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Pretty pictures version of [[Read]].
[[File:Read.jpg|thumb|A graphic showing the list's dependencies.]]


[[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__
== Version 2 ==
 
=== Fill in Gaps ===
== 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 = ==== Basic Mathematics ====
| 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 = ==== Calculus ====
| 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 ===
== 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 = ==== Sets for Methematics ====
| 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 = ==== Linear Algebra ====
| 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 = ==== Mechanics ====
| 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 = ==== The Classical Theory of Fields ====
| 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 = ==== 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.
}}
}}
{{BookListing
{{BookListing
| cover = Sternberg Differential Geometry Cover.jpg
| cover = Sternberg Differential Geometry Cover.jpg
| title = ==== Lectures on Differential Geometry ====
| 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 = ==== Cohomology & Differential Forms ====
| title = === Cohomology & Differential Forms ===
| desc = Cohomology and differential forms by Isu Vaisman.
| desc = Cohomology and differential forms by Isu Vaisman.
}}
}}
</div>
</div>
=== Backbone ===
== 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 = ==== Ordinary Differential Equations ====
| 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 = ==== Set Theory and Metric Spaces ====
| 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 = ==== Foundations of Analysis ====
| 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 = ==== Principles of Mathematical Analysis ====
| 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 = ==== Topology: A Categorical Approach ====
| 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 = ==== Complex Analysis ====
| 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 = ==== Applications of Lie Groups to Differential Equations ====
| 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 = ==== Algebra Chapter 0 ====
| 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 = ==== Algebra ====
| title = === Algebra ===
| desc = Algebra by Serge Lang.
| desc = Algebra by Serge Lang.
}}
}}
</div>
</div>
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