math

Posting some math related latex documents

Development Environment

• 安裝LaTeX：
  • 一般Linux有 pdflatex command 可使用。
  • Windows: https://miktex.org/ , https://www.texniccenter.org/
• Web
  • mathURL
  • Overleaf
• IDE
  • GNU TeXmacs
  • Visual Studio Code
    • Markdown All in One
    • LaTeX Workshop
  • TeXstudio
• Docker:
  • 如果你不想安裝LaTeX，可以使用Docker。以下是一個例子：
    • 下載：

      docker pull ghcr.io/xu-cheng/texlive-full:latest
      

    • 編譯：

      docker run --rm -it -v $(pwd):/src -w /src/Books/BabyRudin ghcr.io/xu-cheng/texlive-full:latest latexmk -pdf -file-line-error -halt-on-error -interaction=nonstopmode ./BabyRudin.tex
      

    • 開啟：

      open ./Books/BabyRudin/BabyRudin.pdf
      

Books

• Mathematics for Computer Science, Eric Lehman, F Thomson Leighton, Albert R Meyer
• Algorithm Design, Jon Kleinberg, Eva Tardos
• Combinatorial Optimization: Algorithms and Complexity, Christos H. Papadimitriou, Kenneth Steiglitz
• Principles of Mathematical Analysis, Walter Rudin
  • Errata
• Basic Analysis: Introduction to Real Analysis, Jiří Lebl
• Analysis I, Terence Tao
• Understanding Analysis, Stephen Abbott
• Problems in Mathematical Analysis, Boris Demidovich
• A Problem Book in Real Analysis, Asuman G. Aksoy, Mohamed A. Khamsi
• Linear Algebra Done Right, Sheldon Axler
• Linear Algebra Done Wrong, Sergei Treil
• Abstract Algebra: Theory and Applications, Thomas W. Judson, Robert A. Beezer
• Measure Theory, Donald L. Cohn
• Algebraic Number Theory, Jürgen Neukirch

Papers

• Mathematical method and proof, Jeremy Avigad

Courses

• Calculus 1, Chen-Yu Chi, NTU OCW
• Calculus 2, Chen-Yu Chi, NTU OCW
• Analytics, Chen-Yu Chi, NTU OCW
• Advanced Calculus 1, Shu-Jung Kao, NTHU OCW
• Advanced Calculus 2, Shu-Jung Kao, NTHU OCW
• Advanced Calculus 1, Chi-Kaung Pai, NYCU OCW
• Advanced Calculus 2, Chi-Kaung Pai, NYCU OCW
• Real Analysis, Casey Rodriguez, MIT OCW
• Probability Theory and Stochastic Processes, Todd Kemp, UCSD

YouTube Channel

• The Bright Side of Mathematics
• James Cook

FAQ on LaTeX and PGF/TikZ

如果我不懂 LaTeX 怎麼辦？

• Quick Start: https://latex-tutorial.com/tutorials/amsmath/
• Quick Reference: https://en.wikipedia.org/wiki/Help:Displaying_a_formula
• LaTeX Tutorials (featuring Texmaker), Michelle Krummel

如果我不懂 PGF/TikZ 怎麼辦？

• PGF/TikZ Manual - Complete Online Documentation
• LaTeX/PGF/TikZ - Wikibooks, open books for an open world
• TikZ.net – Graphics with TikZ in LaTeX
• LaTeX Graphics with TikZ
• TikZ and PGF | TeXample.net

用電腦typeset數學證明是學習數學證明的最佳方法嗎？

不，根據研究（ref: https://www.youtube.com/watch?v=7PQbidoBPBc ），手寫對長遠記憶的效果更好。可是，如果你想別人看到你的練習／作品，或者方便保存日後參考／分享，使用 LaTeX 吧！

References

• Graphic notes on Gilbert Strang's "Linear Algebra for Everyone"