Mathematical intuition better explained.
Intuition Cheatsheet – BetterExplained

    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?
        

        
            Quadratic Formula
            Rearrange a square
        

        
            Polynomial Intuition
            Decmials, interactions, function DNA
        
    

    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.
        
        
            Hyperbolic Trig
            Mini exponentials and logarithms
        
    

    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
            Adjust for false positives
        

        
            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
        

        
            Integral of sin
            Whoa: the horizontal change
        

        
            Taylor Series
            DNA of a function
        
    

    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
        
        
            Convolution
            Fancy, programmable multiplication
        
    

    
        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 RailsGet 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.
        
    
