Made-Up Courses

These are courses that do not exist at the University of Waterloo — at least not under these names or in quite this form. The subject matter is real mathematics, music history, or critical thinking; the course number and syllabus are invented. Each entry below gives the course title, a short description of what it covers, and a note on why this particular gap was worth filling fictionally.

Pure Mathematics

PMATH 841: Class Field Theory

The crowning theorem of classical algebraic number theory: every abelian extension of a number field is determined by congruence conditions, and the Galois group is canonically isomorphic to a quotient of an idèle class group. The notes cover local and global reciprocity laws, the Artin map, class formations, and the idèlic formulation.

PMATH 842: Automorphic Forms and the Langlands Program

Modular forms as automorphic representations of GL(2), local representation theory over p-adic and archimedean fields, L-functions and their functional equations, and a panoramic view of the Langlands correspondence. The notes build carefully from classical modular forms to the adèlic reformulation.

PMATH 847: Geometric Representation Theory

Representations of Lie algebras realised as geometric objects: the Borel–Weil–Bott theorem, Beilinson–Bernstein localisation, D-modules on flag varieties, perverse sheaves, and the geometric proof of the Kazhdan–Lusztig conjecture. Algebra, algebraic geometry, and topology woven together.

PMATH 852: Several Complex Variables and Hodge Theory

Holomorphic functions of several variables, the ∂̄-operator and Dolbeault cohomology, Kähler manifolds, and the Hodge decomposition theorem. The notes also cover the Hard Lefschetz theorem and the Kodaira vanishing theorem.

PMATH 855: Microlocal Analysis

Pseudodifferential operators, the symbol calculus, wavefront sets, propagation of singularities for hyperbolic equations, and semiclassical analysis. The approach follows Hörmander and Zworski, with applications to spectral theory and scattering.

PMATH 856: Geometric Measure Theory

Hausdorff measure, rectifiable sets, the area and coarea formulas, sets of finite perimeter, currents, and the regularity theory for area-minimising surfaces. The notes address Plateau’s problem and the techniques that underlie its solution.

PMATH 864: Infinite-Dimensional Lie Algebras and Vertex Algebras

Kac–Moody algebras and their root systems, the Virasoro algebra, highest-weight representations, the Weyl–Kac character formula, and vertex operator algebras as the mathematical language of two-dimensional conformal field theory.

PMATH 867: Geometric Group Theory

Cayley graphs, quasi-isometries, the Švarc–Milnor lemma, hyperbolic groups in the sense of Gromov, CAT(0) spaces, ends of groups, and the large-scale geometry of lattices in Lie groups.

PMATH 869: Knot Theory and Low-Dimensional Topology

Knot diagrams and Reidemeister moves, the knot group, Seifert surfaces and genus, the Alexander polynomial, the Jones polynomial via the Kauffman bracket, Khovanov homology, and an introduction to 3-manifold topology and Thurston’s geometrisation.

Combinatorics and Optimization

CO 740: Additive Combinatorics

Additive structure in abelian groups: Freiman’s theorem and the structure of sets with small doubling, the Balog–Szemerédi–Gowers theorem, Fourier analytic methods, the cap-set problem, and Szemerédi’s theorem on arithmetic progressions.

CO 741: Extremal Combinatorics and Ramsey Theory

Turán-type problems, the Kruskal–Katona theorem, the Bollobás set-pairs inequality, Ramsey numbers and their bounds, Ramsey multiplicity, Hales–Jewett, and the probabilistic method as a systematic tool.

CO 743: Discrete and Computational Geometry

Convexity, Carathéodory–Radon–Helly theorems, polytope combinatorics, Voronoi diagrams, Delaunay triangulations, point-location, epsilon-nets, and the polynomial method applied to combinatorial geometry problems.

CO 760: Online Algorithms and Competitive Analysis

The competitive ratio framework, ski rental and rent-or-buy problems, paging and the k-server conjecture, online matching, the secretary problem, and primal-dual techniques for online algorithm design.

CO 770: Polynomial Optimization and Sum-of-Squares

Nonnegative polynomials and sums of squares, Hilbert’s 17th problem, the Positivstellensatz, the Lasserre SDP hierarchy, moment problems, and applications to combinatorial optimisation and control theory.

Music

MUSIC 141: Popular Music After 1980

A direct continuation of MUSIC 140 (Simon Wood, UW): MTV and the visual turn, Michael Jackson, Madonna, hip-hop from the Bronx to global dominance, electronic dance music, alternative and grunge, and the internet’s disruption of the music industry.

MUSIC 142: Popular Music in Other Cultures

Japanese city pop, enka, and the idol system; Korean pop from trot to K-pop; Bollywood and Indian film music; Latin pop and reggaeton; Southeast Asian popular traditions. Each is treated as a living culture with its own internal logic, not as an exotic supplement to the Western canon.

MUSIC 143: The Other Side of the Record

Country, gospel, jazz (beyond the swing chapter in MUSIC 140), reggae, progressive rock, singer-songwriters, and African popular music — the traditions that outsold or outlasted rock but were marginalised by a textbook organised around the “blues-to-rock-to-punk” spine.

Philosophy

PHIL 145c: Critical Thinking — Case Studies (Chinese)

Three real Chinese internet controversies from 2025–2026 dissected using the argument-analysis tools from PHIL 145: source evaluation, reconstruction of unstated premises, fallacy identification (ad hominem, strawman, appeal to authority), and charitable interpretation.