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Created by [anonymous] at

Paul Crowley v1.12.0 (-367) Reverted edits by [[Special:Contributions/DBAtkins|DBAtkins]] ([[User talk:DBAtkins|talk]]) to last revision by [[User:L29Ah|L29Ah]] LW2

~~Geometry was arguably the first mathematical discipline developed by civilization. The need to define human property (or territory) was of utmost importance (because we don't pee on trees - well not for that reason). Knowing where the system came from can give you a greater understanding of what it means.~~

Geometry was arguably the first mathematical discipline developed by civilization. The need to define human property (or territory) was of utmost importance (because we don't pee on trees - well not for that reason). Knowing where the system came from can give you a greater understanding of what it means.

- How Everything Works: Making Physics out of the Ordinary by Louis Bloomfield (no math though)

- The Simple Math of Everything by Eliezer Yudkowsky
- Creating The Simple Math of Everything by Matt Simpson, calling for more contributions on the topic.
- Eric Drexler on Learning About Everything
~~,~~by Vladimir Nesov

- The Simple Math of Everything by Eliezer Yudkowsky
- Creating The Simple Math of Everything by
~~Matt_Simpson,~~Matt Simpson, calling for more contributions on the topic. - Eric Drexler on Learning About Everything, by Vladimir Nesov

- The Simple Math of Everything by Eliezer Yudkowsky
- Creating The Simple Math of Everything by Matt_Simpson, calling for more contributions on the topic.
- Eric Drexler on Learning About Everything, by Vladimir Nesov

- Khan Academy 800+ Youtube videos covering everything from basic arithmetic and algebra to differential equations, physics, and finance

- How Everything Works: Making Physics out of the Ordinary by Louis Bloomfield

- on Wikipedia, definition and a step-through of the proof
- Halting Problem
- at Michigan State, problem, theorem, and proof
- University of Edinburgh, explanation of proof

An astonishingly elegant technique for proving certain kinds of theorems. Originally introduced by the mathematician Georg Cantor to show that the set of real numbers is uncountable – that is, there is no one-to-one correspondence between real numbers and natural numbers, but was later found to generalize to several other contexts. Perhaps the most notable uses of this technique, in addition to Cantor's proof, are Alan Turing's answer to the Halting problem, and Gödel's proof of his famous first incompleteness theorem.

- on Wikipedia, definition and a step-through of the proof

Relates the speedup of a sub-task to the resulting speedup of the whole. Trivially true, but often needed to knock down false intuition.

- on Wikipedia, long with examples
- on MathWorld, short without examples

Used to abstract away units and fixed overhead when analyzing resource usage.

- on Wikipedia, long
- cheat sheet from the same article

Traditional square one of theoretical computer science, with many practical applications.

- on Wikipedia, definition and example
- homework with solutions (PDF)

Illustrates many recurring themes. Understanding the proof and usage of the pumping lemma will help you understand and apply more famous, advanced results (e.g. anything involving Turing Machines).

- at Penn Engineering, explanation and examples
- handout (PDF) with concise statement and examples

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