PMATH 230 Introduction to Pure MathematicsY 2C,1T 1
Examples and results in modern geometry, number theory and analysis; the historical sources of modern mathematics.
Pure Mathematics (PMATH)
36 courses in the 1977–78 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 341 AlgebraY 3C 1
Fundamentals of group, ring, field theory, and other algebraic structures.
Coreq: Math 231
PMATH 351 Real Analysis 1Y 2C,1T 4
Theory of functions of real variables. The notions of compactness, connectedness, and uniformity are used in a study of continuity, differentiation, and integration. Prereq: Math 230
PMATH 352 Complex Analysis 1Y 2C,1T 1
Analysis of complex numbers; fundamental theorems of holomorphic functions; meromorphic functions. Prereq: Math 230
PMATH 361 Euclidean GeometryF 3c 0.5
Concurrent lines, collinear points, the Euler fine, the Simson line, the nine-point circle. Cross ratio, projection, harmonic range, the quadrilateral and the quadrangle. Properties of circles.
PMATH 362 Projective GeometryF 3C 0.5
Projective spaces over fields, collineations and correlations, quadric curves and surfaces. References to non-euclidean geometries.
Prereq: Math 231
PMATH 363 Geometry of the Complex Numbers |W 3C 0.5
The plane of complex numbers. The group of circlepreserving mappings and its subgroups. Connections with non-euclidean geometries (Laguerre, Minkowski). Prereq: Math 231
PMATH 365 Elementary Differential Geometry and Tensor Analysis Curves in Euclidean 3-space (€*) and the Serret-Frenet/AM 362 F 2C,1T 5 ;
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
PMATH 367 TopologyF 3C 0.5
Intuitive set theory, metric spaces, point set topology.
PMATH 399 Readings in Pure Math
PMATH 430 Introduction to Mathematical LogicF,W,S 2c 1
An introduction to the logic of sentences and predicates with some emphasis on familiar algebraic structures. At first informal, then leading to a forma! axiomatic _ treatment with proofs of consistency and completeness. Prereq: Consent of instructor
PMATH 432 Mathematical LogicY 2c 1
First order languages and theories. A treatment of at least one of the following: set theory, mode! theory, undecidability. This course is more specialized and ata more advanced level! than P Math 430.
PMATH 441A Theory of Numbers 1F 2c 0.5
Multiplicative-algebraic theory of numbers. Foundations of natural number theory. Elements of additivecombinatorial number theory.
Coreq: Math 331 or P Math 341
PMATH 441B Theory of Numbers 2W 2c 0.5
Continuation of Theory of Numbers 1 Prereq: P Math 441a
PMATH 443 Linear Algebra 2F 2C 0.5
Continuation of linear algebra. Main topics: representations of endomorphisms, structure of bilinear forms, multilinear products.
Prereq: Math 331 or P Math 341
PMATH 444A Lattice Theory 1F 2c 0.5
Ordered sets, lattices, and Galois connections. Applications in algebra, geometry and logic. Prereq: Consent of instructor
Course Descriptions Pure Mathematics
PMATH 444B Lattice Theory 2W 2C 0.5
Continuation of Lattice Theory 1 Prereq: P Math 444a
PMATH 445A Ring Theory 12C 5
Continuation of the theory of rings and modules. Prereq: P Math 331 or P Math 341
PMATH 445B Ring Theory 22c 5
Continuation of Ring Theory 1 Prereq: P Math 445a
PMATH 446A Group Theory 1F 2c 0.5
Permutations, Cayley Theorem, Sylow Theorem, Jordan-Holder Theorem, nilpotent and solvable groups, direct and semidirect products, free groups.
Coreq: Math 331 or P Math 341
PMATH 446B Group Theory 2W 2c 0.5
Continuation of Group Theory 1 Prereq: P Math 446a
PMATH 447A Field Theory 12C 5
Field extensions and Galois theory. Prereq: Math 337 or P Math 341
PMATH 447B Field Theory 22C 5
Continuation of Field Theory 1 Prereq: P Math 447a
PMATH 451A Real Analysis 2aF 2c 0.5
An introduction to integration and measure theory with emphasis on the rea! line.
Prereq: Math 332a or P Math 351
PMATH 451B Real Analysis 2bW 2c 0.5
Continuation of Real Analysis 2a. Prereq: P Math 451a
PMATH 452A Complex Analysis 2aF 2c 0.5
Further properties of holomorphic and meromorphic functions. Riemann surfaces.
Prereq: Math 332b or P Math 352
PMATH 452B Complex Analysis 2b ' Continuation of Complex Analysis 2aW 2c 0.5
Prereq: P Math 452a
PMATH 461 Finite GeometriesW 2c 0.5
Finite incidence structures. Designs. Finite projective and affine planes.
Coreq: P Math 362
PMATH 462 Foundations of Geometry
Listed without a description.
PMATH 463 Introduction to Differentiable Manifolds/AM 463 F 20,1T 5
Differentiable manifolds, vector fields, linear connections, tensor fields, differential forms and structure equations.
Prereq: P Math 365/AM 362 or consent of instructor
PMATH 464 Algebraic GeometryW 2c 0.5
An introduction to the theory of algebraic varieties. Special topics such as the Theorem of Riemann-Roch. Prereq: Math 331 or P Math 341
PMATH 465 Introduction to Riemannian ManifoldsW 2C,1T 0.5
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
PMATH 466 Combinatorial! Topology
Listed without a description.
PMATH 467 Topology 2W 2c 0.5
Continuation of general topology; selected topics from other branches of topology.
Prereq: P Math 367
PMATH 470 Functional EquationsY 2C 1
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.
PMATH 499 Readings in Pure Math
Course Descriptions 365