User:Aardvark/Read: Difference between revisions

Revision as of 14:52, 6 July 2021

A graphic showing the list's dependencies.

This list of books provides the most direct and rigorous route to understanding differential geometry.

Fill in Gaps

Basic Mathematics

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

Calculus

Overview of Calculus by Tom Apostol.

Royal Road to Differential Geometry and Physics

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.

Linear Algebra

Linear algebra by Georgi Shilov.

Mechanics

Physics by Lev Landau.

The Classical Theory of Fields

Physics by Lev Landau.

Tensor Analysis on Manifolds

Tensor analysis by Richard Bishop and Samuel Goldberg.

Lectures on Differential Geometry

Differential geometry by Shlomo Sternberg.

Cohomology & Differential Forms

Cohomology and differential forms by Isu Vaisman.

Backbone

Ordinary Differential Equations

Ordinary differential equations by Vladimir Arnold.

Set Theory and Metric Spaces

Set theory and metric spaces by Irving Kaplansky.

Foundations of Analysis

Analysis, intro to numbers, by Edmund Landau.

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.

Complex Analysis

Complex analysis by Lars Ahlfors.

Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations by Peter Olver.

Algebra Chapter 0

Complex analysis by Paolo Aluffi.

Algebra

Algebra by Serge Lang.

@@ Line 34: / Line 34: @@
 {{BookListing
 | cover = Landau Course in Theoretical Physics V1 Cover.jpg
+| link = Mechanics (Book)
 | title = === Mechanics ===
 | desc = Physics by Lev Landau.
@@ Line 39: / Line 40: @@
 {{BookListing
 | cover = Landau Course in Theoretical Physics V2 Cover.jpg
+| link = The Classical Theory of Fields (Book)
 | title = === The Classical Theory of Fields ===
 | desc = Physics by Lev Landau.
@@ Line 44: / Line 46: @@
 {{BookListing
 | 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.
@@ Line 49: / Line 52: @@
 {{BookListing
 | cover = Sternberg Differential Geometry Cover.jpg
+| link = Lectures on Differential Geometry (Book)
 | title = === Lectures on Differential Geometry ===
 | desc = Differential geometry by Shlomo Sternberg.
@@ Line 54: / Line 58: @@
 {{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.
@@ Line 62: / Line 67: @@
 {{BookListing
 | cover = Arnold Ordinary Differential Equations Cover.jpg
+| link = Ordinary Differential Equations (Book)
 | title = === Ordinary Differential Equations ===
 | desc = Ordinary differential equations by Vladimir Arnold.
@@ Line 67: / Line 73: @@
 {{BookListing
 | cover = Kaplansky Set Theory and Metric Spaces Cover.jpg
+| link = Set Theory and Metric Spaces (Book)
 | title = === Set Theory and Metric Spaces ===
 | desc = Set theory and metric spaces by Irving Kaplansky.
@@ Line 72: / Line 79: @@
 {{BookListing
 | cover = E Landau Foundations of Analysis Cover.jpg
+| link = Foundations of Analysis (Book)
 | title = === Foundations of Analysis ===
 | desc = Analysis, intro to numbers, by Edmund Landau.
@@ Line 77: / Line 85: @@
 {{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.
@@ Line 82: / Line 91: @@
 {{BookListing
 | cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
+| link = Topology: A Categorical Approach (Book)
 | title = === Topology: A Categorical Approach ===
 | desc = Mathematical analysis by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla.
@@ Line 87: / Line 97: @@
 {{BookListing
 | cover = Ahlfors Complex Analysis Cover.jpg
+| link = Complex Analysis (Book)
 | title = === Complex Analysis ===
 | desc = Complex analysis by Lars Ahlfors.
@@ Line 92: / Line 103: @@
 {{BookListing
 | cover = Olver Applications of Lie Groups to Differential Equations Cover.jpg
+| link = Applications of Lie Groups to Differential Equations (Book)
 | title = === Applications of Lie Groups to Differential Equations ===
 | desc = Applications of Lie Groups to Differential Equations by Peter Olver.
@@ Line 97: / Line 109: @@
 {{BookListing
 | cover = Aluffi Algebra Chapter 0 Cover.jpg
+| link = Algebra Chapter 0 (Book)
 | title = === Algebra Chapter 0 ===
 | desc = Complex analysis by Paolo Aluffi.
@@ Line 102: / Line 115: @@
 {{BookListing
 | cover = Lang Algebra Cover.jpg
+| link = Algebra (Book)
 | title = === Algebra ===
 | desc = Algebra by Serge Lang.