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Course Criteria
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3.00 Credits
Provides an introduction to combinatorial design and coding theory with a focus on basic concepts and essential tools. Topics are selected from: An introduction to finite fields, difference methods, symmetric designs, orthogonal Latin squares, league schedules, basic concepts in coding theory, linear codes, perfect codes, BCH codes, and Reed-Solomon codes. The focus is on the theoretical aspect of these topics. Prerequisite(s): Discrete Math ( MTH 231 or MTH 331 or equivalent), and Linear Algebra ( MTH 222 or equivalent), or permission of instructor.
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3.00 Credits
Two-person games with applications. N-person cooperative games with side payments. Various solution concepts for games with applications to social and environmental problems. Power indices for voting games including multi-candidate elections. Related topics such as utility theory, decision theory, measurement theory, fair division or partition function games. Prerequisite: MTH 222 or 231 or permission of instructor.
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3.00 Credits
Basic structural properties, trees, connectivity, traversability (Eulerian Tours and Hamiltonian Cycles), vertex and edge colorings, cliques, planarity, and directed graphs. Applications to finding algorithms for shortest path problem, minimum weight tree problem, optimal assignment problem, and other scheduling and transportation problems. Prerequisite: MTH 222 or 231 or permission of instructor.
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3.00 Credits
Counting methods: permutations, combinations, generating functions, recurrence relations, inclusion/exclusion. Incidence structures: block designs, Latin squares, finite geometries. Prerequisite: MTH 222 or 231 or permission of instructor.
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3.00 Credits
Topics selected from an area of analysis. Prerequisite: permission of instructor. Offered infrequently.
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3.00 Credits
Continuity, differentiation, convergence, series and integration, in both one and several variables. Prerequisite: (441/541) MTH 222 or 231 and Calculus III; (442/542) MTH 222 and 441/541.
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3.00 Credits
Continuity, differentiation, convergence, series and integration, in both one and several variables. Prerequisite: (441/541) MTH 222 or 231 and Calculus III; (442/542) MTH 222 and 441/541.
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3.00 Credits
Mathematical methods in options pricing; options and their combinations, arbitrage and put-call parity, stock and option trees, risk neutral pricing, geometric Brownian motion for stock models and derivation of the Black-Scholes formula; and as time allows, additional topics such as futures, forwards, swaps and bond models. Prerequisite: Calculus II and an introduction to statistics such as STA 301 or DSC 205.
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3.00 Credits
Algebra and geometry of complex numbers, elementary functions of a complex variable including integrals, power series, residues and poles, conformal mapping, and their applications. Prerequisite: MTH 222 or 231 and Calculus III.
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3.00 Credits
Errors and error propagation, theory of polynomial equations, difference equations, solutions of nonlinear equations, programming of algorithms, numerical methods for polynomial equations. Prerequisite: MTH 222 and Calculus III and knowledge of computer programming.
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