1. Numbers - what are they? how do we use them? and why they are important.
2. Relationships - algebra, functions, story problems
3. Shapes - triangles, pi, trigonometry
4. Change - calculus, e, vectors
5. Data - normal distribution
6. Frontiers - primes, group theory, sequences.
Throughout these sections he gives multiple examples to help explain the concept and what is going on. He does this in a manner that everyone can understand. The his creative imagines he uses throughout the book and his sense of humor it is an easy read for even a non-mathematician to enjoy.
Even has a person whom has studied math for now 17 years, I learned some new ways to explain some math concepts that others cannot wrap their mind around. For example, why is a negative times a negative positive? This is how he showed it:
-1 x 3 = -3
-1 x 2 = -2
-1 x 1 = -1
-1 x 0 = 0
-1 x -1 = ?
If you follow the pattern on the right hand side, it is counting up by one so the ? would be a positive 1. I have never thought about a way to explain this to others that didn't believe this. However, I now have some what of a reasoning to show them why this is true.
Overall, this book was an easy read and I would recommend this book to anyone who would like to know a little bit more behind how math works. He gives great examples that will stick with you. And you will sure get a kick out of his humor throughout the book.
Some of my favorite quotes from the book:
"...math always involves invention and discovery..." -pg 5
"...even wrong answers can be educational...as long as you realize they're wrong." -pg 63
"Proofs can cause dizziness or excessive drowsiness. Side effects of prolonged exposure may include night sweats, panic attacks, and, in rare cases, euphoria. Ask you doctor if proofs are right for you." -pg 93