ABSTRACT

X Marks the Spot is written from the point of view of the users of mathematics. Since the beginning, mathematical concepts and techniques (such as arithmetic and geometry) were created as tools with a particular purpose like counting sheep and measuring land areas.

Understanding those purposes leads to a greater understanding of why mathematics developed as it did. Later mathematical concepts came from a process of abstracting and generalizing earlier mathematics. This process of abstraction is very powerful, but often comes at the price of intuition and understanding. This book strives to give a guided tour of the development of various branches of mathematics (and what they’re used for) that will give the reader this intuitive understanding.

Features

  • Treats mathematical techniques as tools, and areas of mathematics as the result of abstracting and generalizing earlier mathematical tools
  • Written in a relaxed conversational and occasionally humorous style making it easy to follow even when discussing esoterica.
  • Unravels how mathematicians think, demystifying math and connecting it to the ways non-mathematicians think and connecting math to people’s lives
  • Discusses how math education can be improved in order to prevent future generations from being turned off by math.

chapter 1|6 pages

Why This Book?

part I|124 pages

The Roots of Mathematics

chapter 2|40 pages

Sticks and Stones

chapter 3|20 pages

Abstraction, Mistrust, and Laziness

part II|220 pages

Theory in Practice

chapter 5|50 pages

Analytic Geometry

chapter 6|46 pages

Calculus: Motion and Size

chapter 7|8 pages

The Language of Motion

chapter 8|10 pages

Sound, Notes, and Harmonics

chapter 9|32 pages

Probability and Statistics

chapter 11|36 pages

Algebra and the Rise of Abstraction

part III|104 pages

Toolkit of the Theoretical Universe

chapter 12|12 pages

The Smith and the Knight

chapter 13|14 pages

Building the Theoretical Universe

chapter 14|36 pages

Computers

chapter 16|10 pages

Math Education and Math in Education