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Course Criteria
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3.00 Credits
Topics to be chosen from: Topological spaces and continuous functions, metric spaces, connectivity, separation axioms, compactness, product and quotient spaces, paracompactness, and manifolds. Prerequisites & Corequisites: Prerequisite: MATH 3300 or MATH 5700. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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3.00 Credits
An introduction to Riemannian Geometry with emphasis on curves and surfaces. Topics may include isometries, orientation, differential forms, curvature, metrics, and geodesics. Prerequisites & Corequisites: Prerequisites: MATH 2720 and either MATH 2300 or MATH 3740 (MATH 3140 recommended). Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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3.00 Credits
Properties of finite dimensional abstract vector spaces, linear transformations, and matrix algebra are studied. Prerequisites & Corequisites: Prerequisite: MATH 3300. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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4.00 Credits
This course is devoted to the learning of algebra in elementary and middle grades. Concepts and skills are developed and reinforced using a variety of approaches and materials. Computing technologies are used throughout the course to develop concepts; to explore the connections among numeric, graphic, and symbolic representations of mathematical ideas; and to model and solve problems involving quantitative variables. Prerequisites & Corequisites: Prerequisites: MATH 1500, 1510, 2650, and 3520 with grades of "B" or better or instructor approval. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 4 hours
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4.00 Credits
This course provides experiences in mathematical modeling and problem solving for elementary/middle school teachers. Problem contexts are selected to deepen students' understanding of important ideas in number theory, algebra, geometry, probability, statistics, and the conceptual underpinnings of calculus. Computing technologies are used extensively. Prerequisites & Corequisites: Prerequisites: MATH 5540 with a grade of "C" or better or instructor approval. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 4 hours
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4.00 Credits
Properties of real numbers, Cauchy sequences, series, limits, continuity, differentiation, Riemann integral, sequences and series of functions. Prerequisites & Corequisites: Prerequisites: MATH 2720 and 3140 (3300 is recommended). Notes: Undergraduates with junior status and 12 hours of work inmathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 4 hours
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3.00 Credits
Topology of n-dimensional space, continuity and differentiability of functions of one variable; Riemann-Stieltjes integral; convergence of sequences and series of functions; Fourier series; analysis of functions of several variables. Prerequisites & Corequisites: Prerequisite: MATH 5700 or approval of advisor. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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4.00 Credits
Functions of several variables, implicit and inverse functions, Jacobians, multiple integrals, Green's Theorem, divergence, curl, the Laplacian, Stokes' Theorem, analytic functions, Laurent expansions, residues, argument principle, and conformal mapping. Prerequisites & Corequisites: Prerequisite: MATH 3740. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 4 hours
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3.00 Credits
Series solutions at ordinary and singular points of linear ordinary equations, Bessel and Legendre functions, self-adjoint boundary value problems, Fourier series, solution of partial differential equations by separation of variables. Prerequisites & Corequisites: Prerequisite: MATH 3740. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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3.00 Credits
Diophantine equations, congruences, quadratic residues, and properties of number-theoretic functions. Prerequisites & Corequisites: Prerequisite: MATH 3300. Notes: Undergraduates with junior status and 12 hours of work in mathematics and statistics may enroll in 5000-level courses with prior approval of the department chair. Credits: 3 hours
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