Difference between revisions of "User:Aardvark/Read"

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Pretty pictures version of [[Read]].
[[File:Read.jpg|thumb|A graphic showing the list's dependencies. Click to enlarge.]]
__NOTOC__
 
== Version 2 ==
This list of books provides the most direct and rigorous route to understanding differential geometry. Each selection thoroughly addresses its subject matter. 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 for each idea.  
=== Fill in Gaps ===
 
<div class="flex-container">
See the image on the right for a visual treatment of its dependencies.
    <div class="flex-item">
 
        <div class="book-cover">
The '''Royal Road to Differential Geometry and Physics''' is the list's core. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed or as you desire.
[[File:Lang Basic Mathematics Cover.jpg|center|300px]]
 
        </div>
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.
        <div class="book-title">
 
==== Basic Mathematics ====
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.
        </div>
 
        <div class="book-desc">
The greatest hurdles are motivation and coming to understand the language of mathematics.
Review of arithmetic, basic algegra, trigonemetry, and geometry by Serge Lang.
 
        </div>
See also this list of videos.
    </div>
 
    <div class="flex-item">
== Fill in Gaps ==
[[File:Apostol Calculus V1 Cover.jpg|center|300px]]
<div class="flex-container" style="clear: both;">
==== Calculus ====
{{BookListing
Overview of Calculus by Tom Apostol.
| cover = Lang Basic Mathematics Cover.jpg
    </div>
| link = Basic Mathematics (Book)
| title = === Basic Mathematics ===
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.
}}
{{BookListing
| cover = Apostol Calculus V1 Cover.jpg
| link = Calculus (Book)
| title = === Calculus ===
| desc = Overview of Calculus by Tom Apostol.
}}
</div>
</div>
== Royal Road to Differential Geometry and Physics ==
<div class="flex-container">
<div class="flex-container">
    <div class="flex-item">
{{BookListing
[[File:Lawvere Sets for Mathematics Cover.jpg|center|300px]]
| cover = Lawvere Sets for Mathematics Cover.jpg
==== Sets for Mathematics ====
| link = Sets for Mathematics (Book)
Categorical approach to set theory by F. William Lawvere. Backbone reference: Set Theory and Metric Spaces by Kaplansky, Foundations of Analysis by Edmund Landau.
| title = === Sets for Mathematics ===
    </div>
| desc = Categorical approach to set theory by F. William Lawvere.<br>
    <div class="flex-item">
Backbone reference:
[[File:Shilov Linear Algebra Cover.jpg|center|300px]]
* [[{{FULLPAGENAME}}#Set Theory and Metric Spaces|Set Theory and Metric Spaces]]
==== Linear Algebra ====
* [[{{FULLPAGENAME}}#Foundations of Analysis|Foundations of Analysis]]
Linear Algabra by Georgi Shilov.
}}
    </div>
{{BookListing
    <div class="flex-item">
| cover = Shilov Linear Algebra Cover.jpg
[[File:Landau Course in Theoretical Physics V1 Cover.jpg|center|300px]]
| link = Linear Algebra (Book)
==== Mechanics ====
| title = === Linear Algebra ===
Physics by Lev Landau.
| desc = Overview of linear algebra by Georgi Shilov.
    </div>
}}
    <div class="flex-item">
{{BookListing
[[File:Landau Course in Theoretical Physics V2 Cover.jpg|center|300px]]
| cover = Landau Course in Theoretical Physics V1 Cover.jpg
==== The Classical Theory of Fields ====
| link = Mechanics (Book)
Physics by Lev Landau.
| title = === Mechanics ===
    </div>
| desc = Classical mechanics of physics by Lev Landau.<br>
    <div class="flex-item">
Prerequisite:
[[File:Bishop Tensor Analysis Cover.jpg|center|300px]]
* [[{{FULLPAGENAME}}#Calculus|Calculus]]
==== Tensor Analysis on Manifolds ====
Backbone reference:
Tensor analysis by Richard Bishop and Samuel Goldberg.
* [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]]
    </div>
}}
    <div class="flex-item">
{{BookListing
[[File:Sternberg Differential Geometry Cover.jpg|center|300px]]
| cover = Landau Course in Theoretical Physics V2 Cover.jpg
==== Lectures on Differential Geometry ====
| link = The Classical Theory of Fields (Book)
Differential geometry by Shlomo Sternberg.
| title = === The Classical Theory of Fields ===
    </div>
| desc = Physics by Lev Landau.<br>
    <div class="flex-item">
Prerequisite:
[[File:Vaisman Cohomology and Differential Forms Cover.jpg|center|300px]]
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]]
==== Cohomology & Differential Forms ====
}}
Cohomology and differential forms by Isu Vaisman.
{{BookListing
    </div>
| cover = Bishop Tensor Analysis Cover.jpg
| link = Tensor Analysis on Manifolds (Book)
| title = === Tensor Analysis on Manifolds ===
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br>
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 = Sternberg Differential Geometry Cover.jpg
| link = Lectures on Differential Geometry (Book)
| title = === Lectures on Differential Geometry ===
| desc = Differential geometry by Shlomo Sternberg.<br>
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]]
}}
</div>
</div>
=== Backbone ===
== Backbone ==
<div class="flex-container">
<div class="flex-container">
    <div class="flex-item">
{{BookListing
[[File:Arnold Ordinary Differential Equations Cover.jpg|center|300px]]
| cover = Kaplansky Set Theory and Metric Spaces Cover.jpg
==== Ordinary Differential Equations ====
| link = Set Theory and Metric Spaces (Book)
Ordinary differential equations by Vladimir Arnold.
| title = === Set Theory and Metric Spaces ===
    </div>
| desc = Set theory and metric spaces by Irving Kaplansky.
    <div class="flex-item">
}}
[[File:Kaplansky Set Theory and Metric Spaces Cover.jpg|center|300px]]
{{BookListing
==== Set Theory and Metric Spaces ====
| cover = E Landau Foundations of Analysis Cover.jpg
Set theory and metric spaces by Irving Kaplansky.
| link = Foundations of Analysis (Book)
    </div>
| title = === Foundations of Analysis ===
    <div class="flex-item">
| desc = Analysis, intro to numbers, by Edmund Landau.
[[File:E Landau Foundations of Analysis Cover.jpg|center|300px]]
}}
==== Foundations of Analysis ====
{{BookListing
Analysis, intro to numbers, by Edmund Landau.
| cover = Rudin Principles of Mathematical Analysis Cover.jpg
    </div>
| link = Principles of Mathematical Analysis (Book)
    <div class="flex-item">
| title = === Principles of Mathematical Analysis ===
[[File:Rudin Principles of Mathematical Analysis Cover.jpg|center|300px]]
| desc = Mathematical analysis by Walter Rudin.
==== Principles of Mathematical Analysis ====
}}
Mathematical analysis by Walter Rudin.
{{BookListing
    </div>
| cover = Arnold Ordinary Differential Equations Cover.jpg
    <div class="flex-item">
| link = Ordinary Differential Equations (Book)
[[File:Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg|center|300px]]
| title = === Ordinary Differential Equations ===
==== Topology: A Categorical Approach ====
| desc = Ordinary differential equations by Vladimir Arnold.
Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
}}
    </div>
{{BookListing
    <div class="flex-item">
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
[[File:Ahlfors Complex Analysis Cover.jpg|center|300px]]
| link = Topology: A Categorical Approach (Book)
==== Complex Analysis ====
| title = === Topology: A Categorical Approach ===
Complex analysis by Lars Ahlfors.
| desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
    </div>
}}
    <div class="flex-item">
{{BookListing
[[File:Olver Applications of Lie Groups to Differential Equations Cover.jpg|center|300px]]
| cover = Ahlfors Complex Analysis Cover.jpg
==== Applications of Lie Groups to Differential Equations ====
| link = Complex Analysis (Book)
Complex analysis by Peter Olver.
| title = === Complex Analysis ===
    </div>
| desc = Complex analysis by Lars Ahlfors.
    <div class="flex-item">
}}
[[File:Aluffi Algebra Chapter 0 Cover.jpg|center|300px]]
{{BookListing
==== Algebra Chapter 0 ====
| cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg
Complex analysis by Paolo Aluffi.
| link = Applications of Lie Groups to Differential Equations (Book)
    </div>
| title = === Applications of Lie Groups to Differential Equations ===
    <div class="flex-item">
| desc = Applications of Lie Groups to Differential Equations by Peter Olver.
[[File:Lang Algebra Cover.jpg|center|300px]]
}}
==== Algebra ====
{{BookListing
Algebra by Serge Lang.
| cover = Aluffi Algebra Chapter 0 Cover.jpg
    </div>
| link = Algebra Chapter 0 (Book)
</div>
| title = === Algebra Chapter 0 ===
 
| desc = Algebra by Paolo Aluffi. Easier than Lang's, but less direct.
== Books ==
}}
=== Fill in Gaps ===
{{BookListing
<br>
| cover = Lang Algebra Cover.jpg
<div class="iframe-container books" style="display: flex; flex-wrap: wrap; grid-gap: 1%; align-items: flex-start; grid-gap: 1em;">
| link = Algebra (Book)
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
| title = === Algebra ===
[[File:Lang Basic Mathematics Cover.jpg|center|300px]]
| desc = Algebra by Serge Lang. The most direct approach to the subject.
==== Basic Mathematics ====
}}
Review of arithmetic, basic algegra, trigonemetry, and geometry by Serge Lang.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Apostol Calculus V1 Cover.jpg|center|300px]]
==== Calculus ====
Introduction to Calculus by Tom Apostol.
    </div>
</div>
=== Road to Differential Geometry and Physics ===
<br>
<div class="iframe-container books" style="display: flex; flex-wrap: wrap; grid-gap: 1%; align-items: flex-start; grid-gap: 1em;">
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Lawvere Sets for Mathematics Cover.jpg|center|300px]]
==== Sets for Mathematics ====
Categorical approach to set theory by F. William Lawvere. Backbone reference: Set Theory and Metric Spaces by Kaplansky, Foundations of Analysis by Edmund Landau.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Shilov Linear Algebra Cover.jpg|center|300px]]
==== Linear Algebra ====
Linear Algabra by Georgi Shilov.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Landau Course in Theoretical Physics V1 Cover.jpg|center|300px]]
==== Mechanics ====
Physics by Lev Landau.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Landau Course in Theoretical Physics V2 Cover.jpg|center|300px]]
==== The Classical Theory of Fields ====
Physics by Lev Landau.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Bishop Tensor Analysis Cover.jpg|center|300px]]
==== Tensor Analysis on Manifolds ====
Tensor analysis by Richard Bishop and Samuel Goldberg.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Sternberg Differential Geometry Cover.jpg|center|300px]]
==== Lectures on Differential Geometry ====
Differential geometry by Shlomo Sternberg.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Vaisman Cohomology and Differential Forms Cover.jpg|center|300px]]
==== Cohomology & Differential Forms ====
Cohomology and differential forms by Isu Vaisman.
    </div>
</div>
 
=== Backbone ===
<br>
<div class="iframe-container books" style="display: flex; flex-wrap: wrap; grid-gap: 1%; align-items: flex-start; grid-gap: 1em;">
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Arnold Ordinary Differential Equations Cover.jpg|center|300px]]
==== Ordinary Differential Equations ====
Ordinary differential equations by Vladimir Arnold.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Kaplansky Set Theory and Metric Spaces Cover.jpg|center|300px]]
==== Set Theory and Metric Spaces ====
Set theory and metric spaces by Irving Kaplansky.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:E Landau Foundations of Analysis Cover.jpg|center|300px]]
==== Foundations of Analysis ====
Analysis, intro to numbers, by Edmund Landau.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Rudin Principles of Mathematical Analysis Cover.jpg|center|300px]]
==== Principles of Mathematical Analysis ====
Mathematical analysis by Walter Rudin.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg|center|300px]]
==== Topology: A Categorical Approach ====
Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Ahlfors Complex Analysis Cover.jpg|center|300px]]
==== Complex Analysis ====
Complex analysis by Lars Ahlfors.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Olver Applications of Lie Groups to Differential Equations Cover.jpg|center|300px]]
==== Applications of Lie Groups to Differential Equations ====
Complex analysis by Peter Olver.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Aluffi Algebra Chapter 0 Cover.jpg|center|300px]]
==== Algebra Chapter 0 ====
Complex analysis by Paolo Aluffi.
    </div>
    <div class="iframe-item" style="flex: 0 1 22%; margin-bottom: 1em;">
[[File:Lang Algebra Cover.jpg|center|300px]]
==== Algebra ====
Algebra by Serge Lang.
    </div>
</div>
</div>
__NOTOC__

Latest revision as of 16:12, 6 July 2021

A graphic showing the list's dependencies. Click to enlarge.

This list of books provides the most direct and rigorous route to understanding differential geometry. Each selection thoroughly addresses its subject matter. 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 for each idea.

See the image on the right for a visual treatment of its dependencies.

The Royal Road to Differential Geometry and Physics is the list's core. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed or as you desire.

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.

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.

The greatest hurdles are motivation and coming to understand the language of mathematics.

See also this list of videos.

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 Mathematics

Categorical approach to set theory by F. William Lawvere.
Backbone reference:

Shilov Linear Algebra Cover.jpg

Linear Algebra

Overview of linear algebra by Georgi Shilov.

Landau Course in Theoretical Physics V1 Cover.jpg

Mechanics

Classical mechanics of physics by Lev Landau.
Prerequisite:

Backbone reference:

Landau Course in Theoretical Physics V2 Cover.jpg

The Classical Theory of Fields

Physics by Lev Landau.
Prerequisite:

Bishop Tensor Analysis Cover.jpg

Tensor Analysis on Manifolds

Tensor analysis by Richard Bishop and Samuel Goldberg.
Prerequisite:

Backbone reference:

Sternberg Differential Geometry Cover.jpg

Lectures on Differential Geometry

Differential geometry by Shlomo Sternberg.
Prerequisite:

Backbone reference:

Vaisman Cohomology and Differential Forms Cover.jpg

Cohomology & Differential Forms

Cohomology and differential forms by Isu Vaisman.
Backbone reference:

Backbone

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.

Arnold Ordinary Differential Equations Cover.jpg

Ordinary Differential Equations

Ordinary differential equations by Vladimir Arnold.

Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg

Topology: A Categorical Approach

Topology 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

Algebra by Paolo Aluffi. Easier than Lang's, but less direct.

Lang Algebra Cover.jpg

Algebra

Algebra by Serge Lang. The most direct approach to the subject.