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A Reference Guide to The Road to Reality: Difference between revisions
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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 === | === 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] | ||
=== 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 ==== | ==== Geometry of logarithms, powers, and roots ==== | ||
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==== 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 === | ||
| Line 59: | Line 68: | ||
==== 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] | ||