The Joy of X, A guided Tour of Math, from One to Infinity by Steven Strogatz.

Found this book by accident. An interesting and easy read. So far through a couple chapters and it has been a good review in how to think mathematically without too much reliance on equations.

From Fish to Infinity

Check out Sesame Street Video called 123 Count with Me and the author's article in the NY TImes.

Did humanity invent numbers? Or discover them? The dual aspect of numbers. We event the concept of numbers and then discover the consequences of the concepts.

Rock Groups

Read

• "A Mathematicians Lament" by Paul Lockhart
• "The housekeeper and the Professor" by Yoko Ogawa

Natural Numbers, Odd, Even, Composite, Prime, Perfect Squares,

The word calculate from Latin calculus, meaning a pebble/stone used for counting

Einstein = one stone

The enemy of my Enemy

carrying/borrowing

Subtraction introduces the problem of negative numbers Why a negative times negative is a positive when two wrongs don't make a right!

Commuting

The commutative law of multiplication.

Maybe we doubt the law because in real life it often matters what you do first. really?

Division and Its Discontents

Natural Numbers Integers Rational Numbers (fractions: ratios of integers) Irrational Numbers (decimals that can't be expressed as fractions) Real Numbers

Most decimal numbers are irrational. Rational decimals either stop at some point or have a repeating pattern.

Read

• "My Left Foot" true story of Christy Brown

Location, Location, Location

Introduces us to positional notation using a base. Our system, versus older counting methods. Also introduces base 2.

The Joy of X

Algebra is basically two things

• Solve for x
• Working with formulas

The length of a hallway is Y measured in yards, and F when measured in feet. Write an equation that relates y to f.

identity formulas.

How to square numbers near 50. or 100 etc...

Finding your roots

Real Numbers, Imaginary numbers, complex numbers

Fractals

My Tub Runneth Over

If the cold water faucet fills a tub in a half-hour and a hot water faucet fills a tub in 1 hour, how long to fill the tub when the hot and cold are running together?

Suppose three men can paint three fences in three hours. How long would it take one man to paint one fence?