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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 | Thus, the structure of this book list will be centered around core topics in theoretical physics which have already given direct connection to technology and reality, and the mathematics that follows from the theory rather than simply chasing popular formalisms. Future additions and pages will make an effort to connect with more project-based and experimental content, as our goal of demonstrating computational aspects (PDEs, Representation Theory, Numerical Analysis) have been fully satisfied and the supplementary material nearly completed. 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. We make no claim to complete coverage, especially since one needs to actively engage in experiment and new theoretical calculations to get further into a topic and this is a life's work. We do try to present essential mathematics and promising new directions. | ||
== Related Lists == | == Related Lists == | ||
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<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Fieldsmath3.jpg | ||
| link = The Classical Theory of Fields (Book)#Applications | | link = The Classical Theory of Fields (Book)#Applications | ||
| title = | | title = | ||
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<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Quantmathv3.jpg | ||
| link = Quantum Mechanics (Book)#Applications | | link = Quantum Mechanics (Book)#Applications | ||
| title = | | title = | ||
| Line 246: | Line 246: | ||
| title = === Representation Theory === | | title = === Representation Theory === | ||
| desc = Representation Theory by William Fulton and Joe Harris. | | desc = Representation Theory by William Fulton and Joe Harris. | ||
}} | |||
{{BookListing | |||
| cover = Manin algebra v cover.jpg | |||
| link = Algebra V: Homological Algebra (Book) | |||
| title = === Algebra V: Homological Algebra === | |||
| desc = Algebra V: Homological Algebra by Sergei Gelfand and Yuri Manin. | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| title = === Algebraic Geometry === | | title = === Algebraic Geometry === | ||
| desc = Algebraic Geometry by Robin Hartshorne. | | desc = Algebraic Geometry by Robin Hartshorne. | ||
}} | |||
{{BookListing | |||
| cover = Manin number theory cover.jpg | |||
| link = Introduction to Modern Number Theory (Book) | |||
| title = === Introduction to Modern Number Theory === | |||
| desc = Introduction to Modern Number Theory by Yuri Manin and Alexei Panchishkin. | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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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 | | desc = Cohomology and differential forms by Izu Vaisman. Sheaf theoretic description of the cohomology of real, complex, and foliated manifolds. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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=== Mathematics === | === Mathematics === | ||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | |||
| cover = Brown NAT cover.jpg | |||
| link = Nonabelian Algebraic Topology (Book) | |||
| title = === Nonabelian Algebraic Topology === | |||
| desc = Nonabelian Algebraic Topology by Ronald Brown, Philip Higgins, and Rafael Sivera. | |||
}} | |||
{{BookListing | {{BookListing | ||
| cover = Kacvertex cover.jpg | | cover = Kacvertex cover.jpg | ||
| Line 299: | Line 317: | ||
| title = === Vertex Algebras and Algebraic Curves === | | title = === Vertex Algebras and Algebraic Curves === | ||
| desc = Vertex Algebras and Algebraic Curves by Edward Frenkel and David Ben-Zvi. | | desc = Vertex Algebras and Algebraic Curves by Edward Frenkel and David Ben-Zvi. | ||
}} | |||
{{BookListing | |||
| cover = HHR Kervaire cover .jpg | |||
| link = Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem (Book) | |||
| title = === Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem === | |||
| desc = Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem by Michael A. Hill, Michael J. Hopkins, Douglas C. Ravenel. | |||
}} | |||
{{BookListing | |||
| cover = Mcduff jholomorphic cover.jpg | |||
| link = J-holomorphic Curves and Symplectic Topology (Book) | |||
| title = === J-holomorphic Curves and Symplectic Topology === | |||
| desc = J-holomorphic Curves and Symplectic Topology By Dusa McDuff and Dietmar Salamon. | |||
}} | |||
{{BookListing | |||
| cover = Fukaya intersection cover.jpg | |||
| link = Lagrangian Intersection Floer Theory: Anomaly and Obstruction (Book Series) | |||
| title = === Lagrangian Intersection Floer Theory: Anomaly and Obstruction === | |||
| desc = Lagrangian Intersection Floer Theory: Anomaly and Obstruction by Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono. | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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[[Category:Bot Commands]] | [[Category:Bot Commands]] | ||
[[Category:Mathematics]] | |||
[[Category:Physics]] | |||