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

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


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).


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.



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