Materials from some courses I've taught
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| 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 coursesClicking 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)
|Advanced Calculus (upper division)
Solutions to Rudin's ``Principles of Mathematical Analysis'', chapters 7–9. Available by request only; please email me.
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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