Wikipedia Articles : Mathematical Physics
Blog Physica Tags : Mathematical Physics , Symmetry
Books and Reviews:
 General Books:
 Complex Analysis in Physics
 Symmetries, Groups and other Algebras in Physics
 Differential and Integral equations of Mathematical Physics
 Mathematical Aspects of Classical Mechanics(including Dynamical Systems)
 Mathematical aspects of Quantum Mechanics(Mainly Functional Analysis)
 Mathematical aspects of Field theories including Gauge theories and Gravity(Mainly Topology and Geometry)
 Mathematical aspects of Statistical Mechanics(Combinatorics and Probability(including Number Theory) )
 Numerical analysis and statistics
1. Mathematics for Physicists by Philippe Dennery, Andre Krzywicki [Amazon] [Google]
2. Methods of Theoretical Physics by Philip McCord Morse, Herman Feshbach
Part 1 [Amazon]
Part 2 [Amazon]
3. Methods of Mathematical Physics by R. Courant, D. Hilbert Volume 1 [Amazon]
4. Mathematical Methods of Physics and Engineering by K. F. Riley, M. P. Hobson, S. J. Bence [Amazon]
5. Mathematical Methods For Physicists by George B. Arfken, Hans J. Weber [Amazon]
6. Mathematical Physics by S D Joglekar
Vol. 1 : The Basics
Vol. 2 : Advanced Topics
7. Mathematical Methods of Physics by Jon Mathews , Robert L. Walker [Amazon]
8. Mathematical Methods in the Physical Sciences by Mary L. Boas[Amazon]
9. All the Mathematics You Missed: But Need to Know for Graduate School by Thomas A. Garrity (Author), Lori Pedersen (Illustrator) [Google] [Amazon] [Cambridge Catalogue(Asia)]
1. Schaum’s Outline of Complex Variables by Murray R Spiegel [Amazon]
2. Complex Analysis by Lars Ahlfors [Amazon]
3. Basic Complex Analysis by Jerrold E. Marsden , Michael J. Hoffman [Amazon]
4. An Introduction to Complex Analysis: Classical and Modern Approaches (Modern Analysis Series) by by Wolfgang Tutschke , Harkrishan L. Vasudeva [Amazon]
5. Functions of One Complex Variable I by John Conway[Amazon]
6. The Theory of Functions by Edward C. Titchmarsh [Amazon][Google]
(See the chapters on Complex Analysis)
1. Topics in Algebra by I. N. Herstein [Amazon]
2. Algebra by Michael Artin [Amazon]
3. Linear Algebra by Kenneth M Hoffman, Ray Kunze [Amazon]
4. Lie Algebras in Particle Physics (Frontiers in Physics) by Howard Georgi [Amazon]
5. Group Theory in Physics by John F. Cornwell Volume 1: An Introduction (Techniques of Physics) [Amazon] [Amazon.uk]
6. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Brian C. Hall[Amazon]
[Google]
7. SemiSimple Lie Algebras And Their Representations by Robert N. Cahn [Free Online Copy] [Google] [Amazon]
8. Representation Theory: A First Course by William Fulton, Joe Harris [Amazon] [Google]
1. Introduction to Calculus and Analysis, Volume 1 (Classics in Mathematics) by Richard Courant, Fritz John [Amazon]
2. Differential and Integral Calculus: Volume II (Wiley Classics Library) by R. Courant [Amazon]
3. Calculus by Tom M. Apostol
Vol. 1: OneVariable Calculus with an Introduction to Linear Algebra [Amazon]
Vol. 2: MultiVariable Calculus and Linear Algebra with Applications [Amazon]
4. A Course of Modern Analysis by E. T. Whittaker , G. N. Watson [Amazon][Google]
5. Differential Equations With Applications and Historical Notes by George F Simmons [Amazon]
6. Elements of Partial Differential Equations by Ian N. Sneddon [Amazon]
7. A Treatise on the Theory of Bessel Functions by G. N. Watson [Amazon]
8. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic methods and Perturbation theory by Carl M. Bender , Steven A. Orszag [Amazon]
9. The Theory of Functions by Edward C. Titchmarsh [Amazon][Google]
(See the chapters on Complex Analysis)
1. Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics) by V. I. Arnold, A. Weinstein (Translator), K. Vogtmann (Translator) [Amazon]
1. Principles of Mathematical Analysis by Walter Rudin [Amazon]
2. Methods of Modern Mathematical Physics by Michael Reed, Barry Simon
Vol. 1: Functional Analysis [Amazon]
Vol. 2: Fourier Analysis, SelfAdjointness [Amazon]
Vol. 3: Scattering Theory [Amazon]
Vol. 4: Analysis of Operators [Amazon]
1. Geometry, Topology and Physics by M. Nakahara [Amazon]
2. Analysis, Manifolds and Physics by Yvonne ChoquetBruhat, Cecile DewittMorette :
Part I [Amazon]
Part II [Amazon]
3. The Geometry of Physics: An Introduction by Theodore Frankel [Amazon]
4. Topology (2nd Edition) by James Munkres [Amazon]
5. Differential Forms with Applications to the Physical Sciences by Harley Flanders [Amazon]
6. Tensor Geometry: The Geometric Viewpoint and Its Uses by C. T. J. Dodson, Timothy Poston [Amazon]
7. Basic Topology (Undergraduate Texts in Mathematics) by M.A. Armstrong [Amazon]
American Journal of Physics Resource Letters :
(Selected from the list of Resource Letters published in AJP )

1. SP1 : Symmetry in Physics by David Park [AJP Site]
2. SP2: Symmetry and group theory in physics by Joe Rosen [AJP Site] [Erratum]
There is a mathematical physics series,
Authers: Reed n Simon
I have seen 1st book of that series.
it is on functional analysis…
Note: We have taken a list of topics in mathematics from here to help us classify mathematical physics. We welcome the readers to suggest any other topic which we might have missed.
General Books:
General Mathematical physics books
Complex Analysis in Physics
Complex Variables and complex geometry
Symmetries, Groups and other Algebras in Physics
Algebra(Including Linear Algebra)
Group Theory
Representation Theory
Differential and Integral equations of Mathematical Physics
Classical Analysis and ODEs( Special functions, orthogonal polynomials, harmonic analysis, ODE’s, differential relations, calculus of variations, approximations, expansions, asymptotics)
Analysis of PDEs ( Existence and uniquness, boundary conditions, linear and nonlinear operators, stability, soliton theory, integrable PDE’s, conservation laws, qualitative dynamics)
Mathematical Aspects of Classical Mechanics(including Dynamical Systems)
Dynamical Systems
Dynamics of differential equations and flows, mechanics, classical fewbody problems, iterations, complex dynamics, delayed differential equations
Symplectic Geometry
Hamiltonian systems, symplectic flows, classical integrable systems
Mathematical aspects of Quantum Mechanics(Mainly Functional Analysis)
Functional Analysis
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Operator Algebras
Algebras of operators on Hilbert space, C^*algebras, von Neumann algebras, noncommutative geometry
Spectral Theory
Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, nonselfadjoint operators, random operators/matrices
Quantum Algebra
Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
Mathematical aspects of Field theories including Gauge theories and Gravity(Mainly Topology and Geometry)
General Topology
Continuum theory, pointset topology, spaces with algebraic structure, foundations, dimension theory, local and global properties
Geometric Topology
Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
Algebraic Topology
Homotopy theory, homological algebra, algebraic treatments of manifolds
Differential Geometry
Complex, contact, Riemannian, pseudoRiemannian and Finsler geometry, relativity, gauge theory, global analysis
Metric Geometry
Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces
Mathematical aspects of Statistical Mechanics(Combinatorics and Probability(including Number Theory) )
Combinatorics
Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
Number Theory
Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
Probability
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
Numerical analysis and statistics
Numerical Analysis
Numerical algorithms for problems in analysis and algebra, scientific computation
Statistics
Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
two more very good books i think u should add..
1.)a course of modern analysis by e.t.whittaker and g.n.watson.
2.)mathematical methods of physics by matthews and walker.
Hi aditya,
Thanks for mentioning. I’ve added both the books in the list.
hi
does anyone have links to free books on net… i am badly in need of them … please forward those to me..
3 more good books..
1. basic topology by M.A.Armstrong.(this is an excellent book for first reading.maybe particularly suited for physicists because of its geometric intuitiveness and absence of unnecessary rigorousness)
2.all the mathematics you missed(but need to know for graduate school) by Garrity.(this is also very interesting book.mathematical conceptualness and intuitions.but its mostly for mathematicians)
3.group theory in physics by J.F.Cornwell(seems to be quite good.includes Lie algebras,etc that math ppl consider as a separate topic generally.hence more inclined towards ppl of particle theory(accaording to preface))
more two
1.basic complex analysis by J.Marsden(i find it too good,although amazon says its average decent type)
2.theory of functions by Titschmarsh(too good)
Shantan,
I have sent you an email asking what kind of books are you looking for ?
Aditya,
Included the books you mentioned. Thank you for your comments. If possible, can you also include the corresponding Amazon/Google links ? It would make the job of updating this lists easier.
Tom:
Complex Analysis
1. An Introduction to Complex Analysis: Classical and Modern Approaches (Modern Analysis Series)
http://www.amazon.com/IntroductionComplexAnalysisClassicalApproaches/dp/1584884789/
2. Functions of One Complex Variable [John Conway]
http://www.amazon.com/FunctionsComplexVariableGraduateMathematics/dp/3540903283/
ok,i’ll do that from next time..
Hi,
Does anyone have good references for perturbative QFT?
Hi Ali,
For references on QFT, you can do no better than have a look at the review in the “flip tomato” blog.
pls can u add schaum’s outline seriestheory and problems on vector analysis