User:Aardvark/Read: Difference between revisions

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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>

Revision as of 21:35, 5 July 2021

A graphic showing the list's dependencies.

This list provides the most direct route to understanding differential geometry, the mathematical language of modern physics.


Fill in Gaps

Lang Basic Mathematics Cover.jpg

Basic Mathematics

Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.

Apostol Calculus V1 Cover.jpg

Calculus

Overview of Calculus by Tom Apostol.

Royal Road to Differential Geometry and Physics

Lawvere Sets for Mathematics Cover.jpg

Sets for Methematics

Categorical approach to set theory by F. William Lawvere. Backbone reference: Set Theory and Metric Spaces by Kaplansky, Foundations of Analysis by Edmund Landau.

Shilov Linear Algebra Cover.jpg

Linear Algebra

Linear algebra by Georgi Shilov.

Landau Course in Theoretical Physics V1 Cover.jpg

Mechanics

Physics by Lev Landau.

Landau Course in Theoretical Physics V2 Cover.jpg

The Classical Theory of Fields

Physics by Lev Landau.

Bishop Tensor Analysis Cover.jpg

Tensor Analysis on Manifolds

Tensor analysis by Richard Bishop and Samuel Goldberg.

Sternberg Differential Geometry Cover.jpg

Lectures on Differential Geometry

Differential geometry by Shlomo Sternberg.

Vaisman Cohomology and Differential Forms Cover.jpg

Cohomology & Differential Forms

Cohomology and differential forms by Isu Vaisman.

Backbone

Arnold Ordinary Differential Equations Cover.jpg

Ordinary Differential Equations

Ordinary differential equations by Vladimir Arnold.

Kaplansky Set Theory and Metric Spaces Cover.jpg

Set Theory and Metric Spaces

Set theory and metric spaces by Irving Kaplansky.

E Landau Foundations of Analysis Cover.jpg

Foundations of Analysis

Analysis, intro to numbers, by Edmund Landau.

Rudin Principles of Mathematical Analysis Cover.jpg

Principles of Mathematical Analysis

Mathematical analysis by Walter Rudin.

Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg

Topology: A Categorical Approach

Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.

Ahlfors Complex Analysis Cover.jpg

Complex Analysis

Complex analysis by Lars Ahlfors.

Olver Applications of Lie Groups to Differential Equations Cover.jpg

Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations by Peter Olver.

Aluffi Algebra Chapter 0 Cover.jpg

Algebra Chapter 0

Complex analysis by Paolo Aluffi.

Lang Algebra Cover.jpg

Algebra

Algebra by Serge Lang.