curves, surfaces, differential forms, and divisors. |
MATH 562 : Introduction to Algebraic Geometry.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 671 or concurrent enrollment. |
| DESCRIPTION: | Projective varieties, curves, surfaces, differential forms, and divisors. |
MATH 570 : Matrix Analysis.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| PREREQUISITE: | Math 302 or 343; or equivalents. |
| DESCRIPTION: | Special classes of matrices, canonical forms, matrix and vector norms, localization of eigenvalues, matrix functions, applications. |
MATH 586 : Introduction to Algebraic Number Theory.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | W |
| PREREQUISITE: | Math 372 or equivalent; instructor's consent. |
| DESCRIPTION: | Algebraic integers; different and discriminant; decomposition of primes; class group; Dirichlet unit theorem; Dedekind zeta function; cyclotomic fields; valuations; completions. |
MATH 587 : Introduction to Analytic Number Theory.
(3:3:0)(Credit Hours:Lecture Hours:Lab Hours)| OFFERED: | F |
| PREREQUISITE: | Math 332 or equivalent; instructor's consent. |
| DESCRIPTION: | Arithmetical functions; distribution of primes; Dirichlet characters; Dirichlet's theorem; Gauss sums; primitive roots; Dirichlet L-functions; Riemann zeta-function; prime number theorem; partitions. |