6,480
edits
User:Aardvark/Read: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
[[File:Read.jpg|thumb|250px|A graphic showing the list's dependencies. Click to enlarge.]] | [[File:Read.jpg|thumb|250px|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. | This list of books provides the most direct and rigorous route to understanding differential geometry. Each selection thoroughly addresses its subject matter. There are other books for more specific topics. These are the core. See the image on the right for a visual treatment of its dependencies. | ||
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. | |||
The "Royal Road to Differential Geometry and Physics" is the focus of the list. While on that track, you should refer to the "Fill in Gaps" and "Backbone" sections as needed. | |||
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. | The greatest hurdles are motivation and coming to understand the language of mathematics. | ||
| Line 50: | Line 54: | ||
Prerequisite: | Prerequisite: | ||
* [[{{FULLPAGENAME}}#Calculus|Calculus]] | * [[{{FULLPAGENAME}}#Calculus|Calculus]] | ||
Backbone reference: | |||
* [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]] | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
| Line 74: | Line 80: | ||
| link = Lectures on Differential Geometry (Book) | | link = Lectures on Differential Geometry (Book) | ||
| title = === Lectures on Differential Geometry === | | title = === Lectures on Differential Geometry === | ||
| desc = Differential geometry by Shlomo Sternberg. | | 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 | {{BookListing | ||
| Line 80: | Line 91: | ||
| link = Cohomology & Differential Forms (Book) | | link = Cohomology & Differential Forms (Book) | ||
| title = === Cohomology & Differential Forms === | | title = === Cohomology & Differential Forms === | ||
| desc = Cohomology and differential forms by Isu Vaisman. | | desc = Cohomology and differential forms by Isu Vaisman.<br> | ||
Backbone reference: | |||
* [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]] | |||
* [[{{FULLPAGENAME}}#Algebra|Algebra]] | |||
}} | }} | ||
</div> | </div> | ||