42 courses in the 1978–79 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Course Descriptions
Note Course descriptions are given under the new department course numbers introduced in 1976.
Ideas and examples in geometry, number theory, algebra, and analysis. Modern theories are motivated by consideration of historically important topics such as angle trisection, solution by radicals, the real number system, non-Euclidean geometry, and computability of functions.
Similar to, but independent of, P Math 230a.
Fundamentals of group, ring, field theory, and other algebraic structures.
Coreq: Math 231a.
Continuation of P Math341a Prereq: P Math 341a
Theory of functions of real variabies. The notions of compactness, connectedness and uniformity are used in a study of continuity, differation, and integration. Prereq: Math 230a, b
Continuation of P Math351a Prereq: P Math351a
Analysis of complex numbers; fundamental theorems of holomorphic functions; meromorphic functions. Prereq: Math 230a,b
Prereq: P Math 352a
2C,1T 0.5
Concurrent lines, collinear points, the Euler line, the Simson line, the nine-point circle. Cross ratio, projection, harmonic range, the quadrilateral and the quadrangle. Properties of circles.
Projective spaces over fields, collineations and correlations, quadric curves and surfaces. References to non-euclidean geometries.
Prereq: Math 231
The plane of complex numbers. The group of circlepreserving mappings and its subgroups. Connections with non-euclidean geometries (Laguerre, Minkowski). Prereq: Math 231
formulae; surfaces in E® and their intrinsic geometry, Gaussian curvature and the Gauss-Bonnet theorem. Coordinate transformations and tensors in n-dimensions; n-dimensional Riemannian spaces, covariant differentiation, geodesics, the curvature, Ricci and . Einstein tensors.
Prereq: Math 230, or consent of instructor
~ Intuitive set theory, metric spaces, point set topology.
A broad introduction to Mathematical Logic. The logic of.
sentences: truth-functions and an axiomatic approach (Natural Deduction). The logic of predicates and quantifiers. Foundations of Mathematics.
Prereq: Consent of instructor
Continuation of P Math 430a. Gédel’s incompleteness theorem (in outline). Logicism, intuitionism, formalism. Selected topics (some of intuitionistic logic, modal logic, the representation theorem for Boolean Algebras normally are treated).
Prereq: P Math 430a
Course Descriptions 349 Pure Mathematics
First order languages and thecries. This course is more specialized and at a more advanced level than
P Math 430.
Continuation of P Math 432a. A treatment of at least one of the following: set theory, model theory, undecidability. Prereq: P Math 432a
Multiplicative-algebraic theory of numbers. Foundations of natural number theory. Elements of additivecombinatorial number theory.
Coreq: Math 331 or P Math 341
Continuation of Theory of Numbers 1 Prereq: P Math 441a
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prereq: Math 331 or P Math 341
Ordered sets, lattices, and Galois connections. Applications in algebra, geometry. and logic. Prereq: Consent of instructor
Continuation of Lattice Theory 1 Prereq: P Math 444a
Continuation of the theory of rings and modules. Prereq: P Math 331 or P Math 341
Continuation of Ring Theory 1 Prereq: P Math 445a
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups.
Coreq: Math 337 or P Math 341
Continuation of Group Theory 1 Prereq: P Math 446a
Field extension and Galois theory. Prereq: Math 331 or P Math 341
Continuation of Field Theory 1 Prereq: P Math 447a
An introduction to integration and measure theory with emphasis on the real line.
Prereq: P Math 332a or P Math 351
Continuation of Real Analysis 2a. Prereq: P Math 451a
Further properties of holomorphic and meromorphic functions. Riemann surfaces. Prereq: Math 332b or P Math 352
Complex Analysis 2b ; Continuation of Complex Analysis 2a Prereq: P Math 452a
Finite incidence structures. Designs. Finite projective
and affine planes. Coreg: P Math 362
Listed without a description.
Differentiable manifolds, vector fields, tinear connections, tensor fields, differential forms and structure equations.
Prereq: P Math 365/AM 362 or consent of instructor
An introduction to the theory of algebraic varieties. Special topics such as the Theorem of Riemann-Roch. Prereq: Math 331 or P Math 341
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Linear connections and Riemannian structures, geodesics and variations of geodesics, differential forms, integration theory and Stokes’ theorem.
Prereq: P Math 463/AM 463, or consent of instructor
Listed without a description.
Continuation of general topology; selected topics from other branches of topology.
Prereq: P Math 367
Cauchy’s, Pexider’s, and similar equations. Equations for polynomials and for trigonometric functions. Reduction to differential equations. General methods and theorems. Iteration. Applications. Further topics, such as equations for functions of several variables, or equations for analytic functions, or equations on algebraic structures.
Department of Statistics Course Descriptions
Note Course descriptions are given under the new departmental course numbers introduced in 1976.