Best books for preparation of IIT JAM Mathematics
Real Analysis :- elementary analysis by Ross. It gives a boost to the basic. Bartle and sherbert for its rigour. Malik and arora for few topics like functions of two variable, Taylors theorem, these few topics are nicely given in it. Thomas and Finney's calculus may give you a taste of basic calculus. There is a book available in the internet, LV tarasov's calculus. Its a must read, an interactive book for knowing the basic analysis concepts. Apostol's two volumes of calculus is a bible. Keep it with you along with Thomas Finney.
Abstract algebra :- start with hungerford for basics, it gives you an amazing beginning. J.Gallian's book is an interesting book. Solve I.N hernstein. All in all there are many books for abstract algebra.
Linear Algebra :- go for Lang's linear algebra for the basic. Then Paul shields book. I doubt the availability of this book, still you can search. Its an awesome book. Hoffman kunze is a standard book, but I never liked it. Solve schaum series too.
Vector analysis :- Murray Spiegel's book is the best. For a beautiful understanding you may read the chapter in mathematical methods for physical sciences by Mary boas. Also read the multiple integral section of this book. Thomas Finney's calculus is another must give a try for vector analysis and multiple integrals.
Differential equations :- start with Ross, first four-five chapters are a must do. Then go for some more problems go for zafar ahsan's book.
For a basic idea related to proofs, which may not help you a lot as far as these exams are concerned but may help you in your future endeavour with mathematics. How to think like a mathematician by Kevin Houston. And do also read a mathematician's apology by hardy, iff you haven't read it yet.
