University of Arkansas

Integral calculus of one variable and infinite series. Prerequisite: MATH 2554 with a grade of C or better.

MATH 2564C. Calculus II (Sp, Su, Fa). 4 Hours.

This course overviews the landscape of higher mathematics, touching on many of the themes of modern mathematics: proof, logic, cardinality, analysis, modeling, abstract algebra, number theory, topology and geometry. Pre- or Corequisite: MATH 2564.

MATH 2803. Introduction to Mathematical Proof (Sp, Fa). 3 Hours.

Introduction to methods of mathematical proof, with applications. Pre or corequisite: MATH 2564.

As in-depth study of topics from secondary school mathematics, emphasizing the development of the concept function, function patterns in data sets, connections among the main topics associated with a secondary school curriculum, and the appropriate use of technology. Pre-or Corequisite: MATH 2564.

MATH 3083. Linear Algebra (Sp, Su, Fa). 3 Hours.

Systems of linear equations, vector spaces, linear transformations, matrices, and determinants. Only one of MATH 3083 and MATH 3093 will count for credit. Prerequisite: MATH 2554 or MATH 2043, with a grade of C or better.

A proof-based course on vector spaces, linear transformations, matrices, determinants, eigenspaces and eigenvalues, with applications. Recommended for mathematics majors. Only one of MATH 3083 and MATH 3093 may be counted for credit. Prerequisite: MATH 2564 and MATH 2803 with a C or better.

MATH 3103. Combinatorial and Discrete Mathematics (Sp). 3 Hours.

Basic combinatorial techniques including the study of networks, generating functions, principles of inclusion/ exclusion, Zn, Hamming coding theory, graph theory, and block designs. Prerequisite: MATH 2603.

MATH 3113. Introduction to Abstract Algebra I (Sp, Fa). 3 Hours.

Prerequisite: MATH 2554, and MATH 2603 or MATH 2803, both with a grade of C or better.

Topics in elementary number theory. Prerequisite: MATH 2554, and MATH 2603 or MATH 2803, both with a grade of C or better.

MATH 3423. Advanced Applied Mathematics (Sp, Su, Fa). 3 Hours.

Matrices, Fourier analysis, and partial differential equations. Prerequisite: MATH 2584 with a grade of C or better.

MATH 3513. Elementary Analysis (Sp, Fa). 3 Hours.

A first rigorous course in analysis. The formal basis of the real number system, sequences and series, the Bolzano-Weierstrass Theorem, limits and continuity, the Intermediate Value Theorem, Rolle's Theorem, differentiation, the Mean Value Theorem and its consequences, Taylor's Theorem, L'Hopital's rules, convexity, Riemann integration, the Fundamental Theorem of Calculus. Prerequisite: A grade of C or better in each of MATH 2554, MATH 2564, MATH 2574, MATH 3083 or MATH 3093, and MATH 2803.

MATH 3773. Foundations of Geometry I (Fa). 3 Hours.

Axiomatic method; Euclidean geometry; non-Euclidean geometry. Prerequisite: MATH 2554, and MATH 2603 or MATH 2803, each with a grade of C or better.

MATH 3923H. Honors Colloquium (Irregular). 3 Hours.

Covers a special topic or issue, offered as part of the honors program. Prerequisite: Honors candidacy (not restricted to candidacy in mathematics). May be repeated for degree credit.

MATH 399VH. Honors Mathematics Course (Sp, Su, Fa). 1-6 Hour.

Prerequisite: Departmental consent. May be repeated for up to 12 hours of degree credit.

MATH 400V. Directed Readings (Sp, Su, Fa). 1-6 Hour.

Prerequisite: Departmental consent.

MATH 404V. Classroom Practices in Mathematics (Sp, Fa). 1-3 Hour.

The pedagogy of curricular materials in mathematics acquired through participation in the classroom as an apprentice teacher. Non-major elective credit only. Prerequisite: MATH 2574 and departmental approval.

MATH 4103. Finite Dimensional Vector Spaces (Irregular). 3 Hours.

Linear functionals, matrix representation of linear transformations, scalar product, and spectral representation of linear transformations. Prerequisite: MATH 3083.

MATH 4113. Introduction to Abstract Algebra II (Fa). 3 Hours.

Topics in abstract algebra including finite abelian groups, linear groups, factorization in commutative rings, quadratic field extensions, Gaussian integers, Wedderburn's theorem, and multilinear algebra. Prerequisite: MATH 3113.

MATH 4153. Mathematical Modeling (Irregular). 3 Hours.

Mathematical techniques for formulating, analyzing, and criticizing deterministic models taken from the biological, social, and physical sciences. Techniques include graphical methods, stability, optimization, and phase plane analysis. Prerequisite: MATH 2584.

MATH 4163. Dynamic Models in Biology (Irregular). 3 Hours.

Mathematical and computational techniques for developing, executing, and analyzing dynamic models arising in the biological sciences. Both discrete and continuous time models are studied. Applications include population dynamics, cellular dynamics, and the spread of infectious diseases. Prerequisite: MATH 2554. This course is cross-listed with BIOL 4163.

Rigorous analyses of the concepts of proof, consistency, equivalence, validity, implication, and truth. Full coverage of truth-functional logic and quantification theory (predicate calculus). Discussion of the nature and limits of mechanical procedures (algorithms) for proving theorems in logic and mathematics. Informal accounts of the basic facts about infinite sets. Prerequisite: MATH 2603, MATH 2803, or PHIL 2203. This course is cross-listed with PHIL 3223, PHIL 4253.

MATH 4353. Numerical Linear Algebra (Sp). 3 Hours.

Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors. Prerequisite: MATH 3083 or MATH 3093.

MATH 4363. Numerical Analysis (Fa). 3 Hours.

General iterative techniques, error analysis, root finding, interpolation, approximation, numerical integration, and numerical solution of differential equations. Prerequisite: MATH 2584.

MATH 4443. Complex Variable for Application (Fa). 3 Hours.

Complex analysis, series, and conformal mapping. Additional applications for graduate credit. Prerequisite: MATH 2603 or MATH 2803, and MATH 2584.

MATH 4503. Differential Geometry and Vector Calculus (Irregular). 3 Hours.

Topics include: Vector differential and integral calculus, Stokes' Theorem in 3-space, classical differential geometry in 3-space (curves, surfaces), differential forms, general Stokes' Theorem, applications to hydrodynamics, and electromagnetism. Prerequisite: MATH 2574.

MATH 4513. Advanced Calculus I (Sp, Fa). 3 Hours.

The real and complex number systems, basic set theory and topology, sequences and series, continuity, differentiation, and Taylor's theorem. Emphasis is placed on careful mathematical reasoning. Prerequisite: MATH 2574 and MATH 3083 or MATH 3093.

MATH 4523. Advanced Calculus II (Sp). 3 Hours.

The Riemann-Stieltjes integral, uniform convergence of functions, Fourier series, implicit function theorem, Jacobians, and derivatives of higher order. Prerequisite: MATH 4513.

 MATH 4933. Mathematics Major Seminar (Sp). 3 Hours.

Weekly seminars on topics of historical or cross-disciplinary interest, designed to address students' mathematical knowledge, problem-solving and communication skills, in which student presentations play a part. Also serves as a forum for sharing information about career opportunities and preparation for employment. Prerequisite: Senior standing and a mathematics major, or departmental consent.

MATH 498V. Senior Thesis (Sp, Su, Fa). 1-6 Hour.

MATH 499V. Research Topics in Mathematics (Irregular). 1-3 Hour.

Current research interests in mathematics, at an advanced undergraduate or beginning graduate level. Prerequisite: Departmental consent. May be repeated for up to 12 hours of degree credit.

MATH 499VH. Honors Research Topics in Mathematics (Irregular). 1-3 Hour.

Current research interests in mathematics, at an advanced undergraduate or beginning graduate level. Prerequisite: Departmental consent. May be repeated for up to 12 hours of degree credit