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Intuition Cheatsheet
Math is no more about equations than poetry is about spelling. Find your Aha! moment.
Popular Articles
How To Learn Trigonometry Intuitively
Go beyond SOH-CAH-TOA and visualize trig.
An Interactive Guide To The Fourier Transform
An Intuitive Guide to Linear Algebra
Intuitive Understanding Of Euler’s Formula
Developing Your Intuition For Math
Intuitive Guide to Angles, Degrees and Radians
A Visual, Intuitive Guide to Imaginary Numbers
Rethinking Arithmetic: A Visual Guide
Surprising Uses of the Pythagorean Theorem
Demystifying the Natural Logarithm (ln)
An Intuitive (and Short) Explanation of Bayes’ Theorem
An Intuitive Guide To Exponential Functions & e
Intuitive Learning
ADEPT method
Learning starts with an analogy.
Why Learn Math?
Vocabulary for thinking
Math Intuition
Start with the cat, not its DNA
Bow & Arrow Intuition
First, have a good shot.
Pencil, Then Ink
Don't hide the process
Analogies
Useful, even if "wrong"
Cartoons
Simplify ideas to a caricature
Intuition Isn't Optional
The recipe for knowledge that lasts.
Arithmetic & Numbers
Mental Math Shortcuts
A few memorable conversions
Sum 1 to 100
Rearrange to simplify
Visual Arithmetic
Every operation is a transformation
Sense of Scale
Bring large numbers down to everyday terms
Fencepost Problem
Counting spans or points?
Number Systems
When the odometer ticks over
Everyday Logarithms
Counting digits
Modular Arithmetic
Variations on clocks
Algebra & Counting
Combinations
Multiply possibilities, divide redundancies
Primes
Atoms within numbers
The Equals Sign
Set, check, or define?
Factoring Equations
Break down the tepee
Parametric Equations
Extract the true cause
Types of Graphs
Map (distance matters) or non-map
Square Numbers
Use geometry, algebra, calculus
Navigate a Grid
Convert decisions to letters & permute
Combinations & Multiplication
Choices multiply.
Ratios
How much oomph, how often?
Geometry
Pythagorean Theorem
How every shape changes
Pythagorean Distance
Compare any quantities
Similarity
Step back. Smaller shape, same ratios.
Pythagorean Rescale
Work from a unit triangle
Precalculus & Trigonometry
Radians
Angles from the mover’s perspective
Finding Pi
Surround that critter
Sine Waves
The natural sway found in circles, springs
The Number e
Perfectly smooth growth
Natural Log
Time needed to grow
Imaginary Numbers
Numbers can rotate
Complex Numbers
Arithmetic goes 2d
Complex Multiplication
Scale & rotate
Exponents
Grow numbers in the expand-o-tron
Think With Exponents
Logs are causes, exponents are effects
Trigonometry
Visualize a dome, wall, and ceiling
Law of Sines
Every angle has an equal perspective.
Law of Cosines
Keep track of interacting parts.
Trig Identities
Draw the circles yourself.
Statistics
Statistics
See footprints, guess the animal
Averages
"Typical" depends on the relationship
Birthday Paradox
23 people, many possibilities
Bayes Theorem
Extra info? Adjust the odds.
Short Bayes’ Theorem
Track new info in a table
Monty Hall
Original door vs. best of the other two
Calculus Course
Calculus Guide
Learn the basics, fast.
Lesson 1
1-Minute Summary
Lesson 2
X-Ray Vision
Lesson 3
3D intuition
Lesson 4
Integrals, Derivatives
Lesson 5
Computer Notation
Lesson 6
Improved Algebra
Lesson 7
Linear Changes
Lesson 8
Squared Changes
Lesson 9
Infinity
Lesson 10
Derivatives
Lesson 11
Fundamental Theorem of Calculus
Lesson 12
Rules: Add, Multiply, Invert
Lesson 13
Patterns In the Rules
Lesson 14
Rules: Powers, Division
Lesson 15
Archimedes' Formulas
Calculus Summary
The big insights. All together now.
Calculus (Articles)
1 Minute Calculus
Analyze patterns with x-ray and time-lapse vision
0.999… = 1?
What's your number system?
Limits
Guess what happened when you blinked
Limits / Infinitesimals
Make a model perfect
Integration
Piece-by-piece multiplication
Derivative Intro
Measurements depend on the instrument
Derivatives II
Imagine linked machines
Derivatives III
Quotient, exponents, logs
Calculus Bank Account
Raises change income, changing the balance
Vector Calculus
Circulation & Curl
Total twist, twist at a point
The Gradient
Microwave the doughboy, quick
Gradient Details
Follow the best tradeoff
Flux
Amount of bananas crossing a surface
Divergence
Flux per unit volume
Dot Product
Mario Kart speed boost
Cross Product
All the uneven parts
Engineering / University Math
Linear Algebra
Math with mini-spreadsheets
Euler’s Formula
Imaginary exponents make circles
Fourier Transform
Patterns have circular ingredients
Programming Tools
Version Control
Track files over time
Distributed VCS
Pass around changes
Git Insights
#1: There's a staging area
GDB Debugging
A quickstart guide
Web Development
Faster Javascript
Minify, compress, move to end
HTTP Caching
Don't redownload until expired
Gzip Compression
Zip files before sending
Starting Ruby on Rails
Get past the gotchas
Understanding MVC
Fat models, thin controller, thin view
Javascript Reference
1-page summary
Load XML/JSON
Treat a script as data
XSRF Attacks
Attacker spoofs a legit request
Debugging with Firefox
Use firebug
Making Bookmarklets
A quick javascript snippet
Low-level Programming
GUIDs
You'll never run out. Ever.
Binary Files
Space efficiency vs. marshalling
Byte Order
Computers speak different languages
Unicode
Not every char is 2 bytes
XOR Swap
Cleverness, not for real life
Fast 1/sqrt(x)
Newton's method, magic initializer
Symbol Tables
Deobfuscate object code
Networking
Telnet is an IM conversation
Business
Rule of 72
time = 72/interest
Pareto Principle
Sometimes 80% is enough
Stock Market
A transparent store
Accounting Basics
Everything is owned by someone
Interest Rates
A formula for every type of interest
Debt & Leverage
Invested debt multiplies return
Assorted Musings
Know Thyself
If you're Hulk, be Hulk.
Simplicity vs. Complexity
Complexity, not power, is the enemy.
Notes on Happiness
Passion, foolishness, dancing
Brevity is Beautiful
Zero guilt.