410 STUDIES IN ADVANCED MATHEMATICS (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title). 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 294. Topology. Topics from elementary point set topology . 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 suffic ient demand. Course may be repeated with different content (section title). Fundamental Concepts ofGeometry . Various axiom systems for Euclidean and non-Euclidean geometry. Prerequisite: 205 . Modern Geometry . Homogeneous projective coord inates, in var iants , duality, Desargues' sand Pappus ' s theorems, transformations, point and line conics. Prerequisite: 205 , 294. Differential Geometry. General curve theory, surfaces in the three-dimensional space, funda mental quadratic forms of a surface; the intrinsic geometry of surfaces, extri nsic properties of surfaces . Prerequisite: 206 and 294. 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 ser ies, conformal mappings. Prerequisite: 206 . Vector Analysis. Vector algebra and calcu lus, vector fields, line integrals, vector integral theorems , curvellinear coordinates. Prerequisite: 206 and 294. Differential Equations. Equat ions of first and second orders, linear equations , series so lutions , approximate solutions , systems of ordinary equations , Legendre and Bessel equations. Pre requisite: 206. 470 RESEARCH SEMINARY (1-3) Special studies in mathematics . Prerequisite: Senior standing or consent.
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