Bookshelf

Textbooks I have read or worked through — 47 books, listed alphabetically, each tagged with its area. Book reviews and recommended reading orders will be added over time.

A

• A First Course in Abstract Algebra — John Fraleigh · Algebra & Category Theory
• A First Course in General Relativity — Bernard Schutz · Electrodynamics, Relativity & PDEs
• A Geometric Approach to Differential Forms — David Bachman · Topology & Geometry
• A Logical Introduction to Proof — Daniel W. Cunningham · Analysis & Foundations
• A Primer of Special Relativity — P. L. Sardesai · Electrodynamics, Relativity & PDEs
• A Student’s Guide to Special Relativity — Norman Gray · Electrodynamics, Relativity & PDEs
• An Introduction to Category Theory — Harold Simmons · Algebra & Category Theory
• An Introduction to Manifolds — Loring W. Tu · Topology & Geometry
• An Introduction to Partial Differential Equations — Daniel Arrigo · Electrodynamics, Relativity & PDEs

C

• Categories for the Working Mathematician — Saunders Mac Lane · Algebra & Category Theory
• Classical Mechanics — John R. Taylor · Mathematical Physics & QFT
• Classical Mechanics and Geometry — Si Li · Mathematical Physics & QFT
• Complex Variables and Applications — James W. Brown & Ruel V. Churchill · Analysis & Foundations
• Crash Course on QFT and Symmetry — Si Li · Mathematical Physics & QFT

D

• Differential Geometry — Loring W. Tu · Topology & Geometry

E

• Electromagnetism and Geometry — Si Li · Mathematical Physics & QFT
• Elementary Differential Geometry — Andrew Pressley · Topology & Geometry
• Elementary Number Theory — David Burton · Analysis & Foundations
• Elements of Modern Algebra — Jimmie Gilbert & Linda Gilbert · Algebra & Category Theory

F

• Frobenius Algebras and 2D Topological Quantum Field Theories — Joachim Kock · Algebra & Category Theory

G

• Geometry, Topology and Physics — Mikio Nakahara · Topology & Geometry

I

• Introduction to Electrodynamics — David J. Griffiths · Electrodynamics, Relativity & PDEs
• Introduction to Hilbert Spaces with Applications — Lokenath Debnath · Quantum Mechanics

L

• Lectures on the Geometric Anatomy of Theoretical Physics (lecture notes) — Frederic Schuller · Mathematical Physics & QFT
• Linear Algebra — Kenneth Hoffman & Ray Kunze · Algebra & Category Theory
• Linear Algebra Done Right — Sheldon Axler · Algebra & Category Theory
• Low-Dimensional Geometry — Francis Bonahon · Topology & Geometry

M

• Mathematical Aspects of Quantum Mechanics — Roland Speicher · Mathematical Physics & QFT
• Mathematical Methods of Classical Mechanics — V. I. Arnold · Mathematical Physics & QFT
• Matrix Groups: An Introduction to Lie Group Theory — Andrew Baker · Mathematical Physics & QFT
• Measure, Integration & Real Analysis — Sheldon Axler · Analysis & Foundations
• Metric Spaces — Satish Shirali & Harkishan Vasudeva · Analysis & Foundations

N

• Naive Lie Theory — John Stillwell · Algebra & Category Theory

P

• Partial Differential Equations — Christopher C. Tisdell · Electrodynamics, Relativity & PDEs
• Principles of Quantum Mechanics — R. Shankar · Quantum Mechanics

Q

• Quantum Mechanics and Geometry — Si Li · Mathematical Physics & QFT
• Quantum Mechanics: Concepts and Applications — Nouredine Zettili · Quantum Mechanics
• Quantum Physics — Stephen Gasiorowicz · Quantum Mechanics

T

• Tensors and Manifolds: With Applications to Physics — Robert H. Wasserman · Topology & Geometry
• The Geometry of Discrete Groups — Alan F. Beardon · Topology & Geometry
• Topology — James Munkres · Topology & Geometry

U

• Understanding Analysis — Stephen Abbott · Analysis & Foundations

V

• Vector Calculus — Jerrold Marsden & Anthony Tromba · Electrodynamics, Relativity & PDEs
• Very Introductory Notes on Category Theory — Matteo Paganin · Algebra & Category Theory
• Visual Complex Analysis — Tristan Needham · Analysis & Foundations
• Visual Differential Geometry and Forms — Tristan Needham · Topology & Geometry

W

• What is a Quantum Field Theory? — Michel Talagrand · Mathematical Physics & QFT