Materials from some courses I've taught
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Mathematica animations

To explore convolutions and Fourier series, execute each cell in order. (Later cells depend on functions and variables defined in the earlier cells.) The sliders on the animations are interactive: you can grab them with the mouse and scroll backward and forward. Right-click the file name and choose "Save As..." to download the file to your local drive.
      convolutions.nb shows how convolutions are computed and why they have a smoothing effect
      approximation.nb gives an introduction to Fourier transforms and wavelets

Undergraduate courses

Clicking the course title will take you to a directory containing the available files, as listed. Files which I believe to be most useful have their own designated links. All files were written in LaTeX by me.
¤ indicates a course for which I was the primary instructor.

¤  Linear Algebra (upper division)
Includes complete lecture notes (163 pages) and extra credit problems on least squares, dynamical systems, Markov chains, geometric optics, optical transforms, complex numbers, sociology.
¤  Ordinary Differential Equations (upper division)
Includes partial lecture notes (101 pages) (I'm writing a new version this semester), extra credit assignments on modeling fisheries (esp. harvesting) with logistic equation, container design for a hydrology experiment, linear independence, and a review of the methods of diagonalization, undetermined coefficients, and variation of parameters.
¤  Introduction to Analysis (upper division)
Includes complete lecture notes (155 pages), midterms and final exam (all with solutions), homework, Proof Tips (reading and understanding), Proof Tips (writing), a helpful guide to Sets and Maps, and a brief Guide to Notation and Logic common in analysis and other proof-based courses.
¤  Honors Analysis (upper division)
Includes complete lecture notes (129 pages), midterms and final exam (all with solutions), and auxiliary homework problems.
¤  Linear Algebra for Business (lower division)
Includes complete lecture notes (99 pages), midterms and finals, supplementary homework problems, and review notes for Markov and Leontief models.
¤  Ordinary Differential Equations (lower division)
Includes complete lecture notes (150 pages), midterms and final, and quizzes.
Topology (upper division)
Includes basic survival guide (sets and maps), the mantras of compactness, and various worked problems from the algebraic topology section of Munkres' Topology: a first course. The solutions are available by request only; please email me.
Probability (upper division)
Includes review materials, quizzes, quiz solutions, a take-home quiz on memoryless distributions (solution is also in this directory) and 3 fun problems to get students thinking.
Optimization (upper division)
Includes homework solutions and review materials.
Game Theory (upper division)
Review materials.
Advanced Calculus (upper division)
Solutions to Rudin's ``Principles of Mathematical Analysis'', chapters 7–9. Available by request only; please email me.
 

Graduate courses

¤  Analysis
Includes lecture notes (62 pages) from the qualifying examination preparatory seminars and solutions to four previous qualifiers.
¤  Topology
Includes solutions to three previous qualifying examinations and homework and notes on differential topology.
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