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== Philosophy == | == Philosophy == | ||
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: | 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. Β | * The algebraic topology texts are not "pure" either - focusing on applications to differential or algebraic geometry, and many more. Β | ||
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 | 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. | ||
== Related Lists == | == Related Lists == | ||
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Fredric Schuller's [[Watch|video lectures]] concisely summarize various algebraic and geometric constructions that commonly appear in theoretical physics. | Fredric Schuller's [[Watch|video lectures]] concisely summarize various algebraic and geometric constructions that commonly appear in theoretical physics. | ||
A [ | A [http://sheafification.com/the-fast-track/ related set of texts] works with the same basics to lay a path through gauge field theory, quantum mechanics, algebraic geometry, and quantum field theory. | ||
== List Structure == | == List Structure == | ||
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Calculus is not in the pictured starter pack because it is found more often in high school curricula, while linear algebra (''despite being core to "applied mathematics" topics such as engineering, numerical computing, and statistics'') is often missing at the required level of rigor. Thus, we suggest looking at any '''Basic Mathematics''' to quickly fill in your gaps and as a source of quick and dirty computational techniques used universally. | Calculus is not in the pictured starter pack because it is found more often in high school curricula, while linear algebra (''despite being core to "applied mathematics" topics such as engineering, numerical computing, and statistics'') is often missing at the required level of rigor. Thus, we suggest looking at any '''Basic Mathematics''' to quickly fill in your gaps and as a source of quick and dirty computational techniques used universally. | ||
The | The texts by '''Landau''' are the list's core. While on that track, you should start dipping into the texts listed under the Landau volumes to enhance your perspective on repeated readings | ||
The '''General Mathematics''' section covers the knowledge that would be acquired in standard (but basic) graduate courses on the different areas of mathematics that later develop into modern topics, and should be developed alongside Landau. | The '''General Mathematics''' section covers the knowledge that would be acquired in standard (but basic) graduate courses on the different areas of mathematics that later develop into modern topics, and should be developed alongside Landau. | ||
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<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Fieldsmath2.jpg | ||
| link = The Classical Theory of Fields (Book)#Applications | | link = The Classical Theory of Fields (Book)#Applications | ||
| title = Β | | title = Β | ||
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<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Quantmathv2.jpg | ||
| link = Quantum Mechanics (Book)#Applications | | link = Quantum Mechanics (Book)#Applications | ||
| title = Β | | title = Β | ||
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<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Qftmath.jpg | ||
| link = Quantum Electrodynamics (Book)#Applications | | link = Quantum Electrodynamics (Book)#Applications | ||
| title = Β | | title = Β | ||
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| link = Statistical Physics (Book) | | link = Statistical Physics (Book) | ||
| title = === Statistical Physics === | | title = === Statistical Physics === | ||
| desc = Statistical Physics by Landau and Lifshitz. | | desc = Statistical Physics by Landau and Lifshitz. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Fluid Mechanics (Book) | | link = Fluid Mechanics (Book) | ||
| title = === Fluid Mechanics === | | title = === Fluid Mechanics === | ||
| desc = Fluid Mechanics by Landau and Lifshitz. | | desc = Fluid Mechanics by Landau and Lifshitz. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Statistical Physics part 2 - quantum theory (Book) | | link = Statistical Physics part 2 - quantum theory (Book) | ||
| title = === Statistical Physics part 2 === | | title = === Statistical Physics part 2 === | ||
| desc = Statistical Physics part 2 by Landau and Lifshitz. | | desc = Statistical Physics part 2 by Landau and Lifshitz. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| link = Physical Kinetics (Book) | | link = Physical Kinetics (Book) | ||
| title = === Physical Kinetics === | | title = === Physical Kinetics === | ||
| desc = Physical Kinetics by Landau and Lifshitz. | | desc = Physical Kinetics by Landau and Lifshitz. | ||
}} | }} | ||
</div> | </div> | ||
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}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg | ||
| link = Topology | | link = Topology: A Categorical Approach (Book) | ||
| title = === Topology | | title = === Topology: A Categorical Approach === | ||
| desc = Topology | | desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. [https://topology.mitpress.mit.edu/ Click here for the Open Access version.] | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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| 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 | {{BookListing | ||
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| title = === Algebraic Geometry === | | title = === Algebraic Geometry === | ||
| desc = Algebraic Geometry by Robin Hartshorne. | | desc = Algebraic Geometry by Robin Hartshorne. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
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=== Quantum Fields Beyond Landau === | === Quantum Fields Beyond Landau === | ||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | |||
| cover = Weinberg 1 quantum fields cover.jpg | |||
| link = The Quantum Theory of Fields 1, Foundations (Book) | |||
| title = === The Quantum Theory of Fields 1, Foundations === | |||
| desc = The Quantum Theory of Fields 1, Foundations by Steven Weinberg. | |||
}} | |||
{{BookListing | |||
| cover = Weinberg 2 QFT gauge theory cover.jpg | |||
| link = The Quantum Theory of Fields 2, Gauge Theory (Book) | |||
| title = === The Quantum Theory of Fields 2, Gauge Theory === | |||
| desc = The Quantum Theory of Fields 2, Gauge Theory by Steven Weinberg. | |||
}} | |||
{{BookListing | |||
| cover = Weinberg 3 QFT supersymmetry cover.jpg | |||
| link = The Quantum Theory of Fields 3, Supersymmetry (Book) | |||
| title = === The Quantum Theory of Fields 3, Supersymmetry === | |||
| desc = The Quantum Theory of Fields 3, Supersymmetry by Steven Weinberg. | |||
}} | |||
{{BookListing | {{BookListing | ||
| cover = Dewitt global qft 1 cover.jpg | | cover = Dewitt global qft 1 cover.jpg | ||
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| title = === The Global Approach to Quantum Field Theory === | | title = === The Global Approach to Quantum Field Theory === | ||
| desc = The Global Approach to Quantum Field Theory by Bryce DeWitt. | | desc = The Global Approach to Quantum Field Theory by Bryce DeWitt. | ||
}} | |||
{{BookListing | |||
| cover = Connes Noncommutative Geometry, Quantum Fields and Motives cover.jpg | |||
| link = Noncommutative Geometry, Quantum Fields and Motives (Book) | |||
| title = === Noncommutative Geometry, Quantum Fields and Motives === | |||
| desc = Noncommutative Geometry, Quantum Fields and Motives by Alain Connes and Matilde Marcolli. | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
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=== Mathematics === | === Mathematics === | ||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = Hermann Geometric Computing Science cover.jpg | | cover = Hermann Geometric Computing Science cover.jpg | ||
| link = Geometric Computing Science (Book) | | link = Geometric Computing Science (Book) | ||
| title = === Geometric Computing Science === | | title = === Geometric Computing Science === | ||
| desc = Geometric Computing Science, Interdisciplinary Mathematics XXV by | | desc = Geometric Computing Science, Interdisciplinary Mathematics XXV by Robert Hermann. | ||
}} | }} | ||
</div> | </div> | ||
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[[Category:Bot Commands]] | [[Category:Bot Commands]] | ||