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Course Criteria
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3.00 Credits
A continuation of MATH 187, exploring more advanced topics in logic, set theory, and discrete mathematics. Proof techniques in predicate logic; diagonalization arguments in logic, set theory and computer science; ordered sets; mathematical methods in cryptography; advanced techniques of combinatorial enumeration; selected topics in graph theory. PREREQ: MATH 187.
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3.00 Credits
Topics in group theory, ring theory and field theory with emphasis on finite and solvable groups, polynomials and factorization, extensions of fields. PREREQ: MATH 301 and MATH 305.
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3.00 Credits
Sets, metric and topological spaces, product and quotient topology, continuous mappings, connectedness and compactness, homeomorphisms, fundamental group, covering spaces. PREREQ: MATH 314.
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4.00 Credits
Introduction to fundamental elements of analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: infinite series, sequences and series of function, uniform convergences, theory of integration, implicit function theorem and applications. PREREQ: MATH 275, MATH 301, MATH 314.
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3.00 Credits
Complex numbers, functions of a complex variable, analytic functions, infinite series, infinite products, integration, proofs and applications of basic results of complex analysis. Topics include the Cauchy integral formulas, the residue theorem, the Riemann mapping theorem and conformal mapping. PREREQ: MATH 275.
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3.00 Credits
Theory of linear and nonlinear ordinary differential equations and their systems, including Dynamical systems theory. Properties of solutions including existence, uniqueness, asymptotic behavior, stability, singularities and boundedness. PREREQ: MATH 333.
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3.00 Credits
Theory of partial differential equations and boundary value problems with applications to the physical sciences and engineering. Detailed analysis of the wave equation, the heat equation, and Laplace's equation using Fourier series and other tools. PREREQ: MATH 333.
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3.00 Credits
Linear optimization problems and systems of linear inequalities. Algorithms include simplex method, two-phase method, duality theory, and interior point methods. Programming assignments. PREREQ: MATH 301.
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3.00 Credits
Provides a solid foundation in the mathematical theory of statistics. Topics include probability theory, distributions and expectations of random variables, transformations of random variables, moment-generating functions, basic limit concepts and brief introduction to theory of estimation and hypothesis testing: point estimation, interval estimation and decision theory. PREREQ: MATH 301, MATH 361 and MATH 275.
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3.00 Credits
Introduction to mathematical modeling through case studies. Deterministic and probabilistic models. Optimization. Examples will be drawn from the physical, biological, and social sciences. PREREQ: MATH 361 or PERM/ INST.
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