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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. | 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 video lectures]]. | Also see this [[Watch|list of video lectures]]. | ||
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| 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]] | ||
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| 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]] | ||
}} | }} | ||
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| 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]] | ||
}} | }} | ||
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| 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]] | ||
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| 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]] | ||
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| 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"> | ||
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| 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 | ||
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}} | }} | ||
</div> | </div> | ||
[[Category:Bot Commands]] | |||
__NOTOC__ | __NOTOC__ | ||