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Beautiful Books

This is an (ever-growing and ever-changing) list of books, useful for school and college mathematics students. If you are working …

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I.S.I. Entrance Interview Problems

a and b are two numbers having the same no. of digits and same sum of digits (=28). Can one …

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Math and Basic Science in India after school

We observe a renewed interest in basic science and mathematics in India after decades of engineering mania. This is a …

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Initiating a child into the world of Mathematical Science

“How do I involve my son in challenging mathematics? He gets good marks in school tests but I think he …

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What is RMO and how to prepare for it

What is RMO RMO or Regional Math Olympiad is the first round of mathematics contest (in India) leading to the …

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Number of maps (TIFR 2014 problem 30)

Question: How many maps \(\phi: \mathbb{N} \cup  \{0\} \to \mathbb{N} \cup  \{0\}\) are there satisfying \(\phi(ab)=\phi(a)+\phi(b)\) , for all \(a,b\in …

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Maps from compact spaces (TIFR 2014 problem 29)

Question: Let \(f: X\to Y \) be a continuous map between metric spaces. Then \(f(X)\) is a complete subset of …

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Continuous functions from discrete space (TIFR 2014 problem 28)

Question: Let \(X\) be a topological space such that every function \(f: X \to \mathbb{R}\) is continuous. Then A. \(X\) …

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Homeomorphism of product space with mother space (TIFR 2014 problem 27)

Question: \(X\) is a topological space with infinite cardinality which is homeomorphic to \(X \times X\). Then A. \(X\) is …

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Number of irreducible polynomials (TIFR 2014 problem 26)

Question: The number of irreducible polynomials of the form \(x^2+ax+b\) , with \(a,b\) in the field \(\mathbb{F}_7\) of 7 elements …

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Order of generated subgroup (TIFR 2014 problem 24)

Question:  Let \(H_1, H_2\) be two distinct subgroups of a finite group G, each of order 2. Let \(H\) be …

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Identifying isomorphic groups (TIFR 2014 problem 25)

Question: Which of the following groups are isomorphic? A. \(\mathbb{R}\) and \(\mathbb{C}\) B. \(\mathbb{R}^* \) and   \(\mathbb{C}^*\) C. \(S_3 \times …

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CMI Tesselate Contest

What: Online Contest in Mathematics, Physics and Computer Science. Organizations: Chennai Mathematical Institute Who are eligible: Students of class 8 through 12 When: will …

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Triangles on a Sphere

PROBLEM Suppose the earth is a perfect sphere. You are on its surface at point A. First, you walk 1 …

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