- There are many typos and incorrect information. This is obviously not intentional, many of the notes were taken mid-lecture via LaTeX and I have not had the time to correct them yet. I am working though in order, correcting information, and have made good progress in book 1 on Logic and Set Theory.
- I'm experimenting with writing figures in different languages. I used to use tikz, now I mostly use asymptote. Lately I've been experimenting with a library I've written in C to produce SVG figures. Currently the figures in the text use both tikz and asymptote. This will likely change over time to just asymptote.
- This project is currently incomplete and will remain so for quite some time. I am actively working on it, but there's a lot of cleaning up to do.
You will need:
asy- The Asymptote Vector Graphics Language.pdflatex- A LaTeX compiler.gcc- The GNU C compiler.convert- Image Magick tool for converting images to different formats.
TeX-Live and Mac-Tex (GNU/Linux and macOS, respectively) have both pdflatex
and asy. macOS users can find this at https://www.tug.org/mactex/.
GNU/Linux users for Debian based distributions (Debian, Ubuntu, Pop!_OS, etc.)
can install tex-live using their package manager:
sudo apt-get install texlive-full
Different Linux distributions will need to use their respective package manager.
gcc comes pre-installed on many GNU/Linux distributions. If it is not,
install it via:
sudo apt-get install gcc
macOS users will need to install xcode to use Apple's C compiler
(it is labelled gcc but is actually based on LLVM's clang). This is done
via:
xcode-select --install
As of this writing, convert comes pre-installed on macOS and Debian. If it is
not available for a particular GNU/Linux distribution, try:
sudo apt-get install imagemagick
To make the figures, give the make_figs.sh executable permissions, and then
run it:
chmod +x make_figs.sh
./make_figs.sh
There are several hundred figures, so this will take a while. 10 minutes on a
fast computer, about 30 minutes on a slower one.
To make the C figures, do the same with make_cfigs.sh.
chmod +x make_cfigs.sh
./make_cfigs.sh
Various notes on mathematics and physics organized in several volumes. The books are currently arranged as follows:
Notes on set theory, logic, model theory, arithmetic, and the structure of the real numbers (including the calculus of one variable).
Group theory, rings and fields, as well as vector spaces, modules, and linear algebra.
Point set topology covering topological spaces, continuity, separation, connectedness, compactness, and a myriad of other properties. Many examples and counterexamples are provided and a great number of spaces are discussed. Homotopy, homology, cohomology, and related topics are developed, and topological manifolds are described. Smooth and differentiable manifolds are saved for Geometry since we will need many of the results from Analysis, and hence there's a bit of a gap between studying topological manifolds and studying smooth manifolds.
Calculus, measure theory, functional analysis, probability theory, multivariate calculus, ordinary and partial differential equations, and Fourier analysis. Special functions such as Fresnel integrals and Bessel functions are constructed and discussed throughout.
Differential topology and Riemannian geometry, Convex and Euclidean geometry.
Knot theory, low dimensional topology, and surgery theory.
Classical mechanics, electromagnetism, quantum mechanics, and astronomy.