Pure Mathematics (PMATH)

22 graduate courses in the Fall 2014 Graduate Calendar, from Waterloo’s archived copy.

← Spring 2014 Winter 2015 →

Older calendars, Fall 2006 to Winter 2024

Year	Fall	Winter	Spring
2023–24	Fall	Winter	Spring
2022–23	Fall	Winter	Spring
2021–22	Fall	Winter	Spring
2020–21	Fall	Winter	Spring
2019–20	Fall	Winter	Spring
2018–19	Fall	Winter	Spring
2017–18	Fall	Winter	Spring
2016–17	Fall	Winter	Spring
2015–16	Fall	Winter	Spring
2014–15	Fall	Winter	Spring
2013–14	Fall	Winter	Spring
2012–13	Fall	Winter	Spring
2011–12	Fall	Winter	Spring
2010–11	Fall	Winter	Spring
2009–10	Fall	Winter	Spring
2008–09	Fall	Winter	Spring
2007–08	Fall	Winter	Spring
2006–07	Fall	Winter	Spring

Terms on uwloo come from Waterloo’s archived copies of the calendar. Where uwloo can’t read a term’s calendar, its course list is Waterloo’s course catalog for that term (UW Open Data). Terms marked ↗ aren’t on uwloo yet: they go to Waterloo’s archive.

PMATH 632 First Order Logic and Computability0.50 units

The concepts of formal provability and logical consequence in first order logic are introduced, and their equivalence is proved in the soundness and completeness theorems. Goedel's incompleteness theorem is discussed; making use of the halting problem of computability theory. Relative computability and the Turing degrees are further studied.

Antireq: PMATH 432

LEC · Course ID 002339Archived page PMATH 632 today

PMATH 641 Algebraic Number Theory0.50 units

An introduction to algebraic number theory; unique factorization, Dedekind domains, class numbers, Dirichlet's unit theorem, solutions of Diophantine equations.

Antireq: PMATH 441

LEC · Course ID 002341Archived page PMATH 641 today

PMATH 646 Introduction to Commutative Algebra0.50 units

Module theory: classification of finitely generated modules over PIDs, exact sequences and tensor products, algebras, localisation, chain conditions. Primary decomposition, integral extensions, Noether's normalisation lemma, and Hilbert's Nullstellensatz.

Antireq: PMATH 446

LEC · Course ID 014670Archived page PMATH 646 today

PMATH 650 Lebesgue Integration and Fourier Analysis0.50 units

Lebesgue measure on the line, the Lebesgue integral, monotone and dominated convergence theorems, LP spaces, completeness and dense subspaces; separable Hilbert space, orthonormal bases; Fourier analysis on the circle, Dirichlet kernel, Riemann-Lebesgue lemma, Fejer's theorem and convergence of Fourier series.

Antireq: PMATH 450

LEC · Course ID 013667Archived page PMATH 650 today

PMATH 651 Measure and Integration0.50 units

General measures, measurability, Caratheodory extension theorem and construction of measures, integration theory, convergence theorems, LP spaces, absolute continuity, differentiation of monotone functions, Radon-Nikodym theorem, product measures, Fubini's theorem, signed measures, Urysohn's lemma, Riesz Representation theorems for classical Banach spaces.

Antireq: PMATH 451

LEC · Course ID 002346Archived page PMATH 651 today

PMATH 652 Topics in Complex Analysis0.50 units

The Riemann mapping theorem and several topics such as analytic continuation, harmonic functions, elliptic functions, entire functions, univalent functions, special functions. Students without the required prerequisite may seek consent of the department.

Prereq: PMATH 352 or consent of department.

LEC · Course ID 002347Archived page PMATH 652 today

PMATH 665 Differential Geometry0.50 units

Point-set topology; smooth manifolds, smooth maps, and tangent vectors; the tangent bundle, vector fields, tensor fields, and differential forms; Stokes's Theorem; integral curves, Lie derivatives, and the Frobenius Theorem.

Antireq: PMATH 465

LEC · Course ID 002349Archived page PMATH 665 today

PMATH 667 Algebraic Topology0.50 units

Review of topological spaces and topological manifolds; quotient spaces; cut and paste constructions; classification of two-dimensional manifolds; fundamental group; homology groups. Additional topics may include: covering spaces; homotopy theory; selected applications to knots and combinatorial group theory.

Antireq: PMATH 467

LEC · Course ID 002350Archived page PMATH 667 today

PMATH 690 Literature and Research Studies0.50 units

Reading Course

Department Consent Required

1 Lie Algebras
2 Topology
3 Representation Theory
4 C*-algebras and groups
5 Integration and Probability
6 Kaehler geometry
7 Smooth Mthds in Algbrc Tpology
8 Oprtr Algebras & q - probablty
9 Class Field Theory

RDG · Course ID 002351Archived page PMATH 690 today

PMATH 733 Model Theory and Set Theory0.50 units

Model theory: the semantics of first order logic including the compactness theorem and its consequences, elementary embedding and equivalence, the theory of definable sets and types, quantifier elimination, and w-stability. Set theory: well-orderings, ordinals, cardinals, Zermelo-Fraenkel axioms, axiom of choice, informal discussion of classes and independence results.

LEC · Course ID 013668Archived page PMATH 733 today

PMATH 740 Analytic Number Theory0.50 units

Summation methods; analytic theory of the Riemann zeta function; Prime Number Theorem; primitive roots; quadratic reciprocity; Dirichlet characters and infinitude of primes in arithmetic progressions; assorted topics.

Antireq: PMATH 440

LEC · Course ID 013669Archived page PMATH 740 today

PMATH 745 Representations of Finite Groups0.50 units

Basic definitions and examples: subrepresentations and irreducible representations, tensor products of representations. Character theory. Representations as modules over the group ring, Artin-Wedderburn structure theorem for semisimple rings. Induced representations, Frobenius reciprocity, Mackeys irreducibility criterion.

Antireq: PMATH 445

LEC · Course ID 014343Archived page PMATH 745 today

PMATH 753 Functional Analysis0.50 units

Banach and Hilbert spaces, bounded linear maps, Hahn-Banach theorem, open mapping theorem, closed graph theorem, topologies, nets, Hausdorff spaces, Tietze extension theorem, dual spaces, weak topologies, Tychonoff's theorem, Banach-Alaoglu theorem, reflexive spaces.

Antireq: PMATH 453

LEC · Course ID 013670Archived page PMATH 753 today

PMATH 763 Introduction to Lie Groups and Lie Algebras0.50 units

An introduction to matrix Lie groups and their associated Lie algebras: geometry of matrix Lie groups; relations between a matrix Lie group and its Lie algebra; representation theory of matrix Lie groups.

LEC · Course ID 002391Archived page PMATH 763 today

PMATH 764 Introduction to Algebraic Geometry0.50 units

An introduction to algebraic geometry through the theory of algebraic curves. General algebraic geometry: affine and projective algebraic sets, Hilbert's Nullstellensatz, co-ordinate rings, polynomial maps, rational functions and local rings. Algebraic curves: affine and projective plane curves, tangency and multiplicity, intersection numbers, Bezout's theorem and divisor class groups.

Antireq: PMATH 464

LEC · Course ID 002392Archived page PMATH 764 today

PMATH 810 Banach Algebras and Operator Theory0.50 units

Banach algebras, functional calculus, Gelfan transform, Jacobson radical, Banach space and Hilbert space operators, Fredholm alternative, spectral therorem for compact normal operators, ideals in C^*-algebras, linear functionals and states, Gelfand-Naimark-Segar (GNS) construction, von Neumann algebras, strong/weak operator topologies, Double Commutant theorem, Kaplansky's density theorem, spectral theorem for normal operators.

Prereq: PMATH 753

LEC · Course ID 011875Archived page PMATH 810 today