300

Explores how mathematical ideas have been used to understand and create music, and how musical ideas have influenced math and science. Topics selected from the history of tuning and alternative tuning, the Music of the Spheres doctrine, historical theories of consonance, contributions to music theory by mathematicians, mathematical analysis of sound, philosophical and cognitive connections between math and music, and math in music composition and instrument design. An ability to read music is recommended. This course is not intended for Mathematics majors.

Participation in an approved professional experience applying mathematics or statistics in a real world setting. Students must submit a Learning Contract describing the work experience, its relationship to the mathematical sciences, and how it will be monitored and evaluated. Permission of the department required.

Study of the theory of polynomial equations. Rational, real and complex roots of algebraic equations, the Remainder and Factor theorems, Fundamental Theorem of Algebra, solutions of cubic and bi-quadratic equations and approximation of roots.

Introductory course in partial differential equations with emphasis on boundary value problems encountered in mathematical physics. Fourier series; separation of variables; D'Alembert's solution; the heat, wave and potential equations. Additional topics such as Sturm-Liouville problems or Laplace transforms as time permits.

Careful presentation of the ideas of calculus that are developed intuitively in the usual freshman-sophomore calculus courses. Techniques of proof in analysis; countable sets and cardinality; the real line as a complete ordered field; some topology of the real line; sequences and their limits; continuous functions and their properties; other topics as time permits.

Introductory course in numerical methods for digital computers. Floating point arithmetic, errors, error analysis. Roots of equations, systems of equations. Numerical differentiation and integration. Interpolation and least squares approximations.

An introduction to the development of mathematical models to solve various applied and industrial problems. Topics will include optimization, Lagrange multipliers, sensitivity analysis in optimization models, analysis and simulation of discrete and continuous dynamic models.

Study of algebraic structures, such as groups and rings. The fundamental theorem of finite abelian groups, basic homomorphism theorems for groups, permutation groups and polynomial rings are presented.

Continuation of the study of algebraic structures such as groups, rings, integral domains and fields, with applications such as: geometric symmetry and crystallography, switching networks, and error-correcting codes.

Study of integers and their properties; divisibility; primes; congruencies; multiplicative functions; quadratic residues; quadratic reciprocity; Diophantine equations.

The addition, multiplication and pigeon-hole principles. Permutations and combinations, partitions and distributions; the binomial and multinomial theorems. Generating functions; recurrence relations; principle of inclusion-exclusion; combinatorial algorithms or designs as time permits.

Study of absolute, Euclidean, and hyperbolic geometry from synthetic and analytic viewpoints. Topics include axioms for geometries, transformations, triangles and other basic shapes, and constructions. Some consideration given to finite, spherical, and spatial geometry. Use of geometry software.

Topics chosen from stochastic processes; birth-death processes; queuing theory; inventory theory; reliability; decision analysis; simulation.

Study of basic financial mathematical concepts used in modeling and hedging. Topics include: financial derivatives, call and put options, futures, binomial trees, replicating portfolios and arbitrage, stocks and options pricing, Black-Scholes model, hedging. Additional topics such as swaps, currency markets, and international political risk analysis as time permits.

A rigorous treatment of the mathematical theory associated with financial transactions, including simple and compound interest, annuities, bonds, yield rates, amortization schedules, and sinking funds. Additional topics such as capital asset pricing models and portfolio risk analysis as time permits.

Topics chosen from linear programming and applications; network analysis; game theory; dynamic, integer and nonlinear programming.

Chronological study of the development of mathematics. Emphasis on the solution of selected mathematical problems associated with historical periods.

The course, the second in the Honors Program in Mathematics, will focus on a topic reflecting the interest of the instructor. Examples include combinatorial topology, nonlinear dynamic systems, graph theory, complex analysis, and the theory of partitions. This course is by invitation only.