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.
I also wrote a large number of notes when I taught a second-semester Real Analysis course. Most of these notes cover topics related to measure theory and integration.
Sequences & Series Notes
These notes were written for a Calculus II unit on sequences and series. They take an unusual approach to the material, emphasizing certain ideas from asymptotic analysis
. They are not intended to be a rigorous introduction to the subject, and they do not include very many proofs.
Each set of notes has practice problems at the end. Here are the answers to all of the practice problems:
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:
In case you'd like to use any of these in your classes, here is the original LaTeX code:
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)