A Reference Guide to The Road to Reality: Difference between revisions

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==== Interactive ====
==== Interactive ====


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


==== Videos ====
==== Videos ====


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


==== Books ====
==== Books ====


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


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


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


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


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


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


=== Real-number calculus ===
=== Real-number calculus ===
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==== Videos ====
==== Videos ====


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


=== Books===
==== Books====


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


=== Complex-number calculus ===
=== Complex-number calculus ===
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==== Videos====
==== Videos====


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


==== Books ====
==== Books ====


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


=== Riemann surfaces and complex mappings ===
=== Riemann surfaces and complex mappings ===
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==== Videos ====
==== Videos ====


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


==== Books ====
==== Books ====


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


=== Manifolds of n dimensions ===
=== Manifolds of n dimensions ===
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==== Articles ====
==== Articles ====


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

Latest revision as of 23:11, 28 October 2020

Chapter by Chapter[edit]

The Roots of Science[edit]

Videos[edit]

An ancient theorem and a modern question[edit]

Interactive[edit]

Videos[edit]

Books[edit]

Kinds of number in the physical world[edit]

Books[edit]

Magical complex numbers[edit]

Books[edit]

Geometry of logarithms, powers, and roots[edit]

Videos[edit]

Books[edit]

Real-number calculus[edit]

Videos[edit]

Books[edit]

Complex-number calculus[edit]

Videos[edit]

Books[edit]

Riemann surfaces and complex mappings[edit]

Videos[edit]

Books[edit]

Manifolds of n dimensions[edit]

Articles[edit]