210 / FIELDS OF INSTRUCTION

MS 632-ALGEBRA 2. 3 credits
 Prerequisite: MS 631. Continuation of MS 631.
MS 633-ALGEBRA 3. 3 credits
 Prerequisite: MS 632. Continuation of MS 632.
MS 635-PROJECTIVE GEOMETRY. 3 credits
 Projective planes, perspectivity, and projectivity. Fundamental theorem, quad-
rangles, duality, cross ratio, polarities. Some famous theorems such as those of
Pappus, Pascal, Branchon, etc.
MS 636-NON-EUCLIDEAN GEOMETRY. 3 credits
 Geometric foundation of Euclidean (and non-Euclidean) plane. Plane ge-
 ometry, trigonometry, and calculus of non-Euclidean hyperbolic plane.
 MS 637-HIGHER GEOMETRY. 3 credits
 Homogeneous point and line coordinates, projective coordinates, collineations,
 and correlations. Double points, circular points at infinity, conics, and involutions.
 Classification of geometries such as projective, affine, Euclidean, non-Euclidean,
 metric, finite, etc.
 MS 638-DIFFERENTIAL GEOMETRY 1. 3 credits
 Prerequisites: MS 502, MS 601. Recommended: MS 610. First part of a three-
term sequence. Classical differential geometry of curves and surfaces, differentiable
manifolds, tensor analysis, affine connection, Riemannian geometry, Lie groups, Lie
algebras, applications to physics.
MS 639-DIFFERENTIAL GEOMETRY 2. 3 credits
 Prerequisite: MS 638. Continuation of MS 638.
MS 640-DIFFERENTIAL GEOMETRY 3. 3 credits
 Prerequisite: MS 639. Continuation of MS 639.
MS 641-GENERAL THEORY OF MEASURE AND INTEGRATION 1. 3 credits
 Prerequisite: MS 543. Measure and outer measures; extension, completion, and
approximation of the measures; measurable functions; integration; signed measures;
product spaces; approximate differentiation and differentials; applications; inte-
gration over locally compact spaces and locally compact groups.
MS 642-GENERAL THEORY OF MEASURE AND INTEGRATION 2. 3 credits
 Prerequisite: MS 641. Continuation of MS 641.
MS 643-GENERAL THEORY OF MEASURE AND INTEGRATION 3. 3 credits
 Prerequisite: MS 642. Continuation of MS 642.
MS 645-ADVANCED TOPICS IN INTEGRATION 1. 3 credits
 Prerequisites: MS 537, MS 643 and MS 663. Current topics in integration,
reference to function spaces and to spaces provided with algebraic or topological
structures.
MS 646-ADVANCED TOPICS IN INTEGRATION 2. 3 credits
 Prerequisite: MS 645. Continuation of MS 645.
MS 647-ADVANCED TOPICS IN INTEGRATION 3. 3 credits
 Prerequisite: MS 646. Continuation of MS 646.
MS 648-MATHEMATICAL ANALYSIS FOR STATISTICIANS. 4 credits
 Corequisite: STA 610. Set theory, cardinality, metric spaces, limits, continuity,
differentiation, approximation of functions, series of functions. Applications to
probability and statistics are stressed.
MS 649-MATHEMATICAL ANALYSIS FOR STATISTICIANS. 4 credits
 Prerequisite: MS 648. Measure and integration; additive set functions and meas-
ures; Lebesgue measure in R", Egorov's theorem, Lebesgue and Lebesgue-Stieltjes