• 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: Number Sense/Systems

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

  • Existence of $\sqrt{-1}$
  • Types of Reasoning
  • Proof
  • Limits of Knowledge

Discovering the Art of Mathematics: Patterns

  • The Use of Patterns and Language in the Creation of Powerful Number Systems

Discovering the Art of Mathematics: Number Theory

  • Primes and Congruences
  • Partitions
  • Power Partitions
  • The World's Greatest Mathematical Problem

Discovering the Art of Mathematics: The Infinite

  • Grasping Infinity
  • Rigor and Divergence
  • The Ordered and Surreal Landscapes of Infinity

Discovering the Art of Mathematics: Calculus

  • The Banach—Tarski Paradox