From the Book - First edition.
Part I: The roots of mathematics
Units of multiply like rabbits
3. Abstraction, mistrust, and laziness
Methods of reasoning in proofs
Putting the three together
4. Algebra, geometry, analysis: the mathematical mindsets
Here it is: value abstraction. Let's bring him out again, x the unknown, variable extraordinaire!
When are shapes the same?
Function behavior and unknown functions
Part II: Theory in practice
Planes and space, numbers by numbers
The fault is not in our stars
More dimensions than you con shake a stick at
6. Calculus: motion and size
Derivative redux (reduced, that is)
When can we differentiate?
Function approximation and Taylor series
The fundamental theorem of calculus
Logarithm and exponential
The absence and presence of calculus
7. The language of Motion
8. Sound, notes, and harmonics
9. Probability and statistics
Combinatorics: counting without counting
Probability distributions: stick the chances
10. Other geometries: not so straight, these sticks
Shortest distance between two points
Nature spiky in coast and leaf
Why are the called fractals?
11. Algebra and the rise of abstraction
Construction and its limits
Imaginary and complex numbers
Algebraic structures: abstraction spreads wide its arms
Morphisms: preservatives added and multiplied
Algebraic view of geometry: slouching toward topology
Part III: Toolkit of the theoretical universe
How the user sees the tool
The maker's view of the tool
Beauty in the use of tools
Beauty in the making of tools: artists and artisans
13. Building the theoretical universe
Electricity and magnetism
Binary arithmetic embodies
Modular programming, procedures, and functions
Speed, memory, bandwidth, price, size, and efficiency
Human thought and computer "thought"
Computer use in math and science
15. The theoretical universe of modern physics: toolkit included
16. Math education and math in education
Welcome to math problem world
