User:Aardvark/Read: Difference between revisions

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

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 1: / Line 1: @@
-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__
-== Version 2 ==
-=== Fill in Gaps ===
+== Fill in Gaps ==
 <div class="flex-container" style="clear: both;">
 {{BookListing
 | cover = Lang Basic Mathematics Cover.jpg
-| title = ==== Basic Mathematics ====
+| title = === Basic Mathematics ===
 | desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.
 }}
 {{BookListing
 | cover = Apostol Calculus V1 Cover.jpg
-| title = ==== Calculus ====
+| title = === Calculus ===
 | desc = Overview of Calculus by Tom Apostol.
 }}
 </div>
-=== Royal Road to Differential Geometry and Physics ===
+== Royal Road to Differential Geometry and Physics ==
 <div class="flex-container">
 {{BookListing
 | 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.
 }}
 {{BookListing
 | cover = Shilov Linear Algebra Cover.jpg
-| title = ==== Linear Algebra ====
+| title = === Linear Algebra ===
 | desc = Linear algebra by Georgi Shilov.
 }}
 {{BookListing
 | cover = Landau Course in Theoretical Physics V1 Cover.jpg
-| title = ==== Mechanics ====
+| title = === Mechanics ===
 | desc = Physics by Lev Landau.
 }}
 {{BookListing
 | 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.
 }}
 {{BookListing
 | 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.
 }}
 {{BookListing
 | cover = Sternberg Differential Geometry Cover.jpg
-| title = ==== Lectures on Differential Geometry ====
+| title = === Lectures on Differential Geometry ===
 | desc = Differential geometry by Shlomo Sternberg.
 }}
 {{BookListing
 | cover = Vaisman Cohomology and Differential Forms Cover.jpg
-| title = ==== Cohomology & Differential Forms ====
+| title = === Cohomology & Differential Forms ===
 | desc = Cohomology and differential forms by Isu Vaisman.
 }}
 </div>
-=== Backbone ===
+== Backbone ==
 <div class="flex-container">
 {{BookListing
 | cover = Arnold Ordinary Differential Equations Cover.jpg
-| title = ==== Ordinary Differential Equations ====
+| title = === Ordinary Differential Equations ===
 | desc = Ordinary differential equations by Vladimir Arnold.
 }}
 {{BookListing
 | 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.
 }}
 {{BookListing
 | cover = E Landau Foundations of Analysis Cover.jpg
-| title = ==== Foundations of Analysis ====
+| title = === Foundations of Analysis ===
 | desc = Analysis, intro to numbers, by Edmund Landau.
 }}
 {{BookListing
 | cover = Rudin Principles of Mathematical Analysis Cover.jpg
-| title = ==== Principles of Mathematical Analysis ====
+| title = === Principles of Mathematical Analysis ===
 | desc = Mathematical analysis by Walter Rudin.
 }}
 {{BookListing
 | 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.
 }}
 {{BookListing
 | cover = Ahlfors Complex Analysis Cover.jpg
-| title = ==== Complex Analysis ====
+| title = === Complex Analysis ===
 | desc = Complex analysis by Lars Ahlfors.
 }}
 {{BookListing
 | 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.
 }}
 {{BookListing
 | cover = Aluffi Algebra Chapter 0 Cover.jpg
-| title = ==== Algebra Chapter 0 ====
+| title = === Algebra Chapter 0 ===
 | desc = Complex analysis by Paolo Aluffi.
 }}
 {{BookListing
 | cover = Lang Algebra Cover.jpg
-| title = ==== Algebra ====
+| title = === Algebra ===
 | desc = Algebra by Serge Lang.
 }}
 </div>