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[[File:Read.jpg|thumb|A graphic showing the list's dependencies.]] | |||
This list provides the most direct route to understanding differential geometry, the mathematical language of modern physics. | |||
__NOTOC__ | __NOTOC__ | ||
== Fill in Gaps == | |||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = Lang Basic Mathematics Cover.jpg | | cover = Lang Basic Mathematics Cover.jpg | ||
| title | | title = === Basic Mathematics === | ||
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang. | | desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Apostol Calculus V1 Cover.jpg | | cover = Apostol Calculus V1 Cover.jpg | ||
| title | | title = === Calculus === | ||
| desc = Overview of Calculus by Tom Apostol. | | desc = Overview of Calculus by Tom Apostol. | ||
}} | }} | ||
</div> | </div> | ||
== Royal Road to Differential Geometry and Physics == | |||
<div class="flex-container"> | <div class="flex-container"> | ||
{{BookListing | {{BookListing | ||
| cover = Lawvere Sets for Mathematics Cover.jpg | | cover = Lawvere Sets for Mathematics Cover.jpg | ||
| title | | 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. | | 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 | {{BookListing | ||
| cover = Shilov Linear Algebra Cover.jpg | | cover = Shilov Linear Algebra Cover.jpg | ||
| title | | title = === Linear Algebra === | ||
| desc = Linear algebra by Georgi Shilov. | | desc = Linear algebra by Georgi Shilov. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Landau Course in Theoretical Physics V1 Cover.jpg | | cover = Landau Course in Theoretical Physics V1 Cover.jpg | ||
| title | | title = === Mechanics === | ||
| desc = Physics by Lev Landau. | | desc = Physics by Lev Landau. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Landau Course in Theoretical Physics V2 Cover.jpg | | cover = Landau Course in Theoretical Physics V2 Cover.jpg | ||
| title | | title = === The Classical Theory of Fields === | ||
| desc = Physics by Lev Landau. | | desc = Physics by Lev Landau. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Bishop Tensor Analysis Cover.jpg | | cover = Bishop Tensor Analysis Cover.jpg | ||
| title | | title = === Tensor Analysis on Manifolds === | ||
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg. | | desc = Tensor analysis by Richard Bishop and Samuel Goldberg. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Sternberg Differential Geometry Cover.jpg | | cover = Sternberg Differential Geometry Cover.jpg | ||
| title | | title = === Lectures on Differential Geometry === | ||
| desc = Differential geometry by Shlomo Sternberg. | | desc = Differential geometry by Shlomo Sternberg. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Vaisman Cohomology and Differential Forms Cover.jpg | | cover = Vaisman Cohomology and Differential Forms Cover.jpg | ||
| title | | title = === Cohomology & Differential Forms === | ||
| desc = Cohomology and differential forms by Isu Vaisman. | | desc = Cohomology and differential forms by Isu Vaisman. | ||
}} | }} | ||
</div> | </div> | ||
== Backbone == | |||
<div class="flex-container"> | <div class="flex-container"> | ||
{{BookListing | {{BookListing | ||
| cover = Arnold Ordinary Differential Equations Cover.jpg | | cover = Arnold Ordinary Differential Equations Cover.jpg | ||
| title | | title = === Ordinary Differential Equations === | ||
| desc = Ordinary differential equations by Vladimir Arnold. | | desc = Ordinary differential equations by Vladimir Arnold. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Kaplansky Set Theory and Metric Spaces Cover.jpg | | cover = Kaplansky Set Theory and Metric Spaces Cover.jpg | ||
| title | | title = === Set Theory and Metric Spaces === | ||
| desc = Set theory and metric spaces by Irving Kaplansky. | | desc = Set theory and metric spaces by Irving Kaplansky. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = E Landau Foundations of Analysis Cover.jpg | | cover = E Landau Foundations of Analysis Cover.jpg | ||
| title | | title = === Foundations of Analysis === | ||
| desc = Analysis, intro to numbers, by Edmund Landau. | | desc = Analysis, intro to numbers, by Edmund Landau. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Rudin Principles of Mathematical Analysis Cover.jpg | | cover = Rudin Principles of Mathematical Analysis Cover.jpg | ||
| title | | title = === Principles of Mathematical Analysis === | ||
| desc = Mathematical analysis by Walter Rudin. | | desc = Mathematical analysis by Walter Rudin. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg | | cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg | ||
| title | | title = === Topology: A Categorical Approach === | ||
| desc = Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. | | desc = Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Ahlfors Complex Analysis Cover.jpg | | cover = Ahlfors Complex Analysis Cover.jpg | ||
| title | | title = === Complex Analysis === | ||
| desc = Complex analysis by Lars Ahlfors. | | desc = Complex analysis by Lars Ahlfors. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg | | cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg | ||
| title | | title = === Applications of Lie Groups to Differential Equations === | ||
| desc = Applications of Lie Groups to Differential Equations by Peter Olver. | | desc = Applications of Lie Groups to Differential Equations by Peter Olver. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Aluffi Algebra Chapter 0 Cover.jpg | | cover = Aluffi Algebra Chapter 0 Cover.jpg | ||
| title | | title = === Algebra Chapter 0 === | ||
| desc = Complex analysis by Paolo Aluffi. | | desc = Complex analysis by Paolo Aluffi. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = Lang Algebra Cover.jpg | | cover = Lang Algebra Cover.jpg | ||
| title | | title = === Algebra === | ||
| desc = Algebra by Serge Lang. | | desc = Algebra by Serge Lang. | ||
}} | }} | ||
</div> | </div> | ||