Bookshelf

Bookshelf

I'm very much a textbooks-and-lecture-notes person — I find going through them to be far more effective at building a deep understanding than listening to live lectures. Here are the documents that I have read significant portions of and found helpful in my studies. They are roughly sorted by stars in their difficulty. Their categories are approximate, and get increasingly blended with each other at the more advanced levels.

* light: no prerequisites
** introductory: requires some mathematical maturity
*** medium: a more sophisticated second exposure
**** advanced: requires specialized mathematical background
***** hella advanced

• Math
  • Discrete: logic, groups, graphs, and cryptography
    • * Rosen, Discrete Mathematics (book) - Introductory concepts in sets, groups, and graphs. Good starting point in learning proof-based math.
  • Analysis: continuity, derivatives, and integrals
    • ** Abbott, Understanding Analysis (book) - The romantic's introduction to real analysis, interweaving math and history together into an enthralling story.
    • ** Stein, Complex Analysis (book) - Solid introduction to the calculus of complex-valued functions, very useful to field theories, such as electrodynamics and QFT.
  • Linear algebra: vectors, operators, and inner products
    • * Strang, Linear Algebra and Its Applications (book) - Illustrates the many practical uses of matrices in math, science, and engineering.
    • ** Eigenchris, Tensors for Beginners (videos) - For fans of special and general relativity. Incidentally, this was how my journey into modern physics started.
    • *** Axler, Linear Algebra Done Right (book) - The most important proof-based mathematics book for any physicist, with broad applications anywhere the system is linear or can be approximated as such, including quantum mechanics, electrodynamics, relativity.
  • Geometry and topology: curvature and invariants
    • ** Armstrong, Basic Topology (book) - Motivates why categorizing shapes is so useful.
    • ** 't Hooft, Lie Groups in Physics (notes) - Fastest way to understand spin in quantum mechanics and gauge groups in particle physics.
    • *** Nakahara, Geometry, Topology, and Physics (book)
    • *** Eigenchris, Tensor Calculus (videos)
    • *** Eigenchris, Spinors for Beginners (videos)
    • **** Fecko, Differential Geometry and Lie Groups for Physicists (book)
  • Miscellaneous
    • * Boas, Mathematical Physics (book) - Handy reference text for basic results in complex analysis, Fourier analysis, and linear algebra.
• Physics
  • Astrophysics: stars, planets, galaxies, cosmology
    • * Fix, Astronomy: Journey to the Cosmic Frontier (book) - Qualitative tour of all the major fields in astrophysics. Good place to start without any physics knowledge.
    • ** Liddle, An Introduction to Modern Cosmology (book) - Very accessible introduction to the field of cosmology.
    • ** Carroll & Ostlie, Introduction to Modern Astrophysics (book) - Good stuff to learn alongside a first course in physics. Also serves as a compendium of key theoretical derivations in all the major fields in astrophysics.
    • ** Tong, Cosmology (notes)
    • **** Dodelson & Schmidt, Modern Cosmology (book)
  • Classical mechanics: newtonian, lagrangian, hamiltonian, special relativity
    • ** Giancoli - Principles of Physics (part I) (book)
    • *** Kleppner & Kolenkow - Introduction to Classical Mechanics (book)
    • *** Morin - Introduction to Classical Mechanics (book)
    • **** Tong - Classical Dynamics (notes)
    • **** Helliwell & Sahakian - Modern Classical Mechanics (book)
  • Electromagnetism: circuits, fields, radiation, and optics
    • * Giancoli, Principles of Physics (part II)
    • ** Hughes, Electricity and Magnetism (notes)
    • ** Purcell, Electricity and Magnetism (book)
    • *** Griffiths, Introduction to Electrodynamics (book)
    • **** Jackson, Classical Electrodynamics (book)
    • **** Born & Wolf, Principles of Optics (book)
  • General relativity:
    • **** Eigenchris, Relativity (videos)
    • **** Tong, General Relativity (notes)
    • **** Carroll, Spacetime and Geometry (book)
  • Quantum mechanics:
    • ** Quantum Sense, Maths of Quantum Mechanics (videos)
    • ** Tong, Quantum Mechanics (notes)
    • ** Griffiths, Introduction to Quantum Mechanics (book)
    • *** Shankar, Principles of Quantum Mechanics (book)
  • High-energy physics: elementary particles and beyond
    • ** Tong, Introduction to Particle Physics (notes)
    • *** Kuster, Raffelt, & Beltran, Axions (notes) - Balanced summary of axion theory and experiments.
    • **** Tong, Quantum Field Theory (notes)
    • **** Peskin & Schroeder, Quantum Field Theory (book)
    • **** Tong, Gauge Theory (notes)
    • ***** Quevedo & Schachner, The Standard Model (notes) - Attacks QFT and the standard model from a purer, more elegant mathematical perspective.
  • Statistical mechanics
    • ** Blundell & Blundell, Concepts in Thermal Physics (book)
    • ** Tong, Statistical Physics (notes)
    • *** Schroeder, An Introduction to Thermal Physics (book)
  • Miscellaneous
    • * Susskind & Hrabovsky, The Theoretical Minimum (book)
    • ** Susskind & Friedman, Special Relativity and Classical Field Theory (book)
    • *** Lindner, A Complete Guide to Theoretical Physics (book) - A grand tour of modern theoretical physics.
    • **** Blandford & Thorne, Applications of Classical Physics - Another grand-tour book. Has the best optics chapters I've ever read.