View source for A Reference Guide to The Road to Reality

== Chapter by Chapter ==

=== The Roots of Science ===

==== Videos ====

* [https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdYldNkMybYIHKR CrashCourse Philosophy Episodes 1-8]

=== An ancient theorem and a modern question ===

==== Interactive ====

* [https://mathcs.clarku.edu/~djoyce/java/elements/elements.html Euclidia]
* [https://mathcs.clarku.edu/~djoyce/java/elements/elements.html Euclid’s Elements]

==== Videos ====

* [https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab The Essence of Linear Algebra]

==== Books ====

* [https://mathblog.com/pillars-geometry The Four Pillars of Geometry by John Stillwell]
* [https://mathblog.com/linear-algebra Linear Algebra Done Right by Sheldon Axler]

=== Kinds of number in the physical world ===

==== Books ====

* [https://mathblog.com/baby-rudin Principles of Mathematical Analysis, Third Edition by Walter Rudin]
* [https://mathblog.com/real-analysis Real Analysis by N.L. Carothers]
* [https://mathblog.com/big-rudin Real and Complex Analysis by Walter Rudin]

=== Magical complex numbers ===

==== Books ====

* [https://mathblog.com/comples-analysis A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan]
* [https://mathblog.com/visual-complex Visual Complex Analysis by Tristan Needham]
* [https://mathblog.com/big-rudin Real and Complex Analysis by Walter Rudin]

==== Geometry of logarithms, powers, and roots ====

==== Videos ====

* [https://www.youtube.com/watch?v=mvmuCPvRoWQ Euler’s formula with introduction to group theory]

==== Books ====
* [https://mathblog.com/comples-analysis A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan]
* [https://mathblog.com/visual-complex Visual Complex Analysis by Tristan Needham]
* [https://mathblog.com/big-rudin Real and Complex Analysis by Walter Rudin]

=== Real-number calculus ===

==== Videos ====

* [https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr The Essence of Calculus]
* [https://www.youtube.com/watch?v=v0YEaeIClKY Understanding e to the i pi in 3.14 minutes]

=== Books===

* [https://mathblog.com/calculus1 Calculus, Vol. 1 by Tom M. Apostol]
* [https://mathblog.com/calculus2 Calculus, Vol. 2 by Tom M. Apostol]
* [https://mathblog.com/calculus Calculus by Michael Spivak’
]

=== Complex-number calculus ===

==== Videos====

* [https://www.youtube.com/watch?v=sD0NjbwqlYw Visualizing the Riemann hypothesis and analytic continuation]

==== Books ====

* [https://mathblog.com/comples-analysis A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan]
* [https://mathblog.com/visual-complex Visual Complex Analysis by Tristan Needham]
* [https://mathblog.com/big-rudin Real and Complex Analysis by Walter Rudin]

=== Riemann surfaces and complex mappings ===

==== Videos ====

* [https://www.youtube.com/watch?v=sD0NjbwqlYw Visualizing the Riemann hypothesis and analytic continuation]

==== Books ====

* [https://mathblog.com/comples-analysis A First Course in Complex Analysis With Applications by Dennis Zill and Patrick Shanahan]
* [https://mathblog.com/visual-complex Visual Complex Analysis by Tristan Needham]
* [https://mathblog.com/big-rudin Real and Complex Analysis by Walter Rudin]

=== Manifolds of n dimensions ===

==== Articles ====

* [https://bastian.rieck.me/blog/posts/2019/manifold/ What is a manifold? by Bastian Rieck]
* [http://pi.math.cornell.edu/~sjamaar/manifolds/manifold.pdf Manifolds and Differential Forms lecture notes by Reyer Sjamaar]