This page is exclusively for course notes. Other writings can be found elsewhere. See also the Links page for links to others' course notes.

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I would like to warmly thank the following people for their contributions and insights: Peter Barfuss, Li Chen, Raymond Cheng, Hanci Chi, Erik Crevier, Chad Davis, Chen Fei Du, Sam Eisenstat, Mohamed El Alami, Wei Xi (Victor) Fan, Samuel Harris, Joseph Horan, Andrew (Juno) Jung, Jimmy He, Ehsaan Hossain, Ifaz Kabir, Wei Wei (William) Kong, Winnie Lam, Chao Hsien (Jason) Lin, Yuntao Liu, Blake Madill, Apala Mandal, Kevin Matthews, David McLaughlin, Joël Merk, Yossef Musleh, Mateusz Olechnowicz, Kamal Rai, Ritvik Ramkumar, Samin Riasat, John Charles Saunders, Steven Scott, Dmitry Serbin, David Shi, Artane Jeremie Siad, Peter Sinclair, Hao Sun, Saifuddin Syed, Adam Venis, Eeshan Wagh, Shiyang (George) Wen, Jennifer Yeelam (Jenny) Wong, Rui (Philip) Xiao, Hee Sung Yang, Hanmeng (Harmony) Zhan, Leqi (Jimmy) Zhu, and any others I may have forgotten.

I've taken essentially all undergraduate/graduate PMATH courses at Waterloo. Be sure to check the "random scraps" section at the bottom if you can't find the desired course. If you're wondering who taught a Waterloo course and I was sloppy enough to omit it from the notes, see here. If a course is not listed, feel free to contact me at the address below; I may have some other notes lying around:

adex7ehaiyimocxunpaq (at) gmail (dot) com (remove all vowels from first segment Y IS NOT A VOWEL)

Waterloo course notes (BMath/PMATH+CO)

* Some diagrams in the "Greek geometrical constructions" section are missing.
** Many diagrams missing.

Waterloo course notes (MMath/PMATH)

  • [W15] PMATH 763, Lie Groups and Lie Algebras (Spiro's offering; see here and here)
  • [W15] PMATH 810, Banach Algebras and Operator Theory (Nico's offering; see also here)
    • Some nice notes on C*-algebras etc.
  • [F14] PMATH 940, Topics in Number Theory: p-adic Analysis (Cam's offering; incomplete; see here instead)
  • [F14] PMATH 945, Topics in Algebra: Arithmetic Dynamics (Jason's offering; incomplete)
  • [F14] PMATH 950, Topics in Analysis: Non-Selfadjoint Operator Algebras (Ken's offering; incomplete)
  • [W15] PMATH 965, Topics in Geometry: Kähler–Einstein Metrics on Compact Kähler Manifolds (Reza's offering)

Waterloo course notes (why is this guy still here)

  • [W16] PMATH 965, Topics in Geometry: Gauge Theory (Benoit's offering)
  • [W16] ECE whatever

Montreal course notes (PhD/MATH)

  • [F16] MAST 865, Dynamical Systems
  • [F16] MATH 580, Partial Differential Equations
  • [F16] Abelian Functions and Theta Functions (may appear eventually; see here although they seem to be outdated)
  • [W17] Teichmüller Theory and Moduli of Riemann Surfaces (may appear eventually)
  • [W17] MATH 599, Introduction to Mathematical General Relativity
  • [W17] MAT 6340, Special Topics in Topology and Geometry: Symplectic Topology
    • Contains material on e.g. the h-principle, J-holomorphic curves, Gromov compactness, quantum cohomology
    • You're probably better off reading Audin–Lafontaine or McDuff–Salamon

Random scraps from Waterloo courses

Incomplete/abandoned notes.
  • [F11] AMATH 250, Introduction to Differential Equations
  • [F12] CO 330, Combinatorial Enumeration (rough and incomplete)
  • [F11] CO 355, Mathematical Optimization
  • [W14] CO 367, Nonlinear Optimization
  • [W14] CO 434, Combinatorial Designs
  • [S12] CS 341, Algorithms 1 (discontinued; too annoying to typeset)
  • [W12] CS 365, Models of Computation
  • [S11] PMATH 345, Polynomials, Rings and Finite Fields (use notes above instead)
  • [W12] PMATH 365, Differential Geometry 1
  • [F12] PMATH 433/733, Model Theory and Set Theory
  • [W12] PMATH 444/644, Noncommutative Algebra/Module Theory
  • [W14] PMATH 446/646, Commutative Algebra (see here for W15 offering)
  • [S13] PMATH 450/650, Lebesgue Integration and Fourier Analysis
  • [W13] PMATH 467/667, Algebraic Topology
  • [W14] PMATH 467/667, Algebraic Topology
  • [W13] PMATH 499, Spectral Theory of Operators
  • [W13] PMATH 800, Topics in Real and Complex Analysis: Measure-Theoretic Probability Theory
  • [W14] PMATH 800, Topics in Real and Complex Analysis: Riemann Surfaces
  • [W12] PMATH 900, Topics in Algebra: Special Algebraic Structures
  • [F13] QIC 820, Theory of Quantum Information
  • [F13] PMATH 955, Topics in Geometry: Advanced Algebraic Geometry


  1. Thank you very much for the hard work, the notes are formatted in easy-to-read and minimalist style. Those are very useful.

  2. this is a goldmine. Many thanks for this collection of notes.

  3. Where is the donation button?

    1., thanks a lot!

  4. Thank you so much for your sharing. It gives me a huge help.