Burn Math Class: And Reinvent Mathematics for Yourself (2016)

Preface

Prefacer

Act I

1. Ex Nihilo

1.1. Forgetting Mathematics

1.2. How to Invent a Mathematical Concept

1.3. Reunion

Interlude 1: Dilating Time

2. The Infinite Power of the Infinite Magnifying Glass

2.1. Turning Hard Stuff into Easy Stuff

2.2. Inventing Calculus

2.3. Understanding the Magnifying Glass

2.4. Hunting Extremes in the Dark

2.5. A Brief Sermon on Rigor

2.6. Reunion

Interlude 2: How to Get Something from Nothing

3. As If Summoned from the Void

3.1. Who Ordered That?

3.2. !scitamehtaM eht gnikcirT

3.3. An Attractive New Character Enters

3.4. Hammers, Patterns, and Hammer Patterns

3.5. A Phase Transition in the Creation Story

3.6. Hammers and Chains

3.7. Reunion

Interlude 3: A Backωαrd Look to the Future

Act II

4. On Circles and Giving Up

4.1. A Conceptual Centrifuge

4.2. Impostor Syndrome

4.3. Equivalences of Our Ignorances

4.4. The Mixture Separates

4.5. What Is Meaningful

4.6. The Dilemma

4.7. Molière Is Dead! Long Live Molière!

4.8. A Tiresome Cacophony of Superfluous Names

4.9. Calculus of the Incalculable

4.10. Reunion

Interlude 4: The Nostalgia Device

5. Aesthetics and the Immovable Object

5.1. Reaching into the Void

5.2. The Four Species

5.3. The Formal and the Informal

5.4. The Zoology of the MA Species

5.5. The MM Species

5.6. Reunion

Interlude 5: Two Clouds

Act III

6. Two in One

6.1. Two is One

6.2. Field-Testing the Fundamental Hammer

6.3. Forging the Anti-Hammers

6.4. The Second Cloud

6.5. Reunion

Interlude 6: Slaying Sharp

N. New Is Old

N.1. A Bridge

N.2. The Notational Minefield of Multivariable Calculus

N.3. Enough Symbol Games! How Can We Picture This?

N.4. Is That All?

N.5. Reunion

Interlude N: (Mis)interpreted (Readings) (Re)interpreted

The Infinite Beauty of the Infinite Wilderness

1. The Surprising Unity of the Void

2. Crossing the Rubicon

3. Inventing Cannibal Calculus

4. The Pedagogical Mutilation of Infinite-Dimensional Calculus

5. The Infinite Jackpot: Putting Our Ideas to Work for Us

6. Reunion

Chapterlude Ω

Dictionary