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{{Grid2Col
[[File:Read.jpg|thumb|A graphic showing the list's dependencies. Click to enlarge.]]
| content =
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{{CardBook
This list of books provides the most direct and rigorous route to understanding differential geometry. Each selection thoroughly addresses its subject matter. There are other books for more specific topics. These are the core. See the image on the right for a visual treatment of its dependencies.
| img = Lang Basic Mathematics Cover.jpg
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The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and read several at a time to acquire the necessary language and understand the motivations.
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The "Royal Road to Differential Geometry and Physics" is the focus of the list. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed.
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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.
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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.
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The greatest hurdles are motivation and coming to understand the language of mathematics.
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See also this list of videos.
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== Fill in Gaps ==
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| title = === Basic Mathematics ===
| authors = Serge Lang
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| followon =
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
}}
{{CardBook
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Apostol Calculus V1 Cover.jpg
| link = Basic Mathematics (Book)
| link = Calculus (Book)
| title = Basic Mathematics
| title = === Calculus ===
| authors = Serge Lang
| desc = Overview of Calculus by Tom Apostol.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| followon =
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBook
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| followon =
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
</div>
| img = Lang Basic Mathematics Cover.jpg
== Royal Road to Differential Geometry and Physics ==
| link = Basic Mathematics (Book)
<div class="flex-container">
| title = Basic Mathematics
{{BookListing
| authors = Serge Lang
| cover = Lawvere Sets for Mathematics Cover.jpg
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| link = Sets for Mathematics (Book)
| title = === Sets for Mathematics ===
| desc = Categorical approach to set theory by F. William Lawvere.<br>
Backbone reference:
* [[{{FULLPAGENAME}}#Set Theory and Metric Spaces|Set Theory and Metric Spaces]]
* [[{{FULLPAGENAME}}#Foundations of Analysis|Foundations of Analysis]]
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Shilov Linear Algebra Cover.jpg
| link = Basic Mathematics (Book)
| link = Linear Algebra (Book)
| title = Basic Mathematics
| title = === Linear Algebra ===
| authors = Serge Lang
| desc = Overview of linear algebra by Georgi Shilov.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{BookListing
| cover = Landau Course in Theoretical Physics V1 Cover.jpg
| link = Mechanics (Book)
| title = === Mechanics ===
| desc = Classical mechanics of physics by Lev Landau.<br>
Prerequisite:
* [[{{FULLPAGENAME}}#Calculus|Calculus]]
Backbone reference:
* [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]]
}}
}}
{{CardBook
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Landau Course in Theoretical Physics V2 Cover.jpg
| link = Basic Mathematics (Book)
| link = The Classical Theory of Fields (Book)
| title = Basic Mathematics
| title = === The Classical Theory of Fields ===
| authors = Serge Lang
| desc = Physics by Lev Landau.<br>
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
Prerequisite:
| followon = Β 
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]]
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Bishop Tensor Analysis Cover.jpg
| link = Basic Mathematics (Book)
| link = Tensor Analysis on Manifolds (Book)
| title = Basic Mathematics
| title = === Tensor Analysis on Manifolds ===
| authors = Serge Lang
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br>
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
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]]
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Sternberg Differential Geometry Cover.jpg
| link = Basic Mathematics (Book)
| link = Lectures on Differential Geometry (Book)
| title = Basic Mathematics
| title = === Lectures on Differential Geometry ===
| authors = Serge Lang
| desc = Differential geometry by Shlomo Sternberg.<br>
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
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
| cover = Vaisman Cohomology and Differential Forms Cover.jpg
| link = Cohomology & Differential Forms (Book)
| title = === Cohomology & Differential Forms ===
| desc = Cohomology and differential forms by Isu Vaisman.<br>
Backbone reference:
* [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]]
* [[{{FULLPAGENAME}}#Algebra|Algebra]]
}}
}}
{{CardBook
</div>
| img = Lang Basic Mathematics Cover.jpg
== Backbone ==
| link = Basic Mathematics (Book)
<div class="flex-container">
| title = Basic Mathematics
{{BookListing
| authors = Serge Lang
| cover = Arnold Ordinary Differential Equations Cover.jpg
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| link = Ordinary Differential Equations (Book)
| followon = Β 
| title = === Ordinary Differential Equations ===
{{CardBookFollowOnListItem
| desc = Ordinary differential equations by Vladimir Arnold.
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Kaplansky Set Theory and Metric Spaces Cover.jpg
| link = Basic Mathematics (Book)
| link = Set Theory and Metric Spaces (Book)
| title = Basic Mathematics
| title = === Set Theory and Metric Spaces ===
| authors = Serge Lang
| desc = Set theory and metric spaces by Irving Kaplansky.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = E Landau Foundations of Analysis Cover.jpg
| link = Basic Mathematics (Book)
| link = Foundations of Analysis (Book)
| title = Basic Mathematics
| title = === Foundations of Analysis ===
| authors = Serge Lang
| desc = Analysis, intro to numbers, by Edmund Landau.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{BookListing
| cover = Rudin Principles of Mathematical Analysis Cover.jpg
| link = Principles of Mathematical Analysis (Book)
| title = === Principles of Mathematical Analysis ===
| desc = Mathematical analysis by Walter Rudin.
}}
}}
{{CardBook
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
| link = Basic Mathematics (Book)
| link = Topology: A Categorical Approach (Book)
| title = Basic Mathematics
| title = === Topology: A Categorical Approach ===
| authors = Serge Lang
| desc = Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
| followon = Β 
{{CardBookFollowOnListItem
| img = Lang Basic Mathematics Cover.jpg
| link = Basic Mathematics (Book)
| title = Basic Mathematics
| authors = Serge Lang
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Ahlfors Complex Analysis Cover.jpg
| link = Basic Mathematics (Book)
| link = Complex Analysis (Book)
| title = Basic Mathematics
| title = === Complex Analysis ===
| authors = Serge Lang
| desc = Complex analysis by Lars Ahlfors.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{CardBookFollowOnListItem
{{BookListing
| img = Lang Basic Mathematics Cover.jpg
| cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg
| link = Basic Mathematics (Book)
| link = Applications of Lie Groups to Differential Equations (Book)
| title = Basic Mathematics
| title = === Applications of Lie Groups to Differential Equations ===
| authors = Serge Lang
| desc = Applications of Lie Groups to Differential Equations by Peter Olver.
| description = Review of arithmetic, algebra, trigonometry, logic, and geometry
}}
}}
{{BookListing
| cover = Aluffi Algebra Chapter 0 Cover.jpg
| link = Algebra Chapter 0 (Book)
| title = === Algebra Chapter 0 ===
| desc = Algebra by Paolo Aluffi. Easier than Lang's, but less direct.
}}
}}
{{BookListing
| cover = Lang Algebra Cover.jpg
| link = Algebra (Book)
| title = === Algebra ===
| desc = Algebra by Serge Lang. The most direct approach to the subject.
}}
}}
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<summary>Test</summary>
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