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User:Anisomorphism: Difference between revisions
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Our point of view is that the texts typically used in physics and especially mathematics degree tracks are window dressing for the real job of being a mathematical physicist. Excellent texts meet a certain standard we set here; Texts should be concise to respect the reader's time and occupations, interdisciplinary, at least relating mathematical tools between areas of mathematics: | Our point of view is that the texts typically used in physics and especially mathematics degree tracks are window dressing for the real job of being a mathematical physicist or even an engineer. Excellent texts meet a certain standard we set here; Texts should be concise to respect the reader's time and occupations, interdisciplinary, at least relating mathematical tools between areas of mathematics: | ||
* Lang's algebra text contains examples and applications in geometry and number theory throughout | * Lang's algebra text contains examples and applications in geometry and number theory throughout | ||
* Vaisman emphasizes the typically algebro-geometric method of sheaves in a differential geometry setting and to develop the theory of multiple sorts of manifolds | * Vaisman emphasizes the typically algebro-geometric method of sheaves in a differential geometry setting and to develop the theory of multiple sorts of manifolds | ||
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* The algebraic topology texts are not "pure" either - focusing on applications to differential or algebraic geometry, and many more. | * The algebraic topology texts are not "pure" either - focusing on applications to differential or algebraic geometry, and many more. | ||
Thus, the structure of this book list will be centered around core topics in theoretical physics which are already given direct connection to technology and reality, and the mathematics that follows from the theory rather than simply chasing popular formalisms. Future iterations will make an effort to connect with more computational content, such as that seen in representation theory or Olver's text on applications of Lie groups. | Thus, the structure of this book list will be centered around core topics in theoretical physics which are already given direct connection to technology and reality, and the mathematics that follows from the theory rather than simply chasing popular formalisms. Future iterations will make an effort to connect with more computational content, such as that seen in representation theory or Olver's text on applications of Lie groups. This pertains to our last criterion that there should be some elementary aspects in a text - showing the translation of the abstract machinery into basic computations to make the relationships with other areas even more transparent. | ||
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The '''Aspirational''' section contains some of the big ideas, which may be repeated from earlier but deserve emphasis. These are the triumphs of mathematics, peaks that everyone deserves to climb. | The '''Aspirational''' section contains some of the big ideas, which may be repeated from earlier but deserve emphasis. These are the triumphs of mathematics, peaks that everyone deserves to climb. | ||
== | == Basic Mathematics == | ||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
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}} | }} | ||
</div> | </div> | ||
== | == Landau == | ||
<div class="flex-container"> | <div class="flex-container"> | ||
{{BookListing | {{BookListing | ||
| cover = Landau Course in Theoretical Physics V1 Cover.jpg | | cover = Landau Course in Theoretical Physics V1 Cover.jpg | ||
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* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | * [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]] | ||
}} | }} | ||
{{BookListing | |||
| cover = Lawvere Sets for Mathematics Cover.jpg | |||
| link = Sets for Mathematics (Book) | |||
| title = === Sets for Mathematics === | |||
| desc = Categorical approach to set theory by F. William Lawvere.<br> | |||
'''Backbone reference:''' | |||
* [[{{FULLPAGENAME}}#Set Theory and Metric Spaces|Set Theory and Metric Spaces]] | |||
* [[{{FULLPAGENAME}}#Foundations of Analysis|Foundations of Analysis]] | |||
}} | |||
{{BookListing | |||
| cover = Shilov Linear Algebra Cover.jpg | |||
| link = Linear Algebra (Book) | |||
| title = === Linear Algebra === | |||
| desc = Linear algebra of linear equations, maps, tensors, and geometry by Georgi Shilov. | |||
}} | |||
{{BookListing | {{BookListing | ||
| cover = Bishop Tensor Analysis Cover.jpg | | cover = Bishop Tensor Analysis Cover.jpg | ||