MathWiki

A statically-generated Hugo site to host my math course notes in university, inspired by Obsidian.md.

These notes are meant to be a distilled version of the math I've learnt where ideas, formulations, and important results are broken down into their atomic components of definitions, propositions, and theorems for clarity, precision, and accessibility.

Work in progress!

Contents

• Note Types and Templates; the basic templates and outgoing links for each type of note.
• Scripts; snippets, plugins, and my bash scripts.

Note Types and Templates

Each note is currently one of four types:

• Definition/Example, either of an object or of a notion, which links to:

  • Types: Objects/notions of type object/notion with additional restrictions.
  • Examples: Specific examples or counterexamples of object/notion (but not of any of its types).
  • Constructions: Objects/notions derived from object/notion.
  • Generalizations: Abstractions of object/notion.
    
    
  • Properties: Statements regarding object or necessary conditions of notion.
  • Sufficiencies: Proofs that other objects are of type object or sufficient conditions of notion
  • Equivalences: Equivalent definitions for object or biconditionals between notions and notion.
  • Justifications: Proofs of well-definition of object/notion.

• Proposition/Theorem (differentiated by 'importance'), including both statement and proof regarding object/notion, which links to:

  • Proved by: Statements in which proof depends crucially on.
  • References: Notes in which the proofs of statement (or corollaries thereof) are delegated to.
  • Justifications: Proofs of implicit assumptions of object/notion in statement.
    
    
  • Specializations: Reformulations/proofs of instances of statement.
  • Generalizations: Statements and proofs of abstractions of statement.

These templates are automatically inserted whenever a note is created. After the links, the main content is written with remarks where appropriate.

Scripts

I wrote some bash scripts to (try) maintain the consistency of my notes; main.sh acts as a hub for me to run them.

• Global search and replace, including the ability of excluding additional patterns, is handled by searchReplace.sh.
• Basic stats of the site (and updating them below) is handled by stats.sh.
• Displaying all links that have yet to be created and all notes that have those links, are handled by ghost.sh.

Some stats: 11 notes, 35 links (ratio: 0), 4 images (updated every commit).