Books for University Maths and International Maths Olympiad

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 Lavrent’ev
• 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

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