68 COURSE DESCRIPTIONS
305 Advanced Calculus (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and in tegrals. Prerequisite: 298 or consent. 315 Modern Algebra (3) Introduction to abstract algebra with top ics from elementary ring, field and group theories. Emphasis on ring of integers, con gruences, polynomial domains, permutation groups. Prerequisite: 298 or consent. 321 Numerical Analysis (3) Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpola tion theory, numerical differentiation and integration, numerical solutions of ordinary differential equations. Prerequisites: 291, Computer Science 101. Fee: $25. 331 Probability (3) Samples spaces, axioms and elementary theorems of probability, combinatorics, in dependence, conditional probability, Bayes' Theorem, one and higher dimensional ran dom variables, special and multivariate dis tributions. Prerequisites: 112, 205. 332 Statistics (3) Estimation: consistency unbiasedness, maximum likelihood, confidence intervals. Testing hypothesis; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chisquare tests, decision theory, nonpara metric statistics; application of statistical methods. Prerequisite: 331 or consent. 333 Operations Research (3) Mathematical foundations of model building, optimization, linear programming models, game theoretic models. Cross list ed with COS 325. Prerequisites: 105, Computer Science 101. Fee: $25. 410 Topics in Advanced Calculus (3) Implicit function theorems, main theo rems in integral calculus. Jacobian transfor mations, infinite series. Prerequisite: 305. 415 Number Theory and the History of Mathematics (3) The history of mathematics from Euclid through the nineteenth century as seen by exploring developments in number theory including congruences, Diophantine equa tions, divisibility, theorems of Fermat and Wilson, primitive roots, indices, quadratic
reciprocity and the distribution of prime numbers. Prerequisite: 298.
420 Modern Geometry (3) Homogeneous projective coordinates in variants, duality, Desargues's and Pappus's theorems, transformations, point and line conics, various axioms systems for Euclidean and non-Euclidean geometry. Prerequisite: 298. 435 Mathematics for the Physical Sciences (3) First order differential equations and second order linear equations, series solu tions, Laplace transforms, numerical meth ods, partial differential equations and Fourier series, boundary value problems and Sturm-Liouville theory. Prerequisite: 205, 291 or consent. 440 Complex Variables (3) Complex variables, analytic functions, com plex integral theorems, power series, confor mal mappings. Prerequisite: 205 or consent 450 Topics in Abstract Algebra (3) Topics from groups, ring and fields. Galois theory. Prerequisite: 315. 480 Research Seminar (1-3) Special studies in mathematics. Prerequisite: senior standing or consent.
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