• Art and Sculpture Book
  • Calculus Book
  • Dance Book
  • Games and Puzzles Book
  • Geometry Book
  • Knot Theory Book
  • Music Book
  • Number Theory Book
  • Patterns Book
  • Infinite Book
  • Truth, Reasoning, Certainty, and Proof Book

Topic Index: History

Currently, our books are written with a semester long course in mind. However, many of the individual chapters from different books can be grouped together to create a semester long course with a variety of topics or they can be used to supplement a topic in an exisiting course. To use this topic index, click a heading below to view the specific book chapter(s) featuring a given topic.

Discovering the Art of Mathematics: Truth, Reasoning, Certainty, & Proof

  • Doubt
  • Existence of $\sqrt{-1}$
  • Establishing Truth — Certainty and Burdens of Proof
  • Limits of Knowledge
  • $20^{\text{th}}$ Century Revolutions in Thought
  • Knights and Knaves

Discovering the Art of Mathematics: Art & Sculpture

  • The Magical Möbius Band: Cultural Icon and Engineering Marvel
  • Flexagons, Magic, Genius, and the Nobel Prize

Discovering the Art of Mathematics: Number Theory

  • Introduction — Number Theory
  • Primes and Congruences
  • Partitions
  • The World's Greatest Mathematical Problem

Discovering the Art of Mathematics: Patterns

  • Introduction — Mathematics as the Art and Science of Patterns
  • The Use of Patterns and Language in the Creation of Powerful Number Systems
  • Patterns: Linear and Arithmetic
  • Circles, Stars, Gears, and Unity

Discovering the Art of Mathematics: The Infinite

  • Introduction: The Infinite and New Number Systems
  • Rigor and Divergence
  • Sizes of Infinity
  • Georg Cantor: Champion of the Infinite

Discovering the Art of Mathematics: Knot Theory

  • Tangles
  • The Unknotting Number of a Knot

Discovering the Art of Mathematics: Calculus

  • What is Area?
  • Integration
  • The Banach—Tarski Paradox

Discovering the Art of Mathematics: Games & Puzzles

  • Connection Games — Hex, ConHex, ...
  • Straight-cut Origami