mechanics

Introduction to mechanics

thermology

Zemansky heat and thermodynamics

electromagnetism

Purcell electricity and magnetism.

optics

Jenkins/White Optical Foundation

classical mechanics

John tyler's Classical Mechanics (Undergraduate)

Xie ke mechanics (graduate student)

electrodynamics

Introduction to Griffith electrodynamics (undergraduate)

Franklin Classical Electromagnetism (Postgraduate)

quantum mechanics

Introduction to Griffith's quantum mechanics (undergraduate)

Sakurai Modern Quantum Mechanics (Postgraduate)

statistical mechanics

Introduction to Schroeder's Thermophysics (Undergraduate)

Pathria statistical mechanics (postgraduate)

Statistical field theory

Ma Shang-Ken's Modern Critical Phenomenon Theory

Stanley phase transition and critical phenomenon

Solid state physics

Ashcroft/Mermin Solid State Physics

methods of mathematical physics

Mathematical methods in physical science

Theory of relativity

Hartle gravity

Wald's general relativity

high-energy physics

Introduction to Griffith elementary particles

Math:

Differential geometry:

1, peter peterson, riemann geometry: a standard riemann geometry textbook;

2. Riemannian Manifold: Introduction to Curvature: The Latest Riemannian Geometry Textbook;

3.doCarmo, riemann geometry. : standard Riemann geometry textbook;

4.M. spivak, Introduction to Differential Geometry Synthesis I-V: Classic of Differential Geometry Synthesis, suitable for reference books;

5. Helgason, differential geometry, Lie groups and symmetric spaces: a textbook of standard differential geometry;

6. Lang, Fundamentals of Differential Geometry: the latest textbook of differential geometry, which is very suitable for reference books;

7.Kobayashi/Nomizu, Fundamentals of Differential Geometry: A Classic Reference Book of Differential Geometry;

8. Introduction to Busby, Differential Manifolds and Riemannian Geometry: a standard introductory textbook for differential geometry, mainly focusing on differential manifolds;

9. Riemannian Geometry I.Chavel: Classic Riemannian Geometry Reference Book;

10, Modern Geometry-Methods and Applications by Dubrovin, Fomenko and Novikov Volume 1-3: a classic reference book of modern geometry.

Algebraic geometry:

1, Harris, Algebraic Geometry: Lesson 1: Introduction to Algebraic Geometry;

2. Algebraic Geometry Robin Harthorne: a classic textbook of algebraic geometry, which is very difficult;

3. Basic Algebraic Geometry1& Second edition. : Very good introductory textbook of Algebra Geometry;

4.Giffiths/Harris's Principles of Algebraic Geometry: a comprehensive and classic reference book of algebraic geometry, part of complex algebraic geometry;

5.Eisenbud's Alternating Algebra Oriented Algebra Geometry: A Reference Book of Higher Algebra Geometry and Commutative Algebra, and a Comprehensive Reference of the Latest Commutative Algebra;

6. Eisenbard's Schema Geometry: an introductory textbook for graduate students in algebraic geometry;

7. Mountford's red book on variables and schemes: a standard introductory textbook for graduate students in algebraic geometry;

8. Algebraic Geometry I: Complex Projective Change.

Harmonic analysis of partial differential equations

1, Introduction to Harmonic Analysis, third edition Yitzhak Katz Nelson: the standard textbook of harmonic analysis, which is very classic;

2. Evans, Partial Differential Equations: A Classic Textbook of Partial Differential Equations;

3. Alexei. A. Dejin, Partial Differential Equations, springer Publishing House: Reference Book of Partial Differential Equations;

4. L. Hormander's "Linear Partial Differential Operator", I & II: a classic reference book for partial differential equations;

5. Forand's course of abstract harmonic analysis: a textbook of harmonic analysis for senior graduate students;

6. Ross Hewitt's abstract harmonic analysis: a classic reference book of abstract harmonic analysis;

7. Harmonic analysis: standard graduate harmonic analysis textbook;

8. Second-order elliptic partial differential equations: a classic reference book for partial differential equations;

9. Partial differential equations, Jeffrey Lauch: a standard textbook for graduate students with partial differential equations.

Brief introduction of complex analysis and multiple repetition analysis

1, unary complex variable function II, J.B.Conway: a classical textbook of unary complex variable, the second volume is more in-depth;

2. Lectures on Riemann Surfaces O. Foster: Riemann Surfaces Reference Books:

3. Compact Riemannian Surfaces: Riemannian Surfaces Reference Books:

4. Compact Riemannian Surfaces narasimhan: Riemannian Surfaces Reference Book:

5. Helmand's "Introduction to Complex Analysis in Serious Variables": a standard introductory textbook of multivariate;

6. Riemann Surfaces: Riemann Surfaces Reference Books:

7. Riemann Surfaces by Herschel M. Facas: a textbook of standard Riemann Surfaces for graduate students;

8.Steven G. Krantz's Theory of Severe Complex Variables: a multivariable advanced reference book for graduate students;

9. Complex analysis: geometric viewpoint: an advanced reference book for postgraduate reanalysis.

Elective courses in professional direction:

1, multiple repeated analysis; 2. Complex geometry; 3. Geometric analysis; 4. Abstract harmonic analysis; 5. Algebraic geometry; 6. Algebraic number theory; 7. Differential geometry; 8. Algebraic groups, Lie algebras and quantum groups; 9. Functional analysis and operator algebra; 10, mathematical physics; 1 1, probability theory; 12, dynamic system and ergodic theory; 13, pan-algebra.

Mathematical basis:

1, halmos, primary set theory;

2. fraenkel, abstract set theory;

3. Ebbinghaus, mathematical logic;

4. Enderton, a mathematical introduction to logic;

5. Landau, the basis of analysis;

6. McClane, the category of working mathematics. Elective courses should be interspersed in the process of learning core courses.