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
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Doubt
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Existence of $\sqrt{-1}$
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Establishing Truth — Certainty and Burdens of Proof
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Limits of Knowledge
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$20^{\text{th}}$ Century Revolutions in Thought
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Knights and Knaves
Discovering the Art of Mathematics: Art & Sculpture
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The Magical Möbius Band: Cultural Icon and Engineering Marvel
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Flexagons, Magic, Genius, and the Nobel Prize
Discovering the Art of Mathematics: Patterns
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Introduction — Mathematics as the Art and Science of Patterns
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The Use of Patterns and Language in the Creation of Powerful Number Systems
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Patterns: Linear and Arithmetic
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Circles, Stars, Gears, and Unity
Discovering the Art of Mathematics: Number Theory
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Introduction — Number Theory
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Primes and Congruences
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Partitions
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The World's Greatest Mathematical Problem
Discovering the Art of Mathematics: Knot Theory
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Tangles
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The Unknotting Number of a Knot
Discovering the Art of Mathematics: The Infinite
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Introduction: The Infinite and New Number Systems
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Rigor and Divergence
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Sizes of Infinity
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Georg Cantor: Champion of the Infinite
Discovering the Art of Mathematics: Calculus
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What is Area?
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Integration
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The Banach—Tarski Paradox
Discovering the Art of Mathematics: Music
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Tuning and Intervals
Discovering the Art of Mathematics: Geometry
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So, What is Geometry?
Discovering the Art of Mathematics: Games & Puzzles
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Connection Games — Hex, ConHex, ...
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Straight-cut Origami