[Tex/LaTex] Using LaTeX while actively solving math problems

compilingeditorsequationsmacrosmath-mode

The goal is to get those formulas on the page as quickly as you are thinking of them. So that you can actually solve math problems, or experiment with the mathematics itself.

Question:

  • What tools/programs/strategies/tips/tricks/etc. (or combination thereof) can be used to efficiently facilitate mathematics learning/experimenting ?

Givens:

  • Only using keyboard. (no paper, pen, etc.)
  • No access to internet. (preferable, but not required.)
  • Basic knowledge of LaTeX syntax and programs. (or how to find them)

Show how:

  • to use LaTeX, while you are still actively solving a math problem.
  • can preview enough lines of math to focus on problem solving.
  • to LaTeX quickly.

Experiments I have tried:

  • Using a text editor has the simplicity and speed of typing. Using things like pandoc or mathjax to render from markdown are awesome. However for active problem solving, having to constantly compile the code manually can break concentration.

  • Using online websites is good for live previewing, but requires internet access, and therefore isn't ideal.

  • Using a regular LaTeX program, which might be the way to go: when combined the proper extensions (I'm not sure which, or how to find them exactly.)

  • Using something like Lyx, which actually worked pretty well for active math solving… but it didn't seem to work well for typing code (maybe I just need to change the options?)


I almost want to create a program that is specifically designed for this… but I have a feeling that I'm not the first person to attempt this, and that there is already a solution out there.


O' tEx-change, Share upon me your LaTeX wisdoms! =D

(Thanks in advance to anybody who actually reads everything I just wrote here)


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Best Answer

You may find useful looking at Emacs org-mode. It is basically a note-taking utility, with a syntax akin to Markdown, but allows you to do much more than just typing. You can perform complex calculations turning it into a powerful spreadsheet, using whatever Emacs Calc allows you to do (including algebraic manipulation and symbolic calculus). You can also preview LaTeX fragments and export an entire org file to an arbitrarily complex LaTeX files and directly to PDF. So you can make org-mode do the calculations for you and typeset them in LaTeX at the same time.

If this isn't enough, you can run computer algebra systems (like Maxima) inside Emacs.

Org-mode supports literate programming, that coupled with computing capabilities enables you to obtain a fully reproducibly research paper, from computation to typesetting, see: https://github.com/vikasrawal/orgpaper/blob/master/orgpapers.org and these other examples: http://orgmode.org/worg/org-contrib/babel/uses.html#sec-6

Installation

Emacs comes with org-mode already installed, but you can upgrade the package to the latest version with M-x package-install RET org RET. In Emacs lingo, M-x means pressing ALT + x (ALT key and letter x, at the same time, then release them), and RET is the Enter key. For the record, C-x stands for CTRL + x.

Quick start

To start using org-mode, just create a new file with .org extension. From menu: FileVisit New File. Just with the keyboard: C-x C-f (press CTRL + x at the same time, release them, then press CTRL + f at the same time, and release them), enter new file path and name, press RET.

Screenshots

Here are some random screenshots found on the Internet:

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