approximation, numerical differentiation and integration. Prerequisite: Math 205, or Math 106 by permission. Two hours lecture, three hours laboratory. Alternate years, offered 1972-73. Laboratory fee: $15.00.
332 MATHEMATICAL STATISTICS (3) Introduction to theory of probability and statistics based on use of calculus; appli cation of statistical methods. Prerequisite: 205 . Alternate year, offered 1972-73.
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 II.
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.
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. Modern Geometry. Homogeneous projective coordinates, invariants, duality, Desargues's and Pappus's theorems , transformations, point and line conics. Prerequisite: 205, 294. 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: 206 and 294. 430 STUDIES RELATED TO APPLIED MATHMETICS (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: 206. Vector Analysis. Vector algebra and calculus, vector fields, line integrals, vec tor integral theorems, curvellinear coordinates. Prerequisite: 206 and 294. Differential Equations. Equations of first and second orders, linear equations, series solutions, approximate solutions, systems of ordinary equations, Legendre and Bessel equations. Prerequisite: 206. 470 RESEARCH SEMINAR (1-2) Special studies in mathematics. Prerequisite: Senior standing or permission of instruc tor. May not be repeated. 96
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