PMATH 230Y Introduction to Pure Mathematics
Examples and results in modern geometry. number theory and analysis; the historical sources of modern mathematics.
2 hours lectures. Two terms
Pure Mathematics (PMATH)
35 courses in the 1976–77 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
Department of Pure Mathematics Undergraduate Course Descriptions
Note Course descriptions are given under the new departmental course numbers introduced in 1976.
PMATH 341Y Algebra
Fundamentals of group, ring, field theory, and other algebraic structures.
Corequisite: Math 231a{b. 3 hours lectures. Two terms
PMATH 351Y Real Analysis 1
Theory of functions of real variables. The notions of compactness, connectedness, and uniformity are used ina study of continuity, differentiation, and integration. Prerequisite: Math 230a]b. 2 hours lectures. Two terms
PMATH 352Y Complex Analysis 1
Analysis of complex numbers; fundamental theorems of holomorphic functions; meromorphic functions. Prerequisite: Math 230a/b. 2 hours lectures. Two terms
PMATH 361 Euclidean Geometry
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.
3 hours lectures. One term
PMATH 362 Projective Geometry
Projective spaces over fields, collineations and correlations, quadric curves and surfaces. References to non-euclidean geometries.
Prerequisite: Math 23la/b. 3 hours lectures. One term
PMATH 363 Geometry of the Complex Numbers
The plane of complex numbers. The group of circle preserving mappings and its subgroups. Connections with non-euclidean geometries (Laguerre, Minkowski). Prerequisite: Math 23la/b. 3 hours lectures. One term
PMATH 367 Topology 1
Intuitive set theory, metric spaces, point set topology. 3 hours lectures. One term
PMATH 380A Introduction to Information Theory with Applications
Finite probabilistic schemes. Measures of uncertainty. Shannon's Entropy as a measure of uncertainty and expected information. Maximizing expected information. Applications to problem solving in coding, logics and linguistics.
2 hours lectures, | hour tutorial. One term
PMATH 380B Information Theory with Applications
Measures of expected conditional information. Maximizing expected conditional information.
Applications to communication theory and programming.
Basics in questionnaire theory. Prerequisite: PMath 380a 2 hours lectures, | hour tutorial. One term” «+
PMATH 399 Readings in Pure Math
PMATH 430Y Introduction to Mathematical Logic
An introduction to the logic of sentences and predicates with some emphasis .on familiar algebraic structures. At first informal, then Jeading to a formal axiomatic treatment with proofs of consistency and completeness. Prerequisite: Consent of instructor.
2 hours lectures. Two terms
PMATH 432Y Mathematical Logic
First order languages and theories. A treatment of at least one of the following: set theory, model theory, undecidability. This course is more specialized and at a more advanced level than PMath 430.
2 hours lectures. Two terms.
PMATH 441Y Theory of Numbers
Multiplicative-algebraic theory of numbers. Foundations of natural number theory. Elements of additive-combinatorial number theory.
Corequisite: Math 331 or PMath 341.
2 hours lectures. Two terms
PMATH 443 Linear Algebra 2
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prerequisite: Math 331 or PMath 341.
2 hours lectures. One term
PMATH 444A Lattice Theory 1
Ordered sets, lattices, and Galois connections. Applications in algebra, geometry and logic. Consent of instructor. 2 hours lectures. One term
PMATH 444B Lattice Theory 2
2 hours lectures. One term.
Course Descriptions 327 Pure Mathematics
PMATH 445A Ring Theory 1
Continuation of the theory of rings and modules. Prerequisite: Math 331 or PMath 341.
2 hours lectures. One term
PMATH 445B Ring Theory 2
2 hours lectures. One term
PMATH 446A Group Theory I . Permutations, Cayley Theorem, Sylow Theorem,
Jordan-HGlder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups. Corequisite: Math 331 or PMath 341.
2 hours lectures. One term
PMATH 446B Group Theory 2
Continuation of group theory 1 2 hours lectures. One term
PMATH 447A Field Theory 1
Field extensions and Galois theory. Prerequisite: Math 331 or PMath 341. 2 hours lectures. One term.
PMATH 447B Field Theory 2
2 hours lectures. One term.
PMATH 451A Real Analysis 2a
An introduction to integration and measure theory with emphasis on the real line.
Prerequisite: Math 332a or PMath 351.
2 hours lectures. One term.
PMATH 451B Real Analysis 2b
2 hours lectures. One term.
PMATH 452A Complex Analysis 2a ~
Further properties of holomorphic and meromorphic functions. Riemann surfaces.
Prerequisite: Math 332 or PMath 352.
2 hours lectures. One term
PMATH 452B Complex Analysis 2b
2 hours lectures. One term.
PMath 461, C&O 430 Finite Geometries
Finite incidence structures. Designs. Finite projective and affine planes.
Corequisite: PMath 362. 2 hours lectures. One term
PMATH 462 Foundations of Geometry
An axiomatic treatment of geometry. Geometrical structures, such as projective planes and inversive planes. 2 hours lectures. One term.
PMATH 464 Algebraic Geometry
Anintroduction to the theory of algebraic varieties. Special topics such as the Theorem of Riemann-Roch. Prerequisite: Math 331 or PMath 341. 2 hours lectures. One term
PMATH 465A Differential Geometry 1
Selections from: Differentiable manifolds, Tensors and Forms, Connexions, Riemannian manifolds. Prerequisites: Math 231lalb and Math 230alb.
2 hours lectures. One term
PMATH 465B Differential Geometry 2
2 hours lectures. One term
PMATH 466 Combinatorial Topology
Homology theory or complexes. Theorems of invariance, covering, and duality.
2 hours lectures. Two terms.
PMATH 467 Topology 2
Continuation of general topology; selected topics from other branches of topology.
Prerequisite: PMath 367. 2 hours lectures. One term.
PMATH 470Y Functional Equations
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.
2 hours lectures. Two terms
PMATH 499 Readings in Pure Math
Course Descriptions