A Reference Guide to The Road to Reality

Chapter by Chapter

The Roots of Science

Videos

• CrashCourse Philosophy Episodes 1-8

An ancient theorem and a modern question

Interactive

• Euclidia
• Euclid’s Elements

Videos

• The Essence of Linear Algebra

Books

• The Four Pillars of Geometry by John Stillwell
• Linear Algebra Done Right by Sheldon Axler

Kinds of number in the physical world

Books

• Principles of Mathematical Analysis, Third Edition by Walter Rudin
• Real Analysis by N.L. Carothers
• Real and Complex Analysis by Walter Rudin

Magical complex numbers

Books

• A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan
• Visual Complex Analysis by Tristan Needham
• Real and Complex Analysis by Walter Rudin

Videos

• Euler’s formula with introduction to group theory

Books

• A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan
• Visual Complex Analysis by Tristan Needham
• Real and Complex Analysis by Walter Rudin

Real-number calculus

Videos

• The Essence of Calculus
• Understanding e to the i pi in 3.14 minutes

Books

• Calculus, Vol. 1 by Tom M. Apostol
• Calculus, Vol. 2 by Tom M. Apostol
• [https://mathblog.com/calculus Calculus by Michael Spivak’

]

Complex-number calculus

Videos

• Visualizing the Riemann hypothesis and analytic continuation

Books

• A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan
• Visual Complex Analysis by Tristan Needham
• Real and Complex Analysis by Walter Rudin

Riemann surfaces and complex mappings

Videos

• Visualizing the Riemann hypothesis and analytic continuation

Books

• A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan
• Visual Complex Analysis by Tristan Needham
• Real and Complex Analysis by Walter Rudin

Manifolds of n dimensions

Articles

• What is a manifold? by Bastian Rieck
• Manifolds and Differential Forms lecture notes by Reyer Sjamaar