Question

Consider $D_{16}$ and $H =\{ ε,p^4,p^8,p^{12}\}$. Show that $H$ is a normal subgroup of $D_{16}$.

score 58 · Answer 1 · 2026-04-14 17:23:04

58

Views

Consider $D_{16}$ and $H =\{ ε,p^4,p^8,p^{12}\}$. Show that $H$ is a normal subgroup of $D_{16}$.

Published on 14 Apr 2026 - 17:23

score 43 · Answer 2 · 2026-04-16 07:14:20

43

Views

Simplifying the product of $(x-x_j)$'s when $x_k$ has multiplicty $\geq 2$

Published on 16 Apr 2026 - 7:14

score 63 · Answer 3 · 2026-04-15 00:00:00

63

Views

Show $f(x) = |x|^p$ is differentiable at $0$ for $p > 1$

Published on 15 Apr 2026 - 0:00

score 67 · Answer 4 · 2026-04-13 12:37:41

67

Views

Derivative of $\frac x {\log |x|}$ without using L'Hopital's rule?

Published on 13 Apr 2026 - 12:37

score 32 · Answer 5 · 2026-04-14 06:48:01

32

Views

Combination modular arithmetic proof

Published on 14 Apr 2026 - 6:48

score 77 · Answer 6 · 2026-04-14 11:45:30

77

Views

Stein's proof of Lusin's theorem: Is the $E_n$ necessary?

Published on 14 Apr 2026 - 11:45

score 304 · Answer 7 · 2026-04-13 23:05:54

Suppose $R$ is a commutative ring, $a, b$ are zero divisors of $R$ such that $ab$ is nonzero. Show that $ab$ is also a zero divisor of $R$.

score 38 · Answer 8 · 2026-04-12 01:04:15

38

Views

Function $f$ satisfying $f(x,y) = g(ax + by)$ and is continuous everywhere but not differentiable everywhere?

Published on 12 Apr 2026 - 1:04

score 36 · Answer 9 · 2026-03-26 01:23:37

36

Views

$A ∈ GL_n(K)$. Show that there exists a polynomial $P(X) ∈ K[X]$ of degree $< n$ such that $A^{−1} = P(A)$

Published on 26 Mar 2026 - 1:23

score 57 · Answer 10 · 2026-04-11 20:42:42

57

Views

Folland Chapter 5 Exercise 39

Published on 11 Apr 2026 - 20:42

score 74 · Answer 11 · 2026-04-15 06:43:53

74

Views

Covariance of $A$ and $B$

Published on 15 Apr 2026 - 6:43

score 50 · Answer 12 · 2026-04-16 09:16:00

50

Views

Is this way of deriving the formula for the number of decimal digits for positive integers correct or justified?

Published on 16 Apr 2026 - 9:16

score 50 · Answer 13 · 2026-04-14 19:02:31

50

Views

Characterization of Relative Compactness in Complete Metric Spaces

Published on 14 Apr 2026 - 19:02

score 183 · Answer 14 · 2026-04-17 02:56:58

183

Views

Find the limit $\lim_{n\to\infty}\frac{1}{\sqrt{n}}\int\limits_1^n\ln(1+\frac{1}{\sqrt{x}})dx.$

Published on 17 Apr 2026 - 2:56

score 108 · Answer 15 · 2026-04-15 00:31:06

108

Views

If $f'\notin L^1([a,b])$ then $f$ is not a bounded variation on $[a,b]$

Published on 15 Apr 2026 - 0:31

List Question

Consider $D_{16}$ and $H =\{ ε,p^4,p^8,p^{12}\}$. Show that $H$ is a normal subgroup of $D_{16}$.

Simplifying the product of $(x-x_j)$'s when $x_k$ has multiplicty $\geq 2$

Show $f(x) = |x|^p$ is differentiable at $0$ for $p > 1$

Derivative of $\frac x {\log |x|}$ without using L'Hopital's rule?

Combination modular arithmetic proof

Stein's proof of Lusin's theorem: Is the $E_n$ necessary?

Suppose $R$ is a commutative ring, $a, b$ are zero divisors of $R$ such that $ab$ is nonzero. Show that $ab$ is also a zero divisor of $R$.

Function $f$ satisfying $f(x,y) = g(ax + by)$ and is continuous everywhere but not differentiable everywhere?

$A ∈ GL_n(K)$. Show that there exists a polynomial $P(X) ∈ K[X]$ of degree $< n$ such that $A^{−1} = P(A)$

Folland Chapter 5 Exercise 39

Covariance of $A$ and $B$

Is this way of deriving the formula for the number of decimal digits for positive integers correct or justified?

Characterization of Relative Compactness in Complete Metric Spaces

Find the limit $\lim_{n\to\infty}\frac{1}{\sqrt{n}}\int\limits_1^n\ln(1+\frac{1}{\sqrt{x}})dx.$

If $f'\notin L^1([a,b])$ then $f$ is not a bounded variation on $[a,b]$

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