User:Aardvark/Read

From The Portal Wiki
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. See the image on the right for a visual treatment of its dependencies.

Each selection thoroughly addresses its topics.

There are other books for more specific topics. These are the core.

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 Methematics

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

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

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.