The basic properties of groups, rings, integral domains and fields are quickly reviewed. A theoretical treatment of specific structures such as permutation groups, the ring of integers, polynomial rings, modular systems, and algebraic number fields is given. Real Analysis I Suggested topics are functions of several real variables, Jacobians, implicit and inverse function theorems, vector analysis, theorems of Green, Gauss, and Stokes, with applications and additional topics as time permits. The objective of this course is to teach students to design, solve, and apply operations research models to the analysis of systems problems in industry, business, or government. Suggested topics are linear programming, network analysis, dynamic programming, integer programming, nonlinear programming, queueing theory and inventory.
Attention is paid to machine accuracy, error estimation and multiple-precision arithmetic.
Assignments include the coding and running of programs in the Computer Laboratory. No previous computer experience required. A survey course designed to deepen the student's knowledge of the vast literature of mathematics. Historically influential concepts will be examined for their effects on mathematics and the culture in which they evolved. Philosophical and psychological comparisons will be made between the mathematical and scientific developments in Ancient Greek times, in the Renaissance and Newtonian times, and in the 19th and 20th centuries.