(Disclaimer: This is old material, mostly from various expository projects which I subsequently abandoned. Much of it is unfinished, incomplete, and probably full of errors; caveat lector. In retrospect, some of the pedagogical philosophy is somewhat naïve. If I were rewriting this material now, I would do some things quite differently. I am making this material available for archival purposes, because people still occasionally ask for it.)

• Linear Partial Differential Equations and Fourier Theory (2010, published textbook).

• Visual Abstract Algebra(2003; 240 page working draft)

• Analysis, Measure & Probability:A visual Introduction (2004; 181 page working draft)

• Lecture notes in Linear Algebra (2000, lecture notes for a course I taught at the University of Toronto)

  • • Linear Transformations

    • Kernels, Images, Injectivity, Surjectivity

    • Determinants

    • Eigenvectors and Eigenvalues

    • Change of Basis

    • Matrix Representations

    • Matrix Similarity

    • Diagonalization

    • Orthogonal Transformations

    • Orthogonal Diagonalization

    • Quadratic Forms

• Classification of Cellular Automata (2002; 44 page booklet for an informal seminar on cellular automata at the University of Houston).

• Voting, Arbitration, and Fair Division:the mathematics of social choice (2007; 227 page working draft)

  • • Contents: Survey of voting procedures and their shortcomings. Sen's Impossibility Theorem, Arrow's Impossibility Theorem, and the Gibbard-Satterthwaite Impossibility Theorem. Binary voting systems; May's theorem. Weighted and Vector-weighted systems. Bentham's utilitarianism; von Neumann-Morgenstern definition of cardinal utility. Bargaining Games and the Nash Arbitration Scheme. Fair division theory

• The mathematics of voting and elections: Paradox, deception, and chaos (2008, PDF slides for a two-hour presentation).

  • • Contents: Various voting methods (Plurality, antiplurality, Borda count, instant runoff, etc.) and their problems and pathologies. Condorcet cycles. Arrow's impossibility theorem. Nonordinal voting systems (Approval voting, cumulative voting, relative utilitarianism) and their problems. Strategic voting and the Gibbard-Satterthwaite theorem. Representative democracy and compound-majority paradoxes (Ostrogorski, Anscombe). Voting power indices. Liberalism vs. Populism. Social choice and social welfare.

• Walrasian Equilibrium Theory (2006, PDF slides for a two-hour presentation).

  • • Contents: Classical microeconomics: the supply/demand `X' graph and its shortcomings. Complements vs. substitutes; production factors; perverse supply curves; the Law of One Price.

    • Pure Exchange Economies: consumers (utility functions, utility maximization through trade), aggregate excess demand, Walrasian Equilibria. Arrow-Debreu existence theorem and proof.

    • Production Economies: firms (production technology, profit maximization), shareholders, aggregate excess demand, Walrasian Equilibria. Arrow-Debreu existence theorem and proof sketch.

    • Problems with Walrasian paradigm: multiple equilibria; monopolistic competition; Sonnenschein-Mantel-Debreu Theorem (`anything goes') and proof. The prevalance of disequilibrium.

    • Disequilibrium dynamics: Samuelson's tatonnement and shortcomings; Hahn-Negishi dynamics; Fisher price dynamic.