305 ADVANCED CALCULUS (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and
Topics in Advanced Calculus. Implicit function theorems, main theorems in integral calculus. Jacobian transformations, infinite series. Prerequisite: 305. Number Theory. Congruences, Diophantine equations, divisibility, theorems of Fermat and Wilson, primitive roots, indices, quadratic reciprocity. Prerequisite: 206 or 295. Topology. Topics from elementary point set topology. Prerequisite: 305 or consent. Set Theory and Logic. Informal axiomatic set theory and predicate logic as a foundation for modern mathematics. Prerequisite: 315 or consent. 420 STUDIES IN HIGHER GEOMETRIES (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title). Fundamental Concepts of Geometry. Various axiom systems for Euclidean and non-Euclidean geometry. Prerequisite: 205. Modem Geometry. Homogeneous projective coordinates, invariants, duality, Desargues' s and Pappus's theorems, transformations , point and line conics. Prerequisite: 205, 295. Differential Geometry. General curve theory, surfaces in the three-dimensional space, fundamental quadratic forms of a surface; the intrinsic geometry of surfaces, extrinsic properties of surfaces. Prerequisite: 205, 295. 430 STUDIES RELATED TO APPLIED MATHEMATICS (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title). Complex Variables. Complex variables, analytic functions, complex integral theorems, power series, conformal mappings. Prerequisite: 205. Mathematics for the Physical Sciences. First order differential equations and second order linear equations, series solutions, Laplace transforms, numerical methods, partial differential equations and Fourier series, boundary value problems and Sturm-Liouville theory. Prerequisite: 296. Topics in Numerical Analysis. Approximate numerical solutions to partial differential equations, finite difference methods, numerical computations of eigenvectors, error analysis. Prerequisite: 321. 480 RESEARCH SEMINAR (1-3) Special studies in mathematics. Prerequisite: senior standing or consent.
integrals. Prerequisite: 206, 295. 315 MODERN ALGEBRA (3)
Introduction to abstract algebra with topics from elementary ring, field, and group theories. Emphasis on ring of integers, congruences, polynomial domains , permutation groups. Prerequisite: 295 or consent. 321 NUMERICAL ANALYSIS (3) Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpolation theory, numerical differentiation and integration , numerical solutions of ordinary differential equations. Two hours lecture, three hours laboratory (with computer programming.) Prerequisite: 205, 295. 331 PROBABILITY (3) Sample spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probabil ity, Bayes' Theorem, one and higher dimensional random variables, discrete and continuous random variables, special and multivariate distributions. Prerequisite: 205 or consent. 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, Chi-square tests, decision theory, nonparametric statistics; application of statistical methods. Prerequisite: 205 or consent. 333 STUDIES IN APPLIED MATH (3) One section offered alternate years on sufficient demand. Course may be repeated with different content (section title). Prerequisite: 295 or consent. Two hours lecture, three hours laboratory, (with computer programming). Optimization. Mathematical foundations of model building, linear programming models, game-theoretic models. Graph Theory and Combinatorial Mathematics. Fundamental concepts, results, and applications of graph theory and combinatorial mathematics; circuits, flows in network, matching theory, planarity, permutations, combinations, recurrence re lations, difference equations. 410 STUDIES IN ADVANCED MATHEMATICS (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title).
82
Made with FlippingBook flipbook maker