Here are a few books that I came across during my stay at IIT. These have been recommended to me by a senior of mine. These books have received acclaim from a lot of students and I feel it’s best to share the knowledge.

• Mathematical Circles: Russian Experience by Dmitri Fomin, Sergey Genkin and Ilia Itenberg

• The Art and Craft of Problem Solving by Paul Zeitz

• Mathematics: A Very Short Introduction by Timothy Gowers

• Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov and Lavrentev

• What is Mathematics? by Richard Courant

• Letters to a Young Mathematician by Ian Stewart

Analysis:

• Calculus by Spivak

• Principles of Mathematical Analysis by Rudin

• Calculus on Manifolds by Spivak

• Introduction to Topology and Modern Analysis by Simmons

Algebra:

• Linear Algebra Done Right by Sheldon Axler

• Finite Dimensional Vector Space by Halmos

• Algebra by Martin Isaacs

• Algebra by Artin

• Elements of Algebraic Topology by Munkres

Combinatorics:

• A Course in Combinatorics by Van Lint and Wilson

• Combinatorics: Topics, Techniques, Algorithms by Cameron

Number Theory:

• A Classical Introduction to Modern Number Theory by Ireland and Rosen

Algebra: Finite Dimensional Vector Spaces by P. R. Halmos

Abstract Algebra: Algebra by Maclane and Birkoff

Real Analysis: Understanding Analysis by Abott

Measure Theory: Real Analysis by H. L. Royden

Algebraic Geometry: An Invitation to Algebraic Geometry by Karen Smith et al.

Topology: Topology by J. Munkres

Algebraic Topology: Introduction to Algebraic Topology by A. Hatcher

Differential Geometry: Geometry from a Differential Viewpoint by McCleary

Complex Analysis: Complex Analysis by Lars Ahlfors

Number Theory: An Introduction to the Theory of Numbers by Niven and Zuckerman

Partial Differential Equations: PDEs by L. Adams

Combinatorics: Introductory Combinatorics by R. A. Brualdi

Is any of the above books useful for a JEE aspirant?

I don’t think so.