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1 The Primes

• Video Transcript
• 1.1 Introduction
• 1.2 Math at the Dawn of Time
• 1.3 Number for Number's Sake
• 1.4 Primes
• 1.5 Questions about Primes
• 1.6 Encryption
• 1.7 RSA Encryption
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2 Combinatorics Counts

• Video Transcript
• 2.1 Introduction
• 2.2 Egypt and India
• 2.3 Flavors Revisited
• 2.4 Pascal's Triangle
• 2.5 The Order of the Garter
• 2.6 Ramsey Theory
• 2.7 DNA Sequencing
• 2.8 P=NP
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3 How Big is Infinity?

• Video Transcript
• 3.1 Introduction
• 3.2 Rational Numbers
• 3.3 Incommensurability and Irrationality
• 3.4 Zeno's Paradoxes
• 3.5 Re-Learning to Count
• 3.6 Cantor's Theory
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4 Topology's Twists and Turns

• Video Transcript
• 4.1 Introduction
• 4.2 What is Essential about Shape?
• 4.3 Surfaces and Manifolds
• 4.4 Intrinsic Topology
• 4.5 Embedding and the Extrinsic View
• 4.6 Non-Orientability
• 4.7 Connected Sums and the Classification of Surfaces
• 4.8 Robots
• 4.9 The Shape of Space
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5 Other Dimensions

• Video Transcript
• 5.1 Introduction
• 5.2 Degrees of Freedom
• 5.3 Journey into the Fourth Dimension
• 5.4 Slices, Projections, and Shadows
• 5.5 Many Dimensions in Everyday Life
• 5.6 Scaling and the Hausdorff Dimension
• 5.7 Fractal by Nature
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6 The Beauty of Symmetry

• Video Transcript
• 6.1 Introduction
• 6.2 Types of Symmetry Leading to Groups
• 6.3 Frieze and Wallpaper Groups
• 6.4 Card Shuffling
• 6.5 Galois Theory
• 6.6 Physics
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7 Making Sense of Randomness

• Video Transcript
• 7.1 Introduction
• 7.2 History
• 7.3 Simple Probability Counting
• 7.4 Law of Large Numbers
• 7.5 The Galton Board Revisited
• 7.6 Central Limit Theorem
• 7.7 Other Types of Probability
• 7.8 Modern Probability
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8 Geometries Beyond Euclid

• Video Transcript
• 8.1 Introduction
• 8.2 Euclidean Geometry
• 8.3 Non-Euclidean Geometry
• 8.4 Spherical and Hyperbolic Geometry
• 8.5 Shapes on a Plane: Making Maps
• 8.6 Curvature
• 8.7 General Relativity
• 8.8 Geometrization Conjecture
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9 Game Theory

• Video Transcript
• 9.1 Introduction
• 9.2 Origins of Game Theory
• 9.3 Simple Games
• 9.4 Prisoner's Dilemma
• 9.5 Hawks and Doves
• 9.6 Fairness in Different Cultures
• 9.7 Language
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10 Harmonious Math

• Video Transcript
• 10.1 Introduction
• 10.2 The Math of Time
• 10.3 Sound and Waves
• 10.4 Mathematics of Waves
• 10.5 Fourier
• 10.6 Can You Hear the Shape of a Drum?
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11 Connecting with Networks

• Video Transcript
• 11.1 Introduction
• 11.2 The Study of Connections
• 11.3 Random Networks
• 11.4 Small World Networks
• 11.5 Scale-Free Networks
• 11.6 Ecosystems
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12 In Sync

• Video Transcript
• 12.1 Introduction
• 12.2 Unit Overview
• 12.3 Calculus
• 12.4 Differential Equations
• 12.5 Cycles
• 12.6 Many Oscillators and Biological Sync
• 12.7 Mechanical Sync
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13 The Concepts of Chaos

• Video Transcript
• 13.1 Introduction
• 13.2 Linear vs. Nonlinear Systems
• 13.3 Limits of Predictability
• 13.4 Sensitive Dependence
• 13.5 Iteration
• 13.6 The Logistic Map
• 13.7 Fly Me to the Moon
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