Sayan Chattopadhyay's user avatar
Sayan Chattopadhyay's user avatar
Sayan Chattopadhyay's user avatar
Sayan Chattopadhyay
  • Member for 8 years
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11 votes
8 answers
2k views

Interesting questions (with answers) about concepts in topology for an amateur audience

10 votes
2 answers
725 views

A combinatorial proof of the identity $\sum\limits_{k=0}^n\binom{2k}{k}\binom{2(n-k)}{n-k}=4^n$ [duplicate]

5 votes
2 answers
536 views

Where are the transcendental numbers?

5 votes
3 answers
414 views

What is the reason for naming a function odd or even [duplicate]

4 votes
1 answer
91 views

Given $f : \Bbb{R} \to \Bbb{R}$ is a continuous function. To prove that $\int_{0}^{1}f(x)x^2 dx = \frac{f(c)}{3}$ for some $c \in [0,1]$

3 votes
1 answer
121 views

Find the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2(x)}{\sin(x)+\cos(x)}$

2 votes
1 answer
251 views

Classifying functions whose inverse do not have a closed form

2 votes
3 answers
888 views

For $a,b>2$, $a,b\in \Bbb{N}$ , prove that $2^a+1$ is never divisible by $2^b-1$ [duplicate]

2 votes
3 answers
191 views

Definite integral $\int_{\frac{1}{a}}^a \frac{\arctan(x)}{x}$

2 votes
2 answers
75 views

Continuity of a function whose domain is $[0,1] \cup [2,3]$

2 votes
1 answer
146 views

Intuition for this norm in the proof of uniqueness of solutions of an ODE

2 votes
2 answers
66 views

Generalizing chains of connected sets to arbitrary indexing sets

2 votes
0 answers
71 views

Why is $G/K$ a space of non-positive curvature, where $G$ is a complex reductive group and $K$ is its maximal compact subgroup

1 vote
2 answers
418 views

Is there a bounded, closed, uncountable subset of irrational numbers

1 vote
2 answers
177 views

Find the properties of the sum $\sum_{k=0}^n (-1)^k\binom{m+1}{k}\binom{m+n-k}{n-k}$

1 vote
1 answer
57 views

Given a number $k$(for large $k$) find $f(k)$ such that for all $x \geq f(k)$, $\phi(x) > k$

1 vote
2 answers
893 views

Book recommendation on special functions

1 vote
1 answer
56 views

Visualizing a function from the set of all $n\times n$ matrices to all $n\times n$ matrices

0 votes
1 answer
89 views

Bounded sequences without a convergent subsequence converging in a different metric