Table of Contents

There is but one direction, therefore, which I have to give in this part of my work, namely, that he may be able to do all this successfully, let him understand what he reads.

Quintilian, Institutios I.8.2

Introduction

Mathematics

  1. Mathematical Vernacular a formal language for proofs.
  2. Category Theory
    1. Object Oriented Math, a basic introduction to certain aspects of category theory, preliminary focus on mathematical objects and structure-preserving maps between them ("morphisms").
    2. First Taste of Categories, where we first introduced various aspects of category theory in a more heavy duty way.
    3. Fun With Functors, where we introduced the notion of morphisms as mapping objects to objects, and observe that a category is an object, then ask "What's a morphism from a category to a category?"
    4. Classification of Morphisms, setting up the taxonomy of morphisms.
    5. Hierarchy of Functors, setting up the taxonomy of functors.
    6. Natural Question: Morphisms of Functors, a first look at natural transformations.
    7. Products (but not Coproducts yet), wherein we first introduce the notion of the product (but not yet the coproduct!).
    8. Duality Principle, one of the most important concepts involving reversing your arrows.
    9. Coproducts (but not Products!), wherein we first introduce the notion of the coproduct.
    10. Equivalence of Categories, descending the Rabbit hole of "sameness" in category theory.
    11. Morphisms of...Morphisms? A First Look at Slice Categories [Draft!] looking at comma categories (and slice categories) as the category of morphisms.
    12. More Object Orientedness, revisiting the notion of a "mathematical object" with the tools of category theory.
  3. Calculus
    1. Big O Notation for Calculus A big O notation motivation for the derivative.
    2. Differentiation with Big O Notation, including the product and chain rules.
  • Miscellaneous
    1. Proclus on Euclid the "proposition-proof" pattern is more structured than we think.
    2. Role of Examples what role should examples have: worked out calculations, or exercises with the solution given.
    3. Notes on Set Theory discussing my fascicles on set theory, and the open problem: how to come up with good problems?
    4. Epsilon Calculus discussing Hilbert's ε-calculus and lapses into a discussion of Bourbaki's set theory as Zermelo axioms + Axiom of Global Choice.
  • Classics
    1. Notes on "How to Read a Book" which is useful before reading any books...
    2. Resources on Homer which includes some notes on Aristotle and Homer.
    3. Reading Herodotus discusses strategies for reading Herodotus' Histories and some resources.
    4. Herodotus' Histories (Books I and II) outlines the first two books by summarising each chapter.
    5. Ancient Geography is useful for reading ancient history!.
  • Programming
    1. LaTeX on blogger, how to set up LaTeX on blogger.
    2. Setting up a Blogger Client for GNU Emacs 23, how to set up GNU Emacs 23 to post to blogger directly.
    3. Setting up a Table of Contents for Blogger..., how to set up your own table of contents on blogger.
    4. Graphics Posts
      1. Drawing Internal Diagrams, example of Internal Diagrams in Asymptote.
      2. MetaPost, Plotting, and numerical precision discusses how to plot functions with metapost, and the limitations of numerical precision.
    5. LaTeX Macros entries:
      1. LaTeX Macros..., some useful LaTeX macros
      2. LaTeX Macros for Personal Notes, based on the classic "grocery list" writing style mathematicians use.
      3. Basic Physics Macros, where we use a "QEF" delimiter for examples, and discuss the "ISEE" approach.
    6. Emacs LaTeX Macros, macros to help the LaTeX writer in emacs when working on a netbook
    7. Haskell Annotations, a few notes on abstract algebra in Haskell.
    8. Calculus Program generates problems, specifically "Differentiate/Integrate this function" type problems.
  • Problems List periodically updated
  • Bibliography
  • Notation