Basic HTML Version

An introduction to numerical methods of solution and their analysis.

Topics include computer arithmetic, propagation of error, systems of

linear and non-linear equations, numerical integration, curve fitting,

and differential equations. Prerequisite: MA 310.

An introduction to the topology of Euclidean space and/or surfaces.

Topics include continuity, compactness, cell complexes, and the

classification of surfaces. Applications include fixed-point theorems, the

Jordan curve theorem, and map colorings. Prerequisites: MA 310 and

335.

Complex numbers, analytic functions, Cauchy‑Riemann equations,

curves and integrals, Cauchy’s Theorem and applications, Taylor and

Laurent series, analytic continuation, Residue Theorem, harmonic

functions, and conformal mappings. Prerequisites: MA 310 and 335.

A rigorous treatment of sequences, limits, continuity, differentiation,

infinite series, sequences and series of functions, uniform convergence

and its implications for function series. Prerequisites: MA 310 and 335.

A continuation of MA 461. Topics include integrals, derivatives, and

functions of several variables. Prerequisites: MA 317 and 461.

A seminar in reading and presenting advanced mathematics in

preparation for proposing an independent research topic. Each student

will read and present articles of interest to the class, building both

a mathematical foundation upon which a research proposal can be

written, and developing the skills for presenting quantitative work.

Towards the end of the term, each student will write, revise and defend

a proposal for independent research. Prerequisite: MA 335 and senior

standing, or consent of the instructor. Fall.

An independent research project in mathematics where students

investigate a topic proposed in MA 470. Students work closely with a

supervising faculty member, formally write up their results, and present

their research to the campus community for their senior conference.

Students may also be required to present their work at a regional

mathematics conference. Prerequisite: MA 470. Exploration term.