Writing

This page is an archive of things I have written that are unrelated to my research. Many of these were written as notes for classes that I have taught, and also appear on the corresponding course webpages. All of these notes are in PDF format.

You should feel free to use any of these notes or materials for your classes without specific permission from me, though if you do use something here I would love to hear about it.

Topology & Analysis Notes

I have written up extensive notes on a few subjects relating to point-set topology and analysis.

First, here are some notes on function spaces and the product and box topologies. These were intended to supplement a topology course out of Munkres' Topology, but they should be comprehensible to anyone learning point-set topology.

• Function Spaces (Product and Box Topologies)

I also wrote a large number of notes when I taught an advanced analysis course. Most of these notes cover topics related to measure theory and Lebesgue integration.

• Fourier Series & PDE's
• Lebesgue Measure
• Appendix: Sums Over Sets
• Measures In General
• Structure of Measurable Sets
• Non-Measurable Sets
• Introduction to the Lebesgue Integral
• Defining the Integral
• Convexity, Inequalities, and Norms
• L¹ Completeness
• L^p Functions
• Appendix: Norms and Inner Products
• Banach Spaces
• Hilbert Spaces
• More Measure Theory
• Introduction to Probability Theory (With Measures)
• Introduction to Probability Theory II

Science Problems for Calculus

When I teach Calculus classes, I tend to include a lot of applications problems based on science. See this MathOverflow answer for a discussion on my philosophy towards related rates questions in particular. Here is a list of some science-based problems from my Calculus I class:

• Science Problems for Calculus I

In case you'd like to use any of these in your classes, here is the original LaTeX code:

• LaTeX Source

Linear Algebra and Ordinary Differential Equations Notes

Here are some notes that I wrote for the Linear Algebra with Ordinary Differential Equations course at Bard College.

• Week 1 (Differential Equations)
• Week 2 (Growth, Decay, and Oscillation)
• Week 3 (Algebraic Methods)
• Week 4 (Visualization and Approximation)
• Week 5 (Vectors in Two Dimensions)
• Week 6 (Three-Dimensional Geometry, Dot Product)
• Week 7 (Projections, Determinants, Cross Product)
• Week 8 (Higher Dimensions, Planes and Hyperplanes)
• Week 9 (Lines, Geometry of Lines, Planes and Flats)
• Week 10 (Subspaces, Linear Dependence)
• Week 11 (Linear Systems and Row Reduction)
• Week 12 (Matrices, Linear Transformations, Eignevalues and Eigenvectors)