User Sayan Chattopadhyay

11 votes

8 answers

2k views

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

asked Aug 14, 2018 at 9:37

10 votes

2 answers

713 views

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

asked Feb 17, 2016 at 12:32

5 votes

2 answers

525 views

Where are the transcendental numbers?

asked Mar 12, 2016 at 14:31

5 votes

3 answers

408 views

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

asked May 17, 2016 at 17:01

4 votes

1 answer

89 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 $c \in [0,1]$

asked Mar 28, 2018 at 18:12

3 votes

1 answer

121 views

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

asked Mar 16, 2016 at 16:38

2 votes

1 answer

242 views

Classifying functions whose inverse do not have a closed form

asked Mar 20, 2016 at 15:41

2 votes

3 answers

860 views

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

asked Apr 26, 2016 at 13:50

2 votes

3 answers

176 views

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

asked May 6, 2016 at 12:53

2 votes

2 answers

72 views

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

asked Mar 31, 2018 at 15:01

2 votes

1 answer

134 views

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

asked Sep 15, 2019 at 5:53

2 votes

2 answers

66 views

Generalizing chains of connected sets to arbitrary indexing sets

asked Sep 19, 2019 at 13:16

2 votes

0 answers

68 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

asked Apr 5, 2022 at 14:50

1 vote

2 answers

414 views

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

asked Oct 17, 2019 at 4:09

1 vote

2 answers

175 views

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

asked May 21, 2016 at 17:59

1 vote

1 answer

57 views

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

asked Dec 4, 2017 at 17:11

1 vote

2 answers

866 views

Book recommendation on special functions

asked Feb 4, 2016 at 4:41

1 vote

1 answer

56 views

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

asked Apr 1, 2016 at 11:03

0 votes

1 answer

88 views

Bounded sequences without a convergent subsequence converging in a different metric

asked Feb 5, 2016 at 15:36

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19 Questions

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

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

Where are the transcendental numbers?

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

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 $c \in [0,1]$

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

Classifying functions whose inverse do not have a closed form

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

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

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

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

Generalizing chains of connected sets to arbitrary indexing sets

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

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

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

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

Book recommendation on special functions

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

Bounded sequences without a convergent subsequence converging in a different metric