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
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.
- "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
Subtraction introduces the problem of negative numbers Why a negative times negative is a positive when two wrongs don't make a right!
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.
- "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.
How to square numbers near 50. or 100 etc...
Finding your roots
Real Numbers, Imaginary numbers, complex numbers
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?