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 833: Harmonic Analysis (Parts II & III synthesized)

Two synthetic extensions built on top of the abstract harmonic analysis that PMATH 833 actually teaches. Part II (geometric harmonic analysis): oscillatory integrals and the van der Corput lemma, the Hardy-Littlewood maximal function and Calderón-Zygmund theory, the Fourier restriction conjecture, Kakeya sets and Besicovitch’s needle problem, wave packet decomposition, the polynomial method, and the 2024 resolution of the three-dimensional Kakeya conjecture by Hong Wang and Joshua Zahl. Part III (discrete harmonic analysis): the Hardy-Littlewood circle method, Gauss sums and the major/minor arc decomposition of \(\mathbb{T}\), Weyl’s inequality as the discrete analogue of van der Corput differencing, discrete Radon transforms (Stein-Wainger 2001), and Bourgain’s theorem (1988–1990) on almost everywhere convergence of polynomial ergodic averages \((1/N)\sum f(T^{P(n)}x) \to \int f\,d\mu\) for all \(p > 1\) and all measure-preserving systems.

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.

MUSIC 144: History of Musical Theatre

From minstrelsy, vaudeville, operetta, and Tin Pan Alley through Show Boat, Rodgers and Hammerstein, Bernstein, Sondheim, rock musicals, megamusicals, Disney, and Hamilton, then across the Pacific to the rise of Mandarin musical theatre, Super-Vocal, and post-2018 original Chinese works. The notes also include synthetic chapters on musicals versus pop music, musicals versus opera, and a comparative toolkit for analyzing musical numbers.

MUSIC 272: Counterpoint and Fugue

Species counterpoint in two through four voices (Fux’s five species), tonal counterpoint in the Bach style, invertible counterpoint, canon, and fugue — subject, answer, countersubject, exposition, episodes, stretto, and the complete fugue in C minor from WTC I as a model analysis.

MUSIC 273: Jazz Theory and Harmony

Jazz chord symbols and voicings, ii–V–I progressions in major and minor, tritone substitution, backdoor dominants, chord extensions (9th, 11th, 13th), altered dominants, modes for improvisation (Dorian, Mixolydian, Lydian dominant, altered scale, half-whole diminished), blues harmony, rhythm changes, modal jazz, reharmonization, and the bebop vocabulary.

MUSIC 276: Psychoacoustics and the Science of Musical Sound

The auditory system, pitch perception (place vs. temporal theory, virtual pitch), timbre and auditory stream analysis, loudness, masking and critical bands, consonance and dissonance from Helmholtz to Sethares, room acoustics and concert hall design, physical instrument acoustics, and the perceptual basis of musical structure.

MUSIC 277: Popular Music Theory and Analysis

Harmonic schemas in pop and rock (I–V–vi–IV, Aeolian loop, Andalusian cadence), modal mixture, phrase structure and formal analysis of songs, verse-chorus and AABA form, groove and rhythmic feel, timbral analysis of recordings, and analytical methods for hip-hop, R&B, EDM, and country.

MUSIC 278: Electronic Music: History and Aesthetics

Musique concrète (Schaeffer, Henry), elektronische Musik (Stockhausen, Eimert), tape music at the Columbia-Princeton Electronic Music Center, early computer music (Hiller, Xenakis), voltage-controlled synthesis (Moog, Buchla), spectral music (Murail, Grisey), laptop performance, glitch and noise aesthetics.

MUSIC 279: Sound Synthesis and Music Production

Synthesis paradigms (subtractive, FM, additive, wavetable, granular, physical modelling, sampling), synthesizer architecture (oscillators, filters, envelopes, LFOs, modulation routing), the professional production pipeline from pre-production through mastering, beat programming, vocal production, mixing for the small studio, and critical listening.

MUSIC 373: Form and Musical Analysis

Phrase structure (sentences and periods), small forms (binary, ternary, rondo), theme and variations, sonata form using Caplin’s formal functions and Hepokoski-Darcy’s dialogic sonata theory, concerto form, 19th-century formal expansion, and 20th-century form from Bartók to Reich.

MUSIC 375: Songwriting: Analysis and Craft

Song form architecture (AABA, verse-chorus, pre-chorus, bridge), melodic hook design and contour, lyric craft (rhyme, prosody, imagery, narrative arc), harmonic schemas of popular song, arrangement as compositional tool, and detailed formal analysis of songs across Tin Pan Alley, rock, country, R&B, hip-hop, and musical theatre.

MUSIC 377: Post-Tonal Music Theory

Pitch-class sets and Forte’s classification, interval vectors, Z-relations and complementation, the twelve-tone matrix and its four forms, combinatoriality and rotational arrays (Babbitt, Schoenberg, Webern), total serialism (Boulez), stochastic composition (Xenakis), transformational theory (Lewin’s GIS), and Neo-Riemannian theory (PLR operations, the tonnetz).

MUSIC 670: Musicology Research Methods and Scholarly Writing

Archival research, manuscript sources and RISM/RILM/Grove, source criticism and philology (stemma codicum, critical editions), historiography and critical methodology, digital musicology (music21, Humdrum, corpus analysis), scholarly writing (journal articles, conference papers, grant applications), and dissertation prospectus development.

MUSIC 672: Schenkerian Analysis

Schenker’s theory of structural levels (Hintergrund, Mittelgrund, Vordergrund), the Ursatz (Urlinie and Bassbrechung), prolongational techniques (neighbor notes, linear progressions, unfolding, register transfer), interruption and the two-part structure, motivic parallelism across levels, and complete-movement analyses of Bach, Beethoven, Chopin, and Brahms.

MUSIC 674: History of Music Theory

Pythagorean ratio theory, Aristoxenus’s empiricism, Boethius and the medieval quadrivium, Guido’s hexachords, Zarlino’s senario and just intonation, Rameau’s basse fondamentale and chord inversion, Riemann’s Funktionslehre, Schenker’s organicism, Forte’s set theory, Lewin’s transformational theory, and Neo-Riemannian analysis.

MUSIC 675: Critical Musicology and Cultural Theory

New Musicology and the cultural turn (Kerman, Kramer), feminist musicology (McClary, Citron), race and musical imagination (Radano, Eidsheim), postcolonial musicology (Agawu, Born), queer musicology (Brett, Wood), disability and music (Straus), Adorno and the culture industry, sound studies (Sterne, Schafer), and intersectional approaches.

MUSIC 676: Ethnomusicological Methods and Fieldwork

Merriam’s tripartite model, Rice’s revised framework, Turino’s Peircean semiotics, bi-musicality (Hood), participant observation and ethnographic fieldwork, audio and video documentation, transcription and analysis of non-Western repertoires, interview methods, ethics, positionality, repatriation, and writing ethnomusicography.

MUSIC 678: Music Theory Pedagogy

Learning theory applied to music (constructivism, threshold concepts, cognitive load), curriculum design and backward design, teaching tonal harmony and counterpoint, aural skills pedagogy (fixed-do vs. movable-do, Karpinski’s audiation), assessment and rubric design, inclusive pedagogy, universal design for learning, and the theory classroom as a creative space.

Applied Mathematics

AMATH 464: Solid Mechanics

A comprehensive engineering solid-mechanics continuation of amath361. Covers 3D stress and strain, Mohr’s circle and rosettes, axial loading and thermal stress, torsion (circular, non-circular, thin-walled closed and open sections, warping), bending (symmetric, unsymmetric, composite, curved, plastic), shear stress and shear centre, beam deflections (double integration, Macaulay brackets, moment-area, conjugate beam, superposition), energy methods (Castigliano, virtual work, Maxwell-Betti, least work), statically indeterminate structures (flexibility, stiffness, three-moment), column buckling (Euler, Perry-Robertson, secant, Rayleigh-Ritz, lateral-torsional, shell), beams on elastic foundations, plane elasticity and the Airy stress function, Kirchhoff plate theory, failure criteria (Tresca, von Mises, Mohr-Coulomb, Drucker-Prager, Hill), pressure vessels and thick-walled cylinders (Lamé, autofrettage), crack-tip fields and LEFM (Westergaard, K-factors, J-integral, Paris), thermoelasticity, plasticity (flow rules, hardening, limit analysis, slip-lines, shakedown), fatigue and damage tolerance, anisotropic and composite materials (laminate theory, Tsai-Wu), experimental stress analysis (gauges, photoelasticity, DIC), finite element preview, Hertz contact mechanics, and dynamic/impact loading. Material taught across ME 220, AE 204/205, CIVE 204/205/306, BME 553, MTE 219, SYDE 286, and NE 318 at Waterloo.

AMATH 791: Inverse Problems and Data Assimilation

The mathematical theory of recovering unknown parameters, initial conditions, or forcing terms from indirect, noisy observations. The notes cover regularization theory (Tikhonov, iterative methods), the Bayesian formulation of inversion (including Stuart’s well-posedness theorem), MCMC methods, and data assimilation (Kalman filtering, 3D-Var, 4D-Var).

AMATH 843: Integral Equation Methods for PDEs

Boundary integral equations reformulate PDEs as equations on lower-dimensional boundaries. The notes cover potential theory, Fredholm theory, Nyström and collocation methods, singular and hypersingular quadrature, and fast algorithms (the fast multipole method), with applications to acoustic scattering, Stokes flow, and electromagnetics.

AMATH 844: Homogenization and Multiscale Methods

Asymptotic homogenization of PDEs with rapidly oscillating coefficients: two-scale expansions, cell problems, effective coefficients, H-convergence and two-scale convergence, stochastic homogenization, Hashin-Shtrikman bounds, and computational multiscale methods (HMM, MsFEM).

AMATH 845: Combustion Theory and Reactive Flows

Reaction-diffusion equations with Arrhenius kinetics, premixed and diffusion flames, laminar flame speed via the Zeldovich-Frank-Kamenetskii analysis, activation energy asymptotics, ignition and extinction (Semenov theory, S-curve), detonation waves (Chapman-Jouguet and ZND theory), flame instabilities (Darrieus-Landau, Sivashinsky equation), and computational combustion.

AMATH 848: Biological Fluid Dynamics

Low-Reynolds-number hydrodynamics and the scallop theorem, swimming of microorganisms (resistive force theory, slender body theory, Taylor’s swimming sheet), flagellar and ciliary propulsion, blood flow and hemodynamics (Womersley flow, pulse wave propagation), non-Newtonian blood rheology, pulmonary mechanics, biofilm dynamics, and collective locomotion in active suspensions.

AMATH 852: Mathematical Geophysics and Seismic Wave Propagation

Elastic wave equations in heterogeneous media, P-wave and S-wave decomposition, surface waves (Rayleigh, Love), ray theory and the eikonal equation, normal mode theory for the Earth, earthquake source mechanics (moment tensors, radiation patterns), seismic tomography as an inverse problem, and computational seismology (spectral element methods, perfectly matched layers).

AMATH 858: Free Boundary Problems and Phase Transitions

The Stefan problem for solidification and melting, Hele-Shaw flows and Saffman-Taylor instability, morphological instability (Mullins-Sekerka), mushy-zone theory for alloy solidification, variational inequalities and the obstacle problem (Caffarelli regularity theory), phase-field models (Allen-Cahn, Cahn-Hilliard) and their sharp-interface limits, and level set methods for interface tracking.

AMATH 860: Kinetic Theory and Transport Equations

From particle systems to distribution functions: the Boltzmann equation, H-theorem, Chapman-Enskog expansion deriving Euler and Navier-Stokes as hydrodynamic limits, the Vlasov equation and Landau damping, moment methods and closures, and numerical methods (DSMC, spectral methods, asymptotic-preserving schemes).

AMATH 865: Geophysical Fluid Dynamics

The dynamics of rotating and stratified fluids applied to the ocean and atmosphere: geostrophic balance, shallow water theory, Rossby waves, quasi-geostrophic dynamics, baroclinic and barotropic instability, Ekman layers and wind-driven ocean circulation, and equatorial wave dynamics.

AMATH 866: Magnetohydrodynamics and Plasma Physics

The mathematical theory of electrically conducting fluids: derivation and structure of the MHD equations, Alfvén’s frozen-in flux theorem, MHD wave modes, the Grad-Shafranov equation for axisymmetric equilibria, the energy principle for MHD stability, magnetic reconnection (Sweet-Parker and Petschek models), dynamo theory, and kinetic corrections (CGL theory, gyrokinetics).

AMATH 883: Mathematical Epidemiology and Population Dynamics

Compartmental models (SIR, SEIR, SIS) and the basic reproduction number \(R_0\), stability analysis and bifurcations of disease equilibria, age-structured models and the next-generation operator, spatial spread via reaction-diffusion equations and traveling waves, stochastic epidemic models, and classical population dynamics (predator-prey, competition, functional responses).

Philosophy

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

Written in Chinese. Several real Chinese-internet controversies (plus a cross-language elite-discourse case) from 2016–2026 dissected in great detail across multiple aspects: source provenance with timelines and stakeholder analysis, fact-check tables with verifiable citations, reconstruction of unstated premises, ARG-framework evaluation (Acceptability / Relevance / Grounds), fallacy identification at three layers (surface / structural / rhetorical-strategy), charitable interpretation, and multidisciplinary dialectical conclusions drawing on sociology, philosophy, psychology, political economy, media studies, and legal philosophy. Later cases include an identification-and-communication section on how to recognize the embedded logical traps and how to respond constructively to interlocutors who deploy them.

PHIL 145c — Discourse Analysis (Chinese)

Written in Chinese. A topical extension of PHIL 145c that shifts the analytical object from a single text to a corpus of nearly 200 simultaneous answers under one Zhihu question — “which country supports China the most?” The notes develop a new bucket-then-evaluate framework: every answer is sorted into one of seven mutually exclusive buckets, each bucket gets a typical argument skeleton plus an ARG evaluation table plus one most-explanatory social theory, and the chapter opens with an inline SVG distribution chart. A long meta-chapter analyzes the “美国间谍” / “美分” accusation pattern as five stacked fallacies (情境型 ad hominem, genetic, motive, poisoning the well, unfalsifiable conspiracy) and through seven social theories (Kahan identity-protective cognition with the 2007 J. Empirical Legal Studies paper, Kunda motivated reasoning, Whitson–Galinsky 2008 Science on illusory pattern perception, van Prooijen on the three triggers of conspiratorial sense-making, Tajfel + Goffman, Festinger, Han Rongbin on 自干五). Comparative chapters draw on Katzenstein–Keohane’s anti-Americanism typology, Susan Shirk’s 2008-turn argument, Pomfret’s “Buddhist cycle” of US-China relations, Iriye’s “inner history” framework, and a parallel Western-platform chapter showing the same shill-accusation pattern operates on Reddit (r/Sino, r/genzedong), Quora, and X — covering Russiagate, the COVID lab-leak reversal, and 2023 Israel-Hamas Reddit polarization. A closing methodological chapter takes up Mill on liberty, Popper on the open society, and Habermas on the ideal speech situation as standards for what critical thinking can mean in an asymmetric discursive environment.

Psychology

PSYCH 099: The Algorithmic Self — Popular Psychology, Psychoanalysis, and Existentialism on Chinese Short-Video Platforms

A fourteen-chapter critical-analysis course that uses two specific Douyin creators — 小五狼 and 雨宸 — as a sustained primary corpus. The psychoanalytic tradition is covered in depth across the first half: object relations (Klein, Fairbairn, Winnicott, Fonagy), attachment theory (Bowlby, Ainsworth, Mikulincer–Shaver), self psychology (Kohut), and personality disorders (DSM-5-TR alongside the AMPD dimensional alternative). Personality typology occupies its own chapter — Jung’s Psychological Types, MBTI’s drift from its source, and the Big Five as the current empirical consensus. The second half broadens: Adler’s individual psychology and its Japanese popularization; cognitive psychology and the 内耗 (internal consumption) discourse; existentialism from Kierkegaard through Sartre and Camus; the algorithmic psychologization of Chinese classics (Wang Yangming, Laozi, Buddhist thought); gender, mating theory, and the incel debate; and a demarcation chapter on quantum consciousness, NDEs, and manifestation rhetoric. A full comparative chapter examines Western short-video psychology — TikTok-induced functional disorders, the therapy-speak debate, Haidt’s The Anxious Generation, and close readings of fourteen English-language videos — set against the Chinese material throughout. Throughout every chapter, a recurring section isolates what the short-video version systematically loses when compressing its source.

PSYCH 254: Psychology of Persuasion

A stand-alone course on attitude change and compliance, continuing where social psychology leaves off. The notes cover the Yale communication programme, cognitive dissonance, the elaboration likelihood and heuristic-systematic models, Cialdini’s compliance principles, resistance and inoculation, narrative persuasion, and the ethics of influence. Anglophone research is read alongside the Chinese rhetorical tradition — Guiguzi, Confucian renqing and face, Legalist incentive theory, and contemporary debate-competition pedagogy (黄执中) — as a co-equal body of thinking about how one mind moves another.

PSYCH 358: Psychology of Dating

A comparative psychology course on heterosexual dating across mainland Chinese and Anglosphere Western cultures. The notes treat attraction, attachment, gendered expectations, family pressure, sexual timing, jealousy, apps, breakup psychology, and the historical transition from older courtship systems to contemporary dating. Equal weight is given to Chinese and Western cases, and the emphasis stays analytical rather than tactical: not how to date, but what dating reveals about male and female psychology under changing institutions.

PSYCH 359: The Psychology of Romantic Love

A course organised around romantic love as a specific psychological state — not around the relationships that contain it. The notes cover Sternberg’s triangular theory, Hatfield and Berscheid on passionate versus companionate love, Fisher’s neurobiological model, Aron’s self-expansion theory, Hazan and Shaver on adult attachment, Tennov on limerence, and Lee’s love styles, alongside the cross-cultural literature establishing love’s near-universality and a serious treatment of Chinese-language concepts (缘分, 暧昧, 一见钟情, 心动) that carve romantic experience at joints Anglophone psychology rarely notices. Humanities sources — Plato, Stendhal, Barthes, bell hooks, Illouz — are read as genuine observations, not as literary decoration.

PSYCH 360: Criminal Psychology

A comparative criminal-psychology course covering the developmental, clinical, and social roots of offending; the psychology of the criminal-justice process (eyewitness memory, false confessions, juror decision-making, risk assessment); psychopathy and antisocial personality; violent and sexual offending; and rehabilitation. The Anglo-American forensic-psychology tradition (Bartol, Andrews & Bonta, Raine, Hare, Loftus) is read alongside mainland Chinese criminal psychology (犯罪心理学) as a co-equal case: inquisitorial rather than adversarial procedure, professional judges rather than lay juries, and a more centralized state role in defining both crime and rehabilitation. Explicitly not a true-crime course.

Sociology

SOC 418: Gender Conflict, Sexual Politics, and Online Public Discourse

A sociology course built out of the kind of internet argument that PHIL 145C can diagnose but not fully explain. The notes treat online gender conflict in Chinese digital publics as a problem of gender order, social reproduction, platform governance, emotional labour, sexual scripts, moral regulation, and identity-protective cognition, with comparative chapters on South Korea, Japan, North America, and Europe. The course moves from a recognizable discourse case into a full research-driven sociology of how antagonism is produced, circulated, and normalized.

SOC 431: Education, Credentialism, and Social Mobility

A synthetic upper-year sociology course on educational expansion, credential inflation, family strategy, labor-market sorting, housing pressure, and the emotional life of blocked mobility. The notes are China-led but comparative, connecting gaokao competition, elite-university hierarchy, youth precarity, and “学历贬值” discourse to the wider sociology of reproduction, meritocracy, signaling, and status closure. The course asks why education remains socially indispensable even as its mobility promises become unstable.

Rotating-Topics Composites (-rest)

The -rest notes below are not single courses. Each is a synthetic composite that stitches together several offerings of a UW rotating-topics graduate course — one whose subject matter changes every term — into one coherent textbook-style document. The courses themselves exist; the unified narrative, the chapter-by-chapter compression, and the cross-references between offerings are invented here. For any given term, only one of the chapters in a -rest file corresponds to the course as actually taught; the other chapters describe what was taught in other terms. These notes are written for the reader who wants a map of the subject’s rotation across recent years, not for the reader studying for a specific final.

CO 739: Topics in Combinatorics

Seven instances synthesized: stable polynomials, combinatorics of Feynman diagrams, Hopf algebras and renormalization, topological combinatorics, information theory, combinatorial algebraic geometry, and a pointer to the Yeats orthogonal-polynomials offering.

CO 749: Topics in Graph Theory

Geelen’s Fall 2016 lecture course on the Robertson–Seymour graph minors structure theorem, together with a pointer to the Fall 2024 follow-up.

CO 759: Topics in Discrete Optimization

Six instances synthesized: Cheriyan’s Spring 2014 on spectral methods, Cook’s Winter 2015 on computational discrete optimization, Fukasawa’s Winter 2016 on integer programming, Cook’s Winter 2018 on deep learning from an optimization perspective, Fall 2019 on optimization under uncertainty, and Spring 2024 on approximation algorithms and hardness.

CO 769: Topics in Continuous Optimization

Two deeply developed instances: Wolkowicz’s Winter 2016 course on facial reduction in semidefinite programming, and optimal transport (following the modern Villani / Santambrogio / Peyré–Cuturi literature).

CO 781: Topics in Quantum Information

Two Debbie Leung offerings on quantum error correction and fault-tolerant quantum computation, developed through the standard public literature (Nielsen–Chuang, Gottesman, Kitaev, Fowler–Mariantoni–Martinis–Cleland, Terhal, Watrous).

PMATH 930: Topics in Logic

Six instances synthesized across the Moosa / Willard / Zucker offerings: model theory of fields with operators, difference fields, universal algebra, countably infinite Ramsey theory, differential fields II, and the Fall 2025 geometric stability theory offering.

PMATH 940: Topics in Number Theory

Seven instances: Wang’s elliptic curves, three Stewart offerings (Diophantine equations, geometric number theory, Diophantine geometry), Rubinstein’s analytic number theory, Liu’s analytic Diophantine geometry, and the Winter 2026 Fermat’s Last Theorem course.

PMATH 945: Topics in Algebra

Seven instances: Jason Bell (algebraic constructions / rings / category theory), Slofstra (non-local games), Paulsen (operator-algebraic QIT), Karigiannis (Clifford algebras and spin geometry), and the Fall 2026 arithmetic-dynamics course.

PMATH 950: Topics in Analysis

Seven instances on tensor products of C*-algebras, operator algebras and dynamics, quantum representation theory, convex geometric analysis, II₁ factors and subfactor theory, Choquet theory, and operator systems.

PMATH 965: Topics in Geometry and Topology

Nine instances: holonomy groups, deformation theory, algebraic stacks, rational homotopy theory, harmonic maps, spin geometry, higher and derived stacks, gauge theory, and motivic integration.

PMATH 990: Topics in Pure Mathematics

Three densely developed instances: Paulsen’s Winter 2021 course on functional analysis methods for quantum information, Slofstra’s Winter 2022 course on MIP* and quantum complexity, and Nica’s Winter 2023 course on non-commutative random variables and free probability.