Difference between revisions of "User:Aardvark/Read"
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| cover = Lawvere Sets for Mathematics Cover.jpg | | cover = Lawvere Sets for Mathematics Cover.jpg | ||
| link = Sets for Mathematics (Book) | | link = Sets for Mathematics (Book) | ||
| title = === Sets for | | 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]] | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Mechanics (Book) | | link = Mechanics (Book) | ||
| title = === Mechanics === | | title = === Mechanics === | ||
| desc = | | desc = Classical mechanics of physics by Lev Landau.<br> | ||
Prerequisite: | |||
* [[{{FULLPAGENAME}}#Calculus|Calculus]] | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = The Classical Theory of Fields (Book) | | link = The Classical Theory of Fields (Book) | ||
| title = === The Classical Theory of Fields === | | title = === The Classical Theory of Fields === | ||
| desc = Physics by Lev Landau. | | desc = Physics by Lev Landau.<br> | ||
Prerequisite: | |||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Tensor Analysis on Manifolds (Book) | | link = Tensor Analysis on Manifolds (Book) | ||
| title = === Tensor Analysis on Manifolds === | | title = === Tensor Analysis on Manifolds === | ||
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg. | | desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br> | ||
Prerequisite: | |||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | |||
Backbone reference: | |||
* [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]] | |||
* [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]] | |||
}} | }} | ||
{{BookListing | {{BookListing |
Revision as of 15:42, 6 July 2021
This list of books provides the most direct and rigorous route to understanding differential geometry. See the image on the right for a visual treatment of its dependencies.
Each selection thoroughly addresses its topics.
There are other books for more specific topics. These are the core.
The greatest hurdles are motivation and coming to understand the language of mathematics.
See also this list of videos.
Fill in Gaps
Royal Road to Differential Geometry and Physics
Sets for Mathematics
Categorical approach to set theory by F. William Lawvere.
Backbone reference:
Tensor Analysis on Manifolds
Tensor analysis by Richard Bishop and Samuel Goldberg.
Prerequisite:
Backbone reference:
Backbone
Topology: A Categorical Approach
Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
Applications of Lie Groups to Differential Equations
Applications of Lie Groups to Differential Equations by Peter Olver.