I will *try* to collect my *notes* and *solutions* on math and physics, and links to them here.

- Differential Geometry Differential Topology dump, LaTeX file; github repository: mathphysics
- Differential Geometry Differential Topology dump, pdf file; github repository: mathphysics
- (Notes and) Solutions for The Geometry of Physics, by Theodore Frankel; pdf file; github repository: mathphysics
- (Notes and) Solutions for The Geometry of Physics, by Theodore Frankel; (main) LaTeX file; github repository: mathphysics
- directory for (Notes and) Solutions for The Geometry of Physics, by Theodore Frankel; (main) directory, since LaTeX file is split up into separate chapters for modularity; github repository: mathphysics
- (Notes and) Solutions for Mikio Nakahara’s Geometry, Topology, and Physics; LaTeX file; github repository: mathphysics
- (Notes and) Solutions for Mikio Nakahara’s Geometry, Topology, and Physics; pdf file; github repository: mathphysics
- Notes and Solutions to Ideals, varieties, and Algorithms by David A. Cox, John Little, Donal O’Shea; LaTeX file; github repository: mathphysics
- Notes and Solutions to Using Algebraic Geometry by David A. Cox, John Little, Donal O’Shea; (main) LaTeX file; github repository: mathphysics
- Algebraic Geometry with Sage Math/Python on jupyter notebook
**GPU accelerated Tensor networks**

## Open-source; PayPal only

From the beginning of 2016, I decided to cease all explicit crowdfunding for any of my materials on physics, math. I failed to raise *any* funds from previous crowdfunding efforts. I decided that if I was going to live in *abundance*, I must lose a scarcity attitude. I am committed to keeping all of my material **open-sourced**. I give all my stuff *for free*.

In the beginning of 2017, I received a very generous donation from a reader from Norway who found these notes useful, through *PayPal*. If you find these notes useful, feel free to donate directly and easily through **PayPal**, which won’t go through a 3rd. party such as indiegogo, kickstarter, patreon.

Otherwise, under the *open-source MIT license*, feel free to copy, edit, paste, make your own versions, share, use as you wish.

### Algebraic Geometry

#### (symbolic computational) Algebraic Geometry with Sage Math on a jupyter notebook

cf.

https://github.com/ernestyalumni/mathphysics/blob/master/AG_sage.ipynb

http://nbviewer.jupyter.org/github/ernestyalumni/mathphysics/blob/master/AG_sage.ipynb

I did a Google search for “Sage Math groebner” and I came across Martin Albrecht’s slides on “Groebner Bases” (22 October 2013). I implemented fully on Sage Math all the topics on the slides up to the F4 algorithm. In particular, I implemented in Sage Math/Python the generalized division algorithm, and Buchberger’s Algorithm with and without the first criterion (I did plenty of Google searches and couldn’t find someone who had a working implementation on Sage Math/Python). Another bonus is the interactivity of having it on a jupyter notebook. If this jupyter notebook helps yourself (reader), students/colleagues, that’d be good, as I quickly picked up the basic and foundations of using computational algebraic geometry quickly (over the weekend) from looking at the slides and working it out running Sage Math on a jupyter notebook.

I’ll update the github file as much as I can as I’m going through Cox, Little, O’Shea (2015), **Ideals, Varieties, and Algorithms**, and implementing what I need from there.

# Algebraic Geometry and Algebraic Topology dump (AGDT_dump.tex and DGDT_dump.pdf)

20171002 – I’ve consolidated by notes on Algebraic Geometry and Algebraic Topology. Because central extensions of groups, Lie group, Lie algebras play an important role in Conformal Field Theory, I include notes on **Conformal Field Theory (CFT)** in these notes.

Of note, I compare 2 definitions of semi-direct product and show how they’re related and the same.

# Differential Geometry and Differential Topology dump (DGDT_dump.tex and DGDT_dump.pdf)

I continue to take notes on differential geometry and differential topology and its relation to physics, with an emphasis on topological quantum field theory. I dump all my note and thoughts immediately in the LaTeX and compiled pdf file here and here. I don’t try to polish or organize these notes in any way, as I am learning at my own pace. I’ve put this out there, with a permanent home on github, to invite any one to copy, edit, reorganize, and use these notes in anyway they’d like (the power of crowdsourcing).

## Manifolds

20171203 update

I added notes on immersions, submersions, and some immersed submanifolds. Absil, Mahony, and Sepulchre (2008)’s book **Optimization algorithms on Matrix Manifolds** had clearer, more concise, and more to the point definitions in its manifolds review than many of these classic pure math textbooks (Lees).

I finally understood clearly immersions, submersions, and their differences after writing (and drawing) this down:

### Holonomy

#### 20170423 update.

I have been reviewing holonomy by reading Conlon (2008), Clarke and Santoro (2012, 1206.3170 [math.DG]), and Schreiber and Waldorf (2007, 0705.0452 [math.DG]) concurrently. I’ve already put these notes on my github repository mathphysics , in DGDT_dump.tex and DGDT_dump.pdf.