Set at the undergraduate level, with some specialization/graduate level study. Learn by solving problems and always keep the math slightly ahead of the physics.
How to use this guide
- Pick one primary book per subject. Use secondaries only for another pass or curiosity.
- Work through problems.
- Follow prerequisites. Quantum needs linear algebra, stat mech needs quantum, E&M needs vector calculus.
- Expect a multi-year path.
Part 0: Mathematics
Multivariable Calculus
Needed before: everything.
Learn: limits, derivatives, integrals, FTC, integration techniques, sequences/series, Taylor series, vectors, partial derivatives, multiple integrals, vector fields, line/surface integrals, Green/Stokes/divergence theorems.
Primary: George B. Thomas, Thomas' Calculus, or James Stewart, Calculus.
Stronger alternative: Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms.
Optional rigor: Michael Spivak, Calculus.
Linear Algebra
Needed before: quantum mechanics.
Learn: vector spaces, bases, linear maps/matrices, determinants, eigenvalues/eigenvectors, diagonalization, inner products.
Primary: Gilbert Strang, Introduction to Linear Algebra + MIT OCW 18.06.
Optional rigor: Sheldon Axler, Linear Algebra Done Right, or Friedberg, Insel & Spence, Linear Algebra.
Ordinary Differential Equations
Needed before: mechanics and later physics.
Learn: first-order ODEs, second-order linear ODEs, series solutions, Laplace transforms, ODE systems, nonlinear intro.
Primary: Boyce & DiPrima, Elementary Differential Equations and Boundary Value Problems.
Cheaper/friendlier: Tenenbaum & Pollard, Ordinary Differential Equations.
Complex Analysis
Needed before: serious E&M and quantum.
Learn: analytic functions, Cauchy-Riemann, contour integration, Cauchy's theorem/formula, Laurent series, residues, conformal maps.
Primary: Brown & Churchill, Complex Variables and Applications.
Partial Differential Equations
Optional standalone.
Learn: heat/wave/Laplace equations, separation of variables, Fourier methods, boundary values, Sturm-Liouville.
Primary: Richard Haberman, Applied Partial Differential Equations.
Part 1: Introductory Physics
Purpose: one calculus-based pass over all physics before the deeper core.
Standard Route
Primary: Halliday, Resnick & Walker, Fundamentals of Physics, or Young & Freedman, University Physics.
Covers: mechanics, thermodynamics, E&M, optics, modern physics.
Honors Route
- Mechanics: Kleppner & Kolenkow, An Introduction to Mechanics.
- Electromagnetism: Purcell & Morin, Electricity and Magnetism.
- Waves: A. P. French, Vibrations and Waves.
Intro topics: kinematics, dynamics, energy, momentum, rotation, oscillations, gravitation, fluids, thermodynamics, electric/magnetic fields, circuits, EM waves, optics, interference/diffraction, special relativity, quantum ideas.
Part 2: Core Physics
Classical Mechanics
Build on: intro mechanics, multivariable calculus, ODEs.
Learn: Newtonian mechanics, oscillations/resonance, potentials, central forces, non-inertial frames, rigid bodies, coupled oscillators, normal modes, Lagrangians.
Primary: John R. Taylor, Classical Mechanics.
Electromagnetism
Build on: mechanics, multivariable calculus, complex analysis.
Learn: electrostatics, magnetostatics, boundary value problems, multipoles, materials, Faraday's law, AC circuits, Maxwell equations, EM waves, reflection/refraction, waveguides, radiation, relativity.
Primary: David J. Griffiths, Introduction to Electrodynamics.
Optics depth: Eugene Hecht, Optics.
Quantum Mechanics
Build on: mechanics, E&M, linear algebra.
Learn: state vectors/operators, Schrödinger equation, 1D problems, harmonic oscillator, 3D potentials, angular momentum/spin, identical particles, perturbation theory, scattering.
Primary: Griffiths & Schroeter, Introduction to Quantum Mechanics.
Secondary: John Townsend, A Modern Approach to Quantum Mechanics.
Deeper: R. Shankar, Principles of Quantum Mechanics.
Statistical and Thermal Physics
Build on: quantum mechanics.
Learn: thermodynamics, kinetic theory, statistical mechanics, energy & entropy, Boltzmann, Fermi, Bose distributions, gases, blackbody radiation, chemical equilibrium, phase transitions, ferromagnetism.
Primary: Daniel V. Schroeder, An Introduction to Thermal Physics.
Secondary: Kittel & Kroemer, Thermal Physics, Blundell & Blundell, Concepts in Thermal Physics.
Core Threads
- Waves/Optics: French if not done earlier. Hecht for depth.
- Special Relativity: Taylor & Wheeler, Spacetime Physics, or David Morin's relativity chapters.
Part 3: Advanced and Elective Topics
Analytical Mechanics
Build on: classical mechanics.
Learn: Lagrangian/Hamiltonian mechanics, calculus of variations, action principle, rigid bodies, continuum mechanics, chaos.
Primary: Goldstein, Poole & Safko, Classical Mechanics.
Secondary: Landau & Lifshitz, Mechanics.
Mathematical Methods of Physics
Build on: core math + physics.
Learn: ODE/PDE, generalized functions, transforms, Green's functions, nonlinear equations, Hilbert spaces, tensors, probability/statistics.
Primary: Mary L. Boas, Mathematical Methods in the Physical Sciences.
Reference: Arfken, Weber & Harris, Mathematical Methods for Physicists.
General Relativity
Build on: mechanics, E&M, special relativity.
Learn: tensors, curved spacetime, Einstein equation, Schwarzschild solution, orbits, light bending, black holes, gravitational waves, cosmology.
Primary: James B. Hartle, Gravity.
Secondary: Bernard Schutz, A First Course in General Relativity, Sean Carroll, Spacetime and Geometry.
Particle Physics
Build on: quantum mechanics, special relativity.
Learn: Standard Model, interactions, relativistic kinematics, Feynman calculus, QED/QCD/weak interaction, electroweak unification, Higgs, neutrinos, beyond-SM.
Primary: David J. Griffiths, Introduction to Elementary Particles.
Condensed Matter / Solid State
Build on: quantum mechanics, statistical physics.
Learn: crystals, lattices, electrons in metals, band structure, transport, semiconductors, magnetism, superconductivity.
Primary: Charles Kittel, Introduction to Solid State Physics.
Gentler: Steven Simon, The Oxford Solid State Basics.
Reference: Ashcroft & Mermin, Solid State Physics.
Cosmology and Particle Astrophysics
Build on: special relativity, GR helps.
Learn: expanding universe, Friedmann equations, Big Bang thermal history, inflation, CMB, structure formation, dark matter/energy, high-energy astrophysics.
Primary: Barbara Ryden, Introduction to Cosmology.
Next: Dodelson & Schmidt, Modern Cosmology.
String Theory
Build on: mechanics, E&M, quantum, special relativity.
Learn: classical and quantum strings at advanced-undergraduate level.
Primary: Barton Zwiebach, A First Course in String Theory.
Quantum Field Theory
Build on: quantum mechanics, special relativity, E&M, analytical mechanics.
Graduate-level next step.
Primary: Peskin & Schroeder, An Introduction to Quantum Field Theory, or Matthew Schwartz, Quantum Field Theory and the Standard Model.
Companion: David Tong's QFT notes.
Laboratory and Computation
Data Analysis and Uncertainty
Primary: John R. Taylor, An Introduction to Error Analysis.
Computational Physics
Primary: Mark Newman, Computational Physics (Python). Work through it alongside the core.
Electronics
Primary: Horowitz & Hill, The Art of Electronics.
Alternative: Paul Scherz, Practical Electronics for Inventors.
Practice: actually build with a breadboard kit.
Suggested Order
- Multivariable calculus: introductory mechanics and E&M.
- Linear algebra + ODEs: waves and modern physics.
- Classical Mechanics: Taylor.
- Electromagnetism I: Griffiths statics/induction + complex analysis.
- Electromagnetism II: waves/radiation/relativity.
- Quantum Mechanics I.
- Quantum Mechanics II.
- Statistical and Thermal Physics.
- Electives: analytical mechanics, GR, particle physics, condensed matter, cosmology, etc.