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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:
* Later volumes of Landau on emergent/less fundamental physics refer to more engineering applications and numerical analysis (vols. 5-10)
* The numerical analysis texts make an effort to discuss the geometry of tensor spaces, or preserve geometric structures in numerical integration
* 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. 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.
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 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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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 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 decalogy 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. Books in the top rows are generally more basic and can be read at the same time, giving important insight into the structure of the subjects.


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;">
{{BookListing
{{BookListing
| cover = Fieldsmath2.jpg
| 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 = Quantmath.jpg
| cover = Quantmathv3.jpg
| link = Quantum Mechanics (Book)#Applications
| link = Quantum Mechanics (Book)#Applications
| title =  
| title =  
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| link = Quantum Electrodynamics (Book)
| link = Quantum Electrodynamics (Book)
| title = === Quantum Electrodynamics ===
| title = === Quantum Electrodynamics ===
| desc = Quantum Electrodynamics by Landau, written by Berestetskii, Lifshitz, and Pitaevskii.
| desc = Quantum Electrodynamics by Landau, written by Berestetskii, Lifshitz, and Pitaevskii.<br>
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = QFTmathv2.jpg
| link = Quantum Electrodynamics (Book)#Applications
| title =
| desc = Axiomatic and Geometric Structures in Quantum Field Theory
}}
</div>
}}
}}
{{BookListing
{{BookListing
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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.<br>
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Statmechmath.jpg
| link = Statistical Physics (Book)#Applications
| title =
| desc = Symplectic statistical mechanics, lattice, and stochastic quantization methods
}}
</div>
}}
}}
{{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.<br>
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Fluidsmath.jpg
| link = Fluid Mechanics (Book)#Applications
| title =
| desc = Topological hydrodynamics, statistical methods of turbulence, cloud physics, geometric and tensor numerical analysis
}}
</div>
}}
}}
{{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.<br>
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Condensedmath.jpg
| link = Statistical Physics part 2 - quantum theory (Book)#Applications
| title =
| desc = High Tc superconductivity, holography and string theory in condensed matter, emergent gauge fields/Chern-Simons, random matrix theory, the Quantum Hall Effect
}}
</div>
}}
}}
{{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.<br>
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Kineticsmath.jpg
| link = Physical Kinetics (Book)#Applications
| title =
| desc = Open quantum systems, stochastic differential equations, plasma physics, combustion, cloud physics, and stochastic processes on manifolds
}}
</div>
}}
}}
</div>
</div>
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}}
}}
{{BookListing
{{BookListing
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
| cover = Brown groupoids cover.jpg
| link = Topology: A Categorical Approach (Book)
| link = Topology and Groupoids (Book)
| title = === Topology: A Categorical Approach ===
| title = === Topology and Groupoids ===
| desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. [https://topology.mitpress.mit.edu/ Click here for the Open Access version.]
| desc = Topology and Groupoids by Ronald Brown. [https://groupoids.org.uk/pdffiles/topgrpds-e.pdf 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
| 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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=== 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
| 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
| cover = Kacvertex cover.jpg
| link = Vertex Algebras for Beginners (Book)
| title = === Vertex Algebras for Beginners ===
| desc = Vertex Algebras for Beginners by Victor Kac.
}}
{{BookListing
| cover = Frenkelvertex cover.jpg
| link = Vertex Algebras and Algebraic Curves (Book)
| title = === Vertex Algebras and Algebraic Curves ===
| 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
| 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 Robert Hermann.
| desc = Geometric Computing Science, Interdisciplinary Mathematics XXV by [[Robert Hermann]].
}}
}}
</div>
</div>
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[[Category:Bot Commands]]
[[Category:Bot Commands]]
[[Category:Mathematics]]
[[Category:Physics]]
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