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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