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[[File:Read.jpg|thumb|250px|A graphic showing the list's dependencies.]] | |||
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{{ | This list of books provides the most direct and rigorous route to understanding differential geometry. | ||
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Its selections are made because reasons. | |||
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There are other books for more specific topics. These are the core. | |||
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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 = | | title = === Basic Mathematics === | ||
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang. | |||
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}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Apostol Calculus V1 Cover.jpg | ||
| link = | | link = Calculus (Book) | ||
| title = | | title = === Calculus === | ||
| desc = Overview of Calculus by Tom Apostol. | |||
| | |||
}} | }} | ||
{{ | </div> | ||
| | == Royal Road to Differential Geometry and Physics == | ||
| link = | <div class="flex-container"> | ||
| title = | {{BookListing | ||
| cover = Lawvere Sets for Mathematics Cover.jpg | |||
| | | link = Sets for Mathematics (Book) | ||
| title = === Sets for Methematics === | |||
| desc = Categorical approach to set theory by F. William Lawvere. Backbone reference: Set Theory and Metric Spaces by Kaplansky, Foundations of Analysis by Edmund Landau. | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Shilov Linear Algebra Cover.jpg | ||
| link = | | link = Linear Algebra (Book) | ||
| title = | | title = === Linear Algebra === | ||
| desc = Linear algebra by Georgi Shilov. | |||
| | |||
}} | }} | ||
{{BookListing | |||
| cover = Landau Course in Theoretical Physics V1 Cover.jpg | |||
| link = Mechanics (Book) | |||
| title = === Mechanics === | |||
| desc = Physics by Lev Landau. | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Landau Course in Theoretical Physics V2 Cover.jpg | ||
| link = | | link = The Classical Theory of Fields (Book) | ||
| title = | | title = === The Classical Theory of Fields === | ||
| desc = Physics by Lev Landau. | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Bishop Tensor Analysis Cover.jpg | ||
| link = | | link = Tensor Analysis on Manifolds (Book) | ||
| title = | | title = === Tensor Analysis on Manifolds === | ||
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg. | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Sternberg Differential Geometry Cover.jpg | ||
| link = | | link = Lectures on Differential Geometry (Book) | ||
| title = | | title = === Lectures on Differential Geometry === | ||
| desc = Differential geometry by Shlomo Sternberg. | |||
| | |||
}} | }} | ||
{{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. | |||
}} | }} | ||
</div> | |||
== Backbone == | |||
<div class="flex-container"> | |||
{{BookListing | |||
| cover = Arnold Ordinary Differential Equations Cover.jpg | |||
| link = Ordinary Differential Equations (Book) | |||
| title = === Ordinary Differential Equations === | |||
{{ | | desc = Ordinary differential equations by Vladimir Arnold. | ||
| | |||
| link = | |||
| title = | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Kaplansky Set Theory and Metric Spaces Cover.jpg | ||
| link = | | link = Set Theory and Metric Spaces (Book) | ||
| title = | | title = === Set Theory and Metric Spaces === | ||
| desc = Set theory and metric spaces by Irving Kaplansky. | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = E Landau Foundations of Analysis Cover.jpg | ||
| link = | | link = Foundations of Analysis (Book) | ||
| title = | | title = === Foundations of Analysis === | ||
| desc = Analysis, intro to numbers, by Edmund Landau. | |||
| | |||
}} | }} | ||
{{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. | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg | ||
| link = | | link = Topology: A Categorical Approach (Book) | ||
| title = | | title = === Topology: A Categorical Approach === | ||
| desc = Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Ahlfors Complex Analysis Cover.jpg | ||
| link = | | link = Complex Analysis (Book) | ||
| title = | | title = === Complex Analysis === | ||
| desc = Complex analysis by Lars Ahlfors. | |||
| | |||
}} | }} | ||
{{ | {{BookListing | ||
| | | cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg | ||
| link = | | link = Applications of Lie Groups to Differential Equations (Book) | ||
| title = | | title = === Applications of Lie Groups to Differential Equations === | ||
| desc = Applications of Lie Groups to Differential Equations by Peter Olver. | |||
| | |||
}} | }} | ||
{{BookListing | |||
| cover = Aluffi Algebra Chapter 0 Cover.jpg | |||
| link = Algebra Chapter 0 (Book) | |||
| title = === Algebra Chapter 0 === | |||
| desc = Complex analysis by Paolo Aluffi. | |||
}} | }} | ||
{{BookListing | |||
| cover = Lang Algebra Cover.jpg | |||
| link = Algebra (Book) | |||
| title = === Algebra === | |||
| desc = Algebra by Serge Lang. | |||
}} | }} | ||
</div> | |||
__NOTOC__ | |||