A Reference Guide to The Road to Reality: Difference between revisions
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== Chapter by Chapter == | == Chapter by Chapter == | ||
=== The Roots of Science === | === [[Chapter 1: The roots of science|The Roots of Science]] === | ||
==== Videos ==== | ==== Videos ==== | ||
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* [https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdYldNkMybYIHKR CrashCourse Philosophy Episodes 1-8] | * [https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdYldNkMybYIHKR CrashCourse Philosophy Episodes 1-8] | ||
=== An ancient theorem and a modern question === | === [[Chapter 2: An ancient theorem and a modern question|An ancient theorem and a modern question]] === | ||
==== Interactive ==== | ==== Interactive ==== | ||
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==== 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 === | === [[3 Kinds of numbers in the physical world|Kinds of number in the physical world]] === | ||
==== 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 | === [[4 Magical complex numbers|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] | |||
=== [[5 Geometry of logarithms, powers, and roots|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 === | === [[6 Real-number calculus|Real-number calculus]] === | ||
==== 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 === | === [[7 Complex-number calculus|Complex-number calculus]] === | ||
==== 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 === | === [[8 Riemann surfaces and complex mappings|Riemann surfaces and complex mappings]] === | ||
==== 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 === | ||
| Line 83: | Line 91: | ||
==== 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 02:50, 25 November 2025
Chapter by ChapterEdit
The Roots of ScienceEdit
VideosEdit
An ancient theorem and a modern questionEdit
InteractiveEdit
VideosEdit
BooksEdit
Kinds of number in the physical worldEdit
BooksEdit
- Principles of Mathematical Analysis, Third Edition by Walter Rudin
- Real Analysis by N.L. Carothers
- Real and Complex Analysis by Walter Rudin
Magical complex numbersEdit
BooksEdit
- 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
Geometry of logarithms, powers, and rootsEdit
VideosEdit
BooksEdit
- 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 calculusEdit
VideosEdit
BooksEdit
Complex-number calculusEdit
VideosEdit
BooksEdit
- 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 mappingsEdit
VideosEdit
BooksEdit
- 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