User:Aardvark/Read: Difference between revisions
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{{BookListing | {{BookListing | ||
| cover = Lang Basic Mathematics Cover.jpg | | cover = Lang Basic Mathematics Cover.jpg | ||
| link = Basic Mathematics (Book) | |||
| 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. | ||
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| cover = Apostol Calculus V1 Cover.jpg | | cover = Apostol Calculus V1 Cover.jpg | ||
| link = Calculus (Book) | |||
| title = === Calculus === | | title = === Calculus === | ||
| desc = Overview of Calculus by Tom Apostol. | | desc = Overview of Calculus by Tom Apostol. | ||
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| cover = Lawvere Sets for Mathematics Cover.jpg | | cover = Lawvere Sets for Mathematics Cover.jpg | ||
| link = Sets for Mathematics (Book) | |||
| 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. | ||
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| cover = Shilov Linear Algebra Cover.jpg | | cover = Shilov Linear Algebra Cover.jpg | ||
| link = Linear Algebra (Book) | |||
| title = === Linear Algebra === | | title = === Linear Algebra === | ||
| desc = Linear algebra by Georgi Shilov. | | desc = Linear algebra by Georgi Shilov. | ||
Revision as of 14:49, 6 July 2021
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.
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.