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Difference between revisions of "Read"
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[[File:Read.jpg|thumb|A graphic showing the list's dependencies. Click to enlarge.]] | [[File:Read.jpg|thumb|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, the mathematical language of physics. Each selection thoroughly addresses its subject matter. The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and/or read several together to acquire the necessary language and understand the motivations for each idea. The greatest hurdles are the motivation to learn and developing an understanding of the language of mathematics. | This list of books provides the most direct and rigorous route to understanding differential geometry, the mathematical language of physics. Each selection thoroughly addresses its subject matter. | ||
The list does not need to be read linearly or only one book at a time. It is encouraged to go between books and/or read several together to acquire the necessary language and understand the motivations for each idea. The greatest hurdles are the motivation to learn and developing an understanding of the language of mathematics. | |||
See the image on the right for a visual representation of its dependencies. | See the image on the right for a visual representation of its dependencies. | ||
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A further set of texts extending this one, but working with the same basics has been produced leading all the way up and through gauge field theory, quantum mechanics, algebraic geometry, and quantum field theory [http://sheafification.com/the-fast-track/ here] | A further set of texts extending this one, but working with the same basics has been produced leading all the way up and through gauge field theory, quantum mechanics, algebraic geometry, and quantum field theory [http://sheafification.com/the-fast-track/ here]. | ||
== List Structure == | == List Structure == | ||
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| link = Calculus (Book) | | link = Calculus (Book) | ||
| title = === Calculus === | | title = === Calculus === | ||
| desc = Overview of | | desc = Overview of single and multi-variable calculus with applications to differential equations and probability by Tom Apostol. | ||
}} | }} | ||
</div> | </div> | ||
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| link = Linear Algebra (Book) | | link = Linear Algebra (Book) | ||
| title = === Linear Algebra === | | title = === Linear Algebra === | ||
| desc = | | desc = Linear algebra of linear equations, maps, tensors, and geometry by Georgi Shilov. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Mechanics (Book) | | link = Mechanics (Book) | ||
| title = === Mechanics === | | title = === Mechanics === | ||
| desc = Classical mechanics of | | desc = Classical mechanics of particles by Lev Landau.<br> | ||
'''Prerequisite:''' | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Calculus|Calculus]] | * [[{{FULLPAGENAME}}#Calculus|Calculus]] | ||
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| link = The Classical Theory of Fields (Book) | | link = The Classical Theory of Fields (Book) | ||
| title = === The Classical Theory of Fields === | | title = === The Classical Theory of Fields === | ||
| desc = | | desc = Classical field theory of electromagnetism and general relativity by Lev Landau.<br> | ||
'''Prerequisite:''' | '''Prerequisite:''' | ||
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | * [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | ||
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| 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.<br> | | desc = Cohomology and differential forms by Isu Vaisman. Sheaf theoretic description of the cohomology of real, complex, and foliated manifolds.<br> | ||
'''Backbone reference:''' | '''Backbone reference:''' | ||
* [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]] | * [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]] | ||