Course Schedule and Catalog

Long Title: SINGLE VARIABLE CALCULUS I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Differentiation, extrema, Newton's method, integration, fundamental theorem of calculus, area, volume, natural logarithm, exponential, arc length, surface area, Simpson's rule, L'Hopital's rule. May substitute MATH 111-112 or take MATH 101 after completing MATH 111.

Long Title: SINGLE VARIABLE CALCULUS II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Continuation of MATH 101. Includes further techniques of integration, as well as infinite sequences and series, tests for convergence, power series, radius of convergence, polar coordinates, parametric equations, and arc length.

Long Title: FUNDAMENTAL THEOREM OF CALCULUS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of calculus, forming with MATH 112 a slower-paced version of MATH 101/102. Contains less detail in the coverage of infinite series. Students may take MATH 111/112 followed by MATH 102, or MATH 111 followed by MATH 101/102.

Long Title: CALCULUS AND ITS APPLICATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Continuation of the study of calculus from MATH 111.

Long Title: ORDINARY DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of ordinary differential equations (e.g., solutions to separable and linear first-order equations and to higher-order linear equations with constant coefficients, the properties of solutions to differential equations, and numerical solution methods) and linear algebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the application of linear algebra to first-order systems of differential equations and the qualitative theory of nonlinear systems and phase portraits. Use of the computers in Owlnet as part of each homework assignment required. Credit may not be received for both MATH 211 and MATH 213.

Long Title: MULTIVARIABLE CALCULUS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of gradient, divergence, and curl, Lagrange multipliers, multiple integrals, as well as line integrals, conservative vector fields, Green's theorem, Stokes's theorem, and Gauss's theorem. May substitute Math 221 and 222. Equivalency: MATH 222. Mutually Exclusive: Cannot register for MATH 212 if student has credit for MATH 222.

Long Title: BASIC MATHEMATICAL BIOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): MATH 102

Description: Study of systems of differential and difference equations, with special attention to modeling of basic biological processes. Phase plane analysis of ordinary differential systems. Qualitative understanding of solutions of differential equations. Credit may not be received for this course and MATH 211.

Long Title: HONORS CALCULUS III

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: This course and MATH 222 include the material of MATH 212 and much more. Topology of Rn, calculus for functions of several variables, linear and multilinear algebra, theory of determinants, inner product spaces, integration on manifolds.

Long Title: HONORS CALCULUS IV

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: See MATH 221. A student may not receive credit for both MATH 222 and MATH 212. Equivalency: MATH 212. Mutually Exclusive: Cannot register for MATH 222 if student has credit for MATH 212.

Long Title: TOPICS IN UNDERGRADUATE MATH

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 102

Description: Treatment of topics in undergraduate mathematics with an emphasis on writing of clear, cogent compete mathematical proofs. Topics vary by year. May be repeated for credit with permission of department. Pre-requisite: MATH 102 Repeatable for Credit.

Long Title: INTRODUCTION TO ANALYSIS I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Prerequisite(s): MATH 221 or permission of department

Description: A thorough treatment of basic methods of analysis such as metric spaces, compactness, sequences and series of functions. Also further topics in analysis, such as Hilbert spaces, Fourier series, Sturm- Liouville theory.

Long Title: INTRODUCTION TO ANALYSIS II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 321 or permission of instructor

Description: See MATH 321. Includes proofs of the basic results for multivariable calculus (MATH 321 provides proofs for single-variable calculus). Repeatable for Credit.

Long Title: HONORS LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Systems of linear equations, matrices, vector spaces, linear transformations, eigenvalues, canonical forms, inner product spaces, bilinear and quadratic forms. Content is similar to that of MATH 355, but with more emphasis on theory. The course will include instruction on how to construct mathematical proofs. This course is appropriate for potential Mathematics majors and others interested in learning how to construct rigorous mathematical arguments. Credit may not be received for both MATH 354 and MATH 355. Equivalency: MATH 355. Recommended Prerequisite(s): A 200-level math class. Mutually Exclusive: Cannot register for MATH 354 if student has credit for MATH 355.

Long Title: LINEAR ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Linear transformations and matrices, solution of linear equations, eigenvalues and eigenvectors, quadratic forms, Jordan canonical form. Credit may not be received for both MATH 354 and MATH 355. Equivalency: MATH 354. Mutually Exclusive: Cannot register for MATH 355 if student has credit for MATH 354.

Long Title: ABSTRACT ALGEBRA I

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Group theory: normal subgroups, factor groups, Abelian groups, permutations, matrix groups, and group action.

Long Title: NUMBER THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Properties of numbers depending mainly on the notion of divisibility. Continued fractions. Offered alternate years.

Long Title: GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Topics chosen from Euclidean, spherical, hyperbolic, and projective geometry, with emphasis on the similarities and differences found in various geometries. Isometries and other transformations are studied and used throughout. The history of the development of geometric ideas is discussed. This course is strongly recommended for prospective high school teachers.

Long Title: TOPICS IN COMBINATORICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of combinatorics and discrete mathematics. Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games.

Long Title: INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Laplace transform: inverse transform, applications to constant coefficient differential equations. Boundary value problems: Fourier series, Bessel functions, Legendre polynomials.

Long Title: COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of the Cauchy integral theorem, Taylor series, residues, as well as the evaluation of integrals by means of residues, conformal mapping, and application to two-dimensional fluid flow. Equivalency: MATH 427. Mutually Exclusive: Cannot register for MATH 382 if student has credit for MATH 427.

Long Title: UNDERGRADUATE COLLOQUIUM

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 1

Description: Lectures by undergraduate students on mathematical topics not usually covered in other courses. Presentation of one lecture and attendance at all sessions required. Repeatable for Credit.

Long Title: DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of the differential geometry of curves and surfaces in R3. Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem.

Long Title: DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Introduction to Riemannian geometry. Content varies from year to year. Recommended Prerequisite: MATH 401. Repeatable for Credit.

Long Title: CALCULUS OF VARIATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 101 AND MATH 102 AND (MATH 211 OR MATH 212) OR (MATH 221 OR MATH 222)

Description: Study of classical and modern theories about functions having some integral expression which is maximal, minimal, or critical. Geodesics, brachistochrone problem, minimal surfaces, and numerous applications to physics. Euler-Lagrange equations, 1st and 2nd variations, Hamilton's Principle.

Long Title: PARTIAL DIFFERENTIAL EQUATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Wave equation, Laplace's equation, heat equation. Fundamental solutions. Other topics include first order hyperbolic systems, Cauchy-Kowalewski theorem, potential theory, Dirichlet and Neumann problems, integral equations, elliptic equations.

Long Title: PARTIAL DIFFERENTIAL EQUATIONS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 423

Description: Continuation of MATH 423. Repeatable for Credit.

Long Title: INTEGRATION THEORY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Lebesgue theory of measure and integration.

Long Title: TOPICS IN REAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 425

Description: Content varies from year to year. May include Fourier series, harmonic analysis, probability theory, advanced topics in measure theory, ergodic theory, and elliptic integrals. Repeatable for Credit.

Long Title: COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Distribution Group: Distribution Group III

Credit Hours: 3

Description: Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. Emphasis on the theory. Equivalency: MATH 382. Mutually Exclusive: Cannot register for MATH 427 if student has credit for MATH 382.

Long Title: TOPICS IN COMPLEX ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 382 OR MATH 427

Description: Special topics include Riemann mapping theorem, Runge's Theorem, elliptic function theory, prime number theorem, Riemann surfaces, et al. Repeatable for Credit.

Long Title: DYNAMICAL SYSTEMS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 211 AND CAAM 335 OR MATH 355 AND CAAM 401 OR MATH 321

Description: Existence and uniqueness for solutions of ordinary differential equations and difference equations, linear systems, nonlinear systems, stability, periodic solutions, bifurcation theory. Cross-list: CAAM 435.

Long Title: GENERAL TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Study of basic point set topology. Includes a treatment of cardinality and well ordering, as well as metrization.

Long Title: GEOMETRIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 443 or permission of department

Description: Introduction to algebraic methods in topology and differential topology. Elementary homotopy theory. Covering spaces.

Long Title: ALGEBRAIC TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 444

Description: Introduction to the theory of homology. Includes simplicial complexes, cell complexes and cellular homology and cohomology, as well as manifolds, and Poincare duality.

Long Title: ABSTRACT ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 356 or permission of instructor

Description: Ring theory: ideals, polynomials, factorization. Advanced linear algebra: quadratic forms, canonical forms. Field theory: extensions, Galois theory, soluability in radicals. Continuation of MATH 356.

Long Title: ABSTRACT ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Prerequisite(s): MATH 463 or permission of instructor

Description: Continuation of MATH 463. Tensor and exterior algebra, introductory commutative algebra, structure of modules, and elements of homological algebra. Additional advanced topics may include representations of finite groups and affine algebraic geometry.

Long Title: TOPICS IN ALGEBRA

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Content varies from year to year. Repeatable for Credit.

Long Title: TOPICS IN ALGEBRA II

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Content varies from year to year.

Long Title: POTPOURRI

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: This course deals with miscellaneous special topics not covered in other courses. For a description of the topic to be covered in Fall 2008, please see description of CAAM 436. Course repeatable for distinct topics. Cross-listed with CAAM 436 for Fall 2008 only. Repeatable for Credit.

Long Title: SUPERVISED READING

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 6

Description:  Repeatable for Credit.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The course may be repeated multiple times for credit. Cross-listed with CAAM 498 and STAT 498. Repeatable for Credit.

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 3

Description:  Repeatable for Credit.

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN DIFFERENTIAL GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: The Atiyah-Singer theorem, secondary invariants, and related topics. Repeatable for Credit.

Long Title: ADVANCED TOPICS IN REAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: FUNCTIONAL ANALYSIS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: ERGODIC THEORY AND TOPOLOGICAL DYNAMICS

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Long Title: TOPICS IN TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN ADVANCED TOPOLOGY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Topic to be announced. Repeatable for Credit.

Long Title: TOPICS IN ALGEBRAIC GEOMETRY

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Lecture

Credit Hours: 3

Description: Possible topics include rational points on algebraic varieties, moduli spaces, deformation theory, and Hodge structures. Recommended Prerequisite(s): MATH 463 and MATH 464. Repeatable for Credit.

Long Title: CURRENT MATHEMATICS SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1

Description: Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Repeatable for Credit.

Long Title: GRADUATE TEACHING SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1

Description: Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Repeatable for Credit.

Long Title: RESEARCH THEMES IN THE MATHEMATICAL SCIENCES

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Seminar

Credit Hours: 1 TO 3

Description: A seminar course that will cover selected theme of general research in the mathematical sciences from the perspectives of mathematics, computational and applied mathematics and statistics. The cousre may be repeated multiple times for credit. Cross-listed with CAAM 698 and STAT 698. Repeatable for Credit.

Long Title: MATHEMATICAL SCIENCES VIGRE SEMINAR

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Independent Study

Credit Hours: 1 TO 9

Description:  Repeatable for Credit.

Long Title: VISITING RESEARCH TRAINEE

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Research

Credit Hours: 0

Long Title: GRADUATE THESIS AND RESEARCH

Department: Mathematics

Grade Mode: Standard Letter

Course Type: Research

Credit Hours: 1 TO 15

Description:  Repeatable for Credit.