• No products in the cart.

# College Mathematics Corner

### Groups without commuting elements (TIFR 2015 problem 4)

Question: Let $$S$$ be the collection of isomorphism classes of groups $$G$$ such that every element of G commutes with …

### Groups with no subgroups

Claim: If G has no subgroups H /= (e), G, then G must be cyclic of prime order. Proof:  One …

### Trace of product of matrix (TIFR 2015 problem 3)

Question: Let $$A$$ be a $$10\times 10$$ matrix with complex entries such that all its eigenvalues are non-negative real numbers, …

### Image of continuous function (TIFR 2015 problem 2)

Question: Let $$f: \mathbb{R} \to \mathbb{R}$$ be a continuous function. Which of the following can not be the image of …

### Invertible matrix with sum of each row 1 (TIFR 2015 problem 1)

Question: Let $$A$$ be an invertible $$10 \times 10$$ matrix with real entries such that the sum of each row is …

### Homomorphisms from $$S_n$$ (TIFR 2014 problem 23)

Question: There exists an onto group homomorphism A. from $$S_5$$ to $$S_4$$ B. from $$S_4$$ to $$S_2$$ C. from $$S_5$$ …

### 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 …

#### Who’s Online

There are no users currently online

#### Upcoming Events

• Chemistry Olympiad Program February 21, 2018 at 7:30 pm – 9:30 pm

#### Featured Testimonial

"...as soon as the class began mathematics started working through me like caffeine.I was soon drowned in a temptuos ocean of mathematics..."Read more