1,628
edits
Read: Difference between revisions
👀
No edit summary |
(👀) |
||
| (7 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
[[File:Read.jpg|thumb|A graphic showing the list's dependencies. Click to enlarge.]] | [[File:Read.jpg|thumb|A graphic showing the list's dependencies. Click to enlarge.]] | ||
This list of books provides the most direct and rigorous route to understanding differential geometry, the mathematical language of physics. Each selection thoroughly addresses its subject matter. The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and/or read several together to acquire the necessary language and understand the motivations for each idea. | This list of books provides the most direct and rigorous route to understanding differential geometry, the mathematical language of physics. Each selection thoroughly addresses its subject matter. The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and/or read several together to acquire the necessary language and understand the motivations for each idea. The greatest hurdles are the motivation to learn and developing an understanding of the language of mathematics. | ||
See the image on the right for a visual | See the image on the right for a visual representation of its dependencies. | ||
Also see this [[Watch|list of | Also see this [[Watch|list of video lectures]]. | ||
== List Structure == | == List Structure == | ||
The '''Royal Road to Differential Geometry and Physics''' is the list's core. While on that track, you should refer to the | The '''Royal Road to Differential Geometry and Physics''' is the list's core. While on that track, you should refer to the '''Fill in Gaps''' and '''Backbone''' sections as needed or as you desire. | ||
The '''Fill in Gaps''' section covers the knowledge acquired in a strong high school mathematics education. Refer to it as needed, or begin there to develop your core skills. | The '''Fill in Gaps''' section covers the knowledge acquired in a strong high school mathematics education. Refer to it as needed, or begin there to develop your core skills. | ||
The '''Backbone''' section supports the ideas in the '''Royal Road'''. Refer to it to strengthen your understanding of the ideas in the main track and to take those ideas further. | The '''Backbone''' section supports the ideas in the '''Royal Road'''. Refer to it to strengthen your understanding of the ideas in the main track and to take those ideas further. | ||
== Fill in Gaps == | == Fill in Gaps == | ||
| Line 39: | Line 37: | ||
| title = === Sets for Mathematics === | | title = === Sets for Mathematics === | ||
| desc = Categorical approach to set theory by F. William Lawvere.<br> | | desc = Categorical approach to set theory by F. William Lawvere.<br> | ||
Backbone reference: | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Set Theory and Metric Spaces|Set Theory and Metric Spaces]] | * [[{{FULLPAGENAME}}#Set Theory and Metric Spaces|Set Theory and Metric Spaces]] | ||
* [[{{FULLPAGENAME}}#Foundations of Analysis|Foundations of Analysis]] | * [[{{FULLPAGENAME}}#Foundations of Analysis|Foundations of Analysis]] | ||
| Line 54: | Line 52: | ||
| title = === Mechanics === | | title = === Mechanics === | ||
| desc = Classical mechanics of physics by Lev Landau.<br> | | desc = Classical mechanics of physics by Lev Landau.<br> | ||
Prerequisite: | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Calculus|Calculus]] | * [[{{FULLPAGENAME}}#Calculus|Calculus]] | ||
Backbone reference: | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]] | * [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]] | ||
}} | }} | ||
| Line 64: | Line 62: | ||
| title = === The Classical Theory of Fields === | | title = === The Classical Theory of Fields === | ||
| desc = Physics by Lev Landau.<br> | | desc = Physics by Lev Landau.<br> | ||
Prerequisite: | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | * [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | ||
}} | }} | ||
| Line 72: | Line 70: | ||
| title = === Tensor Analysis on Manifolds === | | title = === Tensor Analysis on Manifolds === | ||
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br> | | desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br> | ||
Prerequisite: | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | * [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | ||
Backbone reference: | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]] | * [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]] | ||
* [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]] | * [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]] | ||
| Line 83: | Line 81: | ||
| title = === Lectures on Differential Geometry === | | title = === Lectures on Differential Geometry === | ||
| desc = Differential geometry by Shlomo Sternberg.<br> | | desc = Differential geometry by Shlomo Sternberg.<br> | ||
Prerequisite: | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | * [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | ||
Backbone reference: | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]] | * [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]] | ||
* [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]] | * [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]] | ||
| Line 94: | Line 92: | ||
| title = === Cohomology & Differential Forms === | | title = === Cohomology & Differential Forms === | ||
| desc = Cohomology and differential forms by Isu Vaisman.<br> | | desc = Cohomology and differential forms by Isu Vaisman.<br> | ||
Backbone reference: | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]] | * [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]] | ||
* [[{{FULLPAGENAME}}#Algebra|Algebra]] | * [[{{FULLPAGENAME}}#Algebra|Algebra]] | ||
}} | }} | ||
</div> | </div> | ||
== Backbone == | == Backbone == | ||
<div class="flex-container"> | <div class="flex-container"> | ||
| Line 129: | Line 128: | ||
| link = Topology: A Categorical Approach (Book) | | link = Topology: A Categorical Approach (Book) | ||
| title = === Topology: A Categorical Approach === | | title = === Topology: A Categorical Approach === | ||
| desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. | | desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. [https://topology.mitpress.mit.edu/ Click here for the Open Access version.] | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| Line 156: | Line 155: | ||
}} | }} | ||
</div> | </div> | ||
[[Category:Bot Commands]] | |||
__NOTOC__ | __NOTOC__ | ||