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[[File:Linmechfieldsfolds.jpg|thumb|alt=Linear algebra, Mechanics, Relativity and Fields, Differential Geometry|The starter pack to physics and differential geometry.]]


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 starter pack to physics and differential geometry.


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.
== 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:
* 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
* We choose physics texts which connect to heavy mathematical machinery such as curvature and covariant derivatives in general relativity or symplectic/variational geometry in mechanics
* The algebraic topology texts are not "pure" either - focusing on applications to differential or algebraic geometry, and many more.  


See the image on the right for a visual representation of its dependencies.
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.


Also see this [[Watch|list of video lectures]].
== Related Lists ==


Fredric Schuller's [[Watch|video lectures]] concisely summarize various algebraic and geometric constructions that commonly appear in theoretical physics.


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 [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 ==


The '''Royal Road to Differential Geometry and Physics''' is the list's core. While on that track, you should refer to the '''Fill in Gaps''' and '''Backbone''' sections as needed or as you desire.
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 '''Fill in Gaps''' section covers the knowledge acquired in a strong high school mathematics education. Refer to it as needed, or begin there to develop your core skills.
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 '''Backbone''' section supports the ideas in the '''Royal Road'''. Refer to it to strengthen your understanding of the ideas in the main track and to take those ideas further.
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.


== Fill in Gaps ==
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
Line 27: Line 35:
| title = === Basic Mathematics ===
| title = === Basic Mathematics ===
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.
| desc = Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.
}}
{{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
Line 35: Line 49:
}}
}}
</div>
</div>
== Royal Road to Differential Geometry and Physics ==
== Landau ==
<div class="flex-container">
<div class="flex-container">
{{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 = Landau Course in Theoretical Physics V1 Cover.jpg
| cover = Landau Course in Theoretical Physics V1 Cover.jpg
Line 57: Line 56:
| title = === Mechanics ===
| title = === Mechanics ===
| desc = Classical mechanics of particles by Lev Landau.<br>
| desc = Classical mechanics of particles by Lev Landau.<br>
'''Prerequisite:'''
<div class="flex-container" style="clear: both;">
* [[{{FULLPAGENAME}}#Calculus|Calculus]]
{{BookListing
'''Backbone reference:'''
| cover = Mechmath.jpg
* [[{{FULLPAGENAME}}#Ordinary Differential Equations|Ordinary Differential Equations]]
| link = Mechanics (Book)#Applications
| title =
| desc = Symplectic geometry and other mathematical Structures of Classical Mechanics
}}
</div>
}}
}}
{{BookListing
{{BookListing
Line 67: Line 70:
| title = === The Classical Theory of Fields ===
| title = === The Classical Theory of Fields ===
| desc = Classical field theory of electromagnetism and general relativity by Lev Landau.<br>
| desc = Classical field theory of electromagnetism and general relativity by Lev Landau.<br>
'''Prerequisite:'''
<div class="flex-container" style="clear: both;">
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]]
{{BookListing
| cover = Fieldsmath2.jpg
| link = The Classical Theory of Fields (Book)#Applications
| title =
| desc = Differential/Riemannian geometry and other mathematical Structures in Relativistic Field Theory
}}
</div>
}}
}}
{{BookListing
{{BookListing
| cover = Bishop Tensor Analysis Cover.jpg
| cover = Landau Quantum Mechanics.jpg
| link = Tensor Analysis on Manifolds (Book)
| link = Quantum Mechanics (Book)
| title = === Tensor Analysis on Manifolds ===
| title = === Quantum Mechanics ===
| desc = Tensor analysis by Richard Bishop and Samuel Goldberg.<br>
| desc = Quantum Mechanics of particles, atoms, molecules by Landau and Lifshitz<br>
'''Prerequisite:'''
<div class="flex-container" style="clear: both;">
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]]
{{BookListing
'''Backbone reference:'''
| cover = Quantmath.jpg
* [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]]
| link = Quantum Mechanics (Book)#Applications
* [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]]
| title =
| desc = Generalized functions, spectra of self-adjoint operators, and other mathematical Structures in Quantum Mechanics
}}
</div>
}}
}}
{{BookListing
{{BookListing
| cover = Sternberg Differential Geometry Cover.jpg
| cover = Landau 4 Quantum Electrodynamics cover.jpg
| link = Lectures on Differential Geometry (Book)
| link = Quantum Electrodynamics (Book)
| title = === Lectures on Differential Geometry ===
| title = === Quantum Electrodynamics ===
| desc = Differential geometry by Shlomo Sternberg.<br>
| desc = Quantum Electrodynamics by Landau, written by Berestetskii, Lifshitz, and Pitaevskii.
'''Prerequisite:'''
}}
* [[{{FULLPAGENAME}}#Linear Algebra|Linear Algebra]]
{{BookListing
'''Backbone reference:'''
| cover = Landau statistical physics.jpg
* [[{{FULLPAGENAME}}#Principles of Mathematical Analysis|Principles of Mathematical Analysis]]
| link = Statistical Physics (Book)
* [[{{FULLPAGENAME}}#Topology: A Categorical Approach|Topology: A Categorical Approach]]
| title = === Statistical Physics ===
| desc = Statistical Physics by Landau and Lifshitz.
}}
{{BookListing
| cover = Landau 6 fluid mechanics cover.jpg
| link = Fluid Mechanics (Book)
| title = === Fluid Mechanics ===
| desc = Fluid Mechanics by Landau and Lifshitz.
}}
{{BookListing
| cover = Landau 7 elasticity cover.jpg
| link = Theory of Elasticity (Book)
| title = === Theory of Elasticity ===
| desc = Theory of Elasticity by Landau and Lifshitz.
}}
}}
{{BookListing
{{BookListing
| cover = Vaisman Cohomology and Differential Forms Cover.jpg
| cover = Landau 8 electrodynamics of continuous media cover.jpg
| link = Cohomology & Differential Forms (Book)
| link = Electrodynamics of Continuous Media (Book)
| title = === Cohomology & Differential Forms ===
| title = === Electrodynamics of Continuous Media ===
| desc = Cohomology and differential forms by Isu Vaisman. Sheaf theoretic description of the cohomology of real, complex, and foliated manifolds.<br>
| desc = Electrodynamics of Continuous Media by Landau, Lifshitz, and Pitaevskii.
'''Backbone reference:'''
* [[{{FULLPAGENAME}}#Algebra: Chapter 0|Algebra: Chapter 0]]
* [[{{FULLPAGENAME}}#Algebra|Algebra]]
}}
}}
</div>
== Backbone ==
<div class="flex-container">
{{BookListing
{{BookListing
| cover = Kaplansky Set Theory and Metric Spaces Cover.jpg
| cover = Landau 9 statistical physics part 2 cover.jpg
| link = Set Theory and Metric Spaces (Book)
| link = Statistical Physics part 2 - quantum theory (Book)
| title = === Set Theory and Metric Spaces ===
| title = === Statistical Physics part 2 ===
| desc = Set theory and metric spaces by Irving Kaplansky.
| desc = Statistical Physics part 2 by Landau and Lifshitz.
}}
}}
{{BookListing
{{BookListing
| cover = E Landau Foundations of Analysis Cover.jpg
| cover = Landau 10 physical kinetics cover.jpg
| link = Foundations of Analysis (Book)
| link = Physical Kinetics (Book)
| title = === Foundations of Analysis ===
| title = === Physical Kinetics ===
| desc = Analysis, intro to numbers, by Edmund Landau.
| desc = Physical Kinetics by Landau and Lifshitz.
}}
}}
</div>
== General Mathematics ==
<div class="flex-container" style="clear: both;">
{{BookListing
{{BookListing
| cover = Rudin Principles of Mathematical Analysis Cover.jpg
| cover = Lawvere Sets for Mathematics Cover.jpg
| link = Principles of Mathematical Analysis (Book)
| link = Sets for Mathematics (Book)
| title = === Principles of Mathematical Analysis ===
| title = === Sets for Mathematics ===
| desc = Mathematical analysis by Walter Rudin.
| desc = Categorical approach to set theory by F. William Lawvere.
}}
}}
{{BookListing
{{BookListing
Line 128: Line 150:
| title = === Ordinary Differential Equations ===
| title = === Ordinary Differential Equations ===
| desc = Ordinary differential equations by Vladimir Arnold.
| desc = Ordinary differential equations by Vladimir Arnold.
}}
{{BookListing
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
| link = Topology: A Categorical Approach (Book)
| title = === Topology: A Categorical Approach ===
| desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. [https://topology.mitpress.mit.edu/ Click here for the Open Access version.]
}}
}}
{{BookListing
{{BookListing
Line 148: Line 164:
}}
}}
{{BookListing
{{BookListing
| cover = Aluffi Algebra Chapter 0 Cover.jpg
| cover = Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg
| link = Algebra Chapter 0 (Book)
| link = Topology: A Categorical Approach (Book)
| title = === Algebra Chapter 0 ===
| title = === Topology: A Categorical Approach ===
| desc = Algebra by Paolo Aluffi. Easier than Lang's, but less direct.
| desc = Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. [https://topology.mitpress.mit.edu/ Click here for the Open Access version.]
}}
{{BookListing
| cover = Sternberg Differential Geometry Cover.jpg
| link = Lectures on Differential Geometry (Book)
| title = === Lectures on Differential Geometry ===
| desc = Differential geometry by Shlomo Sternberg.
}}
{{BookListing
| cover = Gelfand Generalized Functions vol 1 cover.png
| link = Generalized Functions (Book Series)
| title = === Generalized Functions: Properties and Operations ===
| desc = Generalized Functions: Properties and Operations by Israel Gel'fand and Georgi Shilov.
}}
{{BookListing
| cover = Gelfand Generalized Functions vol 2 cover.png
| link = Generalized Functions (Book Series)
| title = === Generalized Functions: Spaces of Fundamental and Generalized Functions ===
| desc = Generalized Functions: Spaces of Fundamental and Generalized Functions by Israel Gel'fand and Georgi Shilov.
}}
}}
{{BookListing
{{BookListing
Line 158: Line 192:
| title = === Algebra ===
| title = === Algebra ===
| desc = Algebra by Serge Lang. The most direct approach to the subject.
| desc = Algebra by Serge Lang. The most direct approach to the subject.
}}
{{BookListing
| cover = Bott and Tu Differential Forms in Algebraic Topology.jpg
| link = Differential Forms in Algebraic Topology (Book)
| title = === Differential Forms in Algebraic Topology ===
| desc = Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu.
}}
{{BookListing
| cover = Fulton-Harris Representation Theory cover.jpg
| link = Representation Theory (Book)
| title = === Representation Theory ===
| desc = Representation Theory by William Fulton and Joe Harris.
}}
{{BookListing
| cover = Hartshorne Algebraic Geometry cover.jpg
| link = Algebraic Geometry (Book)
| title = === Algebraic Geometry ===
| desc = Algebraic Geometry by Robin Hartshorne.
}}
{{BookListing
| cover = Vaisman Cohomology and Differential Forms Cover.jpg
| link = Cohomology & Differential Forms (Book)
| title = === Cohomology & Differential Forms ===
| desc = Cohomology and differential forms by Isu Vaisman. Sheaf theoretic description of the cohomology of real, complex, and foliated manifolds.
}}
{{BookListing
| cover = May A Concise Course in Algebraic Topology cover.jpg
| link = A Concise Course in Algebraic Topology (Book)
| title = === A Concise Course in Algebraic Topology ===
| desc = A Concise Course in Algebraic Topology by Peter May.
}}
</div>
== Aspirational ==
Here are some more awesome books.
=== Quantum Fields Beyond Landau ===
<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
| cover = Dewitt global qft 1 cover.jpg
| link = The Global Approach to Quantum Field Theory (Book Series)
| title = === The Global Approach to Quantum Field Theory ===
| 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
| cover = Nima grassmannian scattering cover.jpg
| link = Grassmannian Geometry of Scattering Amplitudes (Book)
| title = === Grassmannian Geometry of Scattering Amplitudes ===
| desc = Grassmannian Geometry of Scattering Amplitudes by Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka .
}}
}}
</div>
</div>
=== Mathematics ===
<div class="flex-container" style="clear: both;">
{{BookListing
| cover = Hermann Geometric Computing Science cover.jpg
| link = Geometric Computing Science (Book)
| title = === Geometric Computing Science ===
| desc = Geometric Computing Science, Interdisciplinary Mathematics XXV by Robert Hermann.
}}
</div>
== Honorable Mentions ==
The following are some other good books, which are either redundant or otherwise didn't fit into the main collection of texts.(Olver PDEs, Coxeter books to be inserted)
{{SHORTDESC:The starter pack to physics and differential geometry.}}


[[Category:Bot Commands]]
[[Category:Bot Commands]]

Revision as of 12:50, 12 April 2023

Linear algebra, Mechanics, Relativity and Fields, Differential Geometry
The starter pack to physics and differential geometry.

The starter pack to physics and differential geometry.

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:

  • 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
  • We choose physics texts which connect to heavy mathematical machinery such as curvature and covariant derivatives in general relativity or symplectic/variational geometry in mechanics
  • 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.

Related Lists

Fredric Schuller's video lectures concisely summarize various algebraic and geometric constructions that commonly appear in theoretical physics.

A 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

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 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 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

Lang Basic Mathematics Cover.jpg

Basic Mathematics

Review of arithmetic, algebra, trigonometry, logic, and geometry by Serge Lang.

Shilov Linear Algebra Cover.jpg

Linear Algebra

Linear algebra of linear equations, maps, tensors, and geometry by Georgi Shilov.

Apostol Calculus V1 Cover.jpg

Calculus

Overview of single and multi-variable calculus with applications to differential equations and probability by Tom Apostol.

Landau

Landau Course in Theoretical Physics V1 Cover.jpg

Mechanics

Classical mechanics of particles by Lev Landau.

Mechmath.jpg

Symplectic geometry and other mathematical Structures of Classical Mechanics

Landau Course in Theoretical Physics V2 Cover.jpg

The Classical Theory of Fields

Classical field theory of electromagnetism and general relativity by Lev Landau.

Fieldsmath2.jpg

Differential/Riemannian geometry and other mathematical Structures in Relativistic Field Theory

Landau Quantum Mechanics.jpg

Quantum Mechanics

Quantum Mechanics of particles, atoms, molecules by Landau and Lifshitz

Quantmath.jpg

Generalized functions, spectra of self-adjoint operators, and other mathematical Structures in Quantum Mechanics

Landau 4 Quantum Electrodynamics cover.jpg

Quantum Electrodynamics

Quantum Electrodynamics by Landau, written by Berestetskii, Lifshitz, and Pitaevskii.

Landau statistical physics.jpg

Statistical Physics

Statistical Physics by Landau and Lifshitz.

Landau 6 fluid mechanics cover.jpg

Fluid Mechanics

Fluid Mechanics by Landau and Lifshitz.

Landau 7 elasticity cover.jpg

Theory of Elasticity

Theory of Elasticity by Landau and Lifshitz.

Landau 8 electrodynamics of continuous media cover.jpg

Electrodynamics of Continuous Media

Electrodynamics of Continuous Media by Landau, Lifshitz, and Pitaevskii.

Landau 9 statistical physics part 2 cover.jpg

Statistical Physics part 2

Statistical Physics part 2 by Landau and Lifshitz.

Landau 10 physical kinetics cover.jpg

Physical Kinetics

Physical Kinetics by Landau and Lifshitz.

General Mathematics

Lawvere Sets for Mathematics Cover.jpg

Sets for Mathematics

Categorical approach to set theory by F. William Lawvere.

Arnold Ordinary Differential Equations Cover.jpg

Ordinary Differential Equations

Ordinary differential equations by Vladimir Arnold.

Ahlfors Complex Analysis Cover.jpg

Complex Analysis

Complex analysis by Lars Ahlfors.

Olver Applications of Lie Groups to Differential Equations Cover.jpg

Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations by Peter Olver.

Bradley Bryson Terrilla Topology A Categorical Appoach Cover.jpg

Topology: A Categorical Approach

Topology by Tai-Danae Bradley, Tyler Bryson, Josn Terrilla. Click here for the Open Access version.

Sternberg Differential Geometry Cover.jpg

Lectures on Differential Geometry

Differential geometry by Shlomo Sternberg.

Gelfand Generalized Functions vol 1 cover.png

Generalized Functions: Properties and Operations

Generalized Functions: Properties and Operations by Israel Gel'fand and Georgi Shilov.

Gelfand Generalized Functions vol 2 cover.png

Generalized Functions: Spaces of Fundamental and Generalized Functions

Generalized Functions: Spaces of Fundamental and Generalized Functions by Israel Gel'fand and Georgi Shilov.

Lang Algebra Cover.jpg

Algebra

Algebra by Serge Lang. The most direct approach to the subject.

Bott and Tu Differential Forms in Algebraic Topology.jpg

Differential Forms in Algebraic Topology

Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu.

Fulton-Harris Representation Theory cover.jpg

Representation Theory

Representation Theory by William Fulton and Joe Harris.

Hartshorne Algebraic Geometry cover.jpg

Algebraic Geometry

Algebraic Geometry by Robin Hartshorne.

Vaisman Cohomology and Differential Forms Cover.jpg

Cohomology & Differential Forms

Cohomology and differential forms by Isu Vaisman. Sheaf theoretic description of the cohomology of real, complex, and foliated manifolds.

May A Concise Course in Algebraic Topology cover.jpg

A Concise Course in Algebraic Topology

A Concise Course in Algebraic Topology by Peter May.

Aspirational

Here are some more awesome books.

Quantum Fields Beyond Landau

Weinberg 1 quantum fields cover.jpg

The Quantum Theory of Fields 1, Foundations

The Quantum Theory of Fields 1, Foundations by Steven Weinberg.

Weinberg 2 QFT gauge theory cover.jpg

The Quantum Theory of Fields 2, Gauge Theory

The Quantum Theory of Fields 2, Gauge Theory by Steven Weinberg.

Weinberg 3 QFT supersymmetry cover.jpg

The Quantum Theory of Fields 3, Supersymmetry

The Quantum Theory of Fields 3, Supersymmetry by Steven Weinberg.

Dewitt global qft 1 cover.jpg

The Global Approach to Quantum Field Theory

The Global Approach to Quantum Field Theory by Bryce DeWitt.

Connes Noncommutative Geometry, Quantum Fields and Motives cover.jpg

Noncommutative Geometry, Quantum Fields and Motives

Noncommutative Geometry, Quantum Fields and Motives by Alain Connes and Matilde Marcolli.

Nima grassmannian scattering cover.jpg

Grassmannian Geometry of Scattering Amplitudes

Grassmannian Geometry of Scattering Amplitudes by Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka .

Mathematics

Hermann Geometric Computing Science cover.jpg

Geometric Computing Science

Geometric Computing Science, Interdisciplinary Mathematics XXV by Robert Hermann.

Honorable Mentions

The following are some other good books, which are either redundant or otherwise didn't fit into the main collection of texts.(Olver PDEs, Coxeter books to be inserted)

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