Elementary theory of groups, rings, and modules. This course traces the development of mathematics from ancient times up to and including the 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problem solving. Numerical solutions of differential and algebraic equations. A rigorous treatment of the calculus of functions of one real variable.
Emphasis is on proofs.
Includes discussion of topology of real line, limits, continuity, differentiation, integration and series. Prerequisite Math 260. Axiomatic theories and completeness. Brief discussion of incompleteness results. Independent Study Work done by a student or group of students under faculty supervision on material not currently offered in a regularly scheduled course.