Standard books for understanding maths with physical realisation

[non LINEAR+-*/]

hellooo all .

 

I just wanna hear from you all people , suggesting me some standard books with author to understand all mathematical concepts with physical realisations and practical Examples....for ALL MATHEmatical topics in PURE and APPLIED mathematics ...

 

 

must feel happy to start with nice books suggested by friends over here....

 

Thanks in Advance

by non LINEAR +-*/

 

 

[ajb]

Since the 1980's geometry and topology has become very useful branch of mathematics in quantum field theory. More amazingly QFT is becoming more and more of a tool in geometry and topology.

 

Some books (I give the most recent versions), more on the physics side include:

 

Geometry, Topology and Physics (Graduate Student Series in Physics), M. Nakahara, Taylor & Francis; 2 edition (June 4, 2003)

 

Topology and Geometry for Physicists, C. Nash & S. Sen, Dover Publications (January 20, 2011) (older version are avaliable)

 

Differential Topology and Quantum Field Theory, C. Nash, Academic Press (December 29, 1992)

 

Modern Differential Geometry for Physicists (World Scientific Lecture Notes in Physics), C.J. Isham, World Scientific Publishing Company; 2 edition (June 1999)

 

Gauge Field Theory and Complex Geometry, Y.I. Manin, Springer Berlin Heidelberg (February 19, 2010)

 

Supermanifolds: Theory and Applications, A. Rogers, World Scientific Publishing Company (April 18, 2007)

 

Supersymmetry for Mathematicians: An Introduction (Courant Lecture Notes), V. S. Varadarajan, American Mathematical Society (July 2004)

 

Gauge Fields, Knots, and Gravity (Series on Knots and Everything), J.C. Baez & J. P. Muniain, World Scientific Publishing Company (September 1994)

 

Plus many others I have not personally used.

 

A little category theory never hurts! Try

 

Mathematical Physics (Chicago Lectures in Physics), R. Geroch, University Of Chicago Press (September 15, 1985)

 

For a general overview of some of the tools employed in mathematical physics I recommend

 

Mathematical Physics, S. Hassani, Springer; 1st edition (February 8, 1999)

 

Of course the list reflects my own tastes and preferences. Other areas of mathematics like group theory, analysis, probability, representation theory, dynamical systems, algebra, etc all have something to say in physics. There are books on this, though I am much less familiar with them. If you have some branch of mathematics in mind let us know.

[Klaynos]

As you want "ALL" concepts, I'm not sure it is even possible to recommend a book. But let me suggest you read everything in your local universities library... The breadth of the field you are trying to concentrate down into one book means that it would be impossible to contain it all.

 

A good starting point, Schaum's advanced mathematics for engineers and scientists.