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25 votes

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Suppose that $f ' (x)$ exists and $f(x)$ has two roots $x_1$ and $x_2$. Try to prove that:

answered Nov 25, 2014 at 2:56

16 votes

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Prove that the center of G has order divisible by p

abstract-algebra group-theory finite-groups abelian-groups

answered Feb 6, 2017 at 7:16

14 votes

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Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

functional-analysis linear-transformations normed-spaces lp-spaces supremum-and-infimum

answered Apr 7, 2017 at 4:23

14 votes

Is there an elegant way to prove a function is linear?

linear-algebra

answered Nov 20, 2016 at 7:41

13 votes

Metric is continuous function

general-topology metric-spaces

answered Dec 3, 2015 at 4:22

9 votes

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A function continuous and bounded on a closed and bounded set but not uniformly continuous there

real-analysis continuity examples-counterexamples uniform-continuity

answered Nov 19, 2016 at 18:31

8 votes

How many matrices are there in the vector space $M_{m \times n} (\mathbb{Z}_2)$?

linear-algebra matrices

answered May 8, 2015 at 10:29

8 votes

Difference between homomorphisms and homomorphic images

abstract-algebra

answered Dec 3, 2014 at 10:51

8 votes

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Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$

sequences-and-series

answered Jan 5, 2015 at 5:42

8 votes

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Give $[0,1]^{\omega}$ the uniform topology. Find an infinite subset of this space that has no limit point.

general-topology examples-counterexamples

answered Nov 19, 2017 at 3:30

6 votes

A subspace $X$ is closed iff $X =( X^\perp)^\perp$

real-analysis functional-analysis hilbert-spaces inner-products

answered Dec 4, 2014 at 15:29

6 votes

Is a continuous bijection function from a hausdorff space to a compact space a homeomorphism?

general-topology algebraic-topology continuity

answered Dec 8, 2014 at 4:55

6 votes

Is that Ring a field?

abstract-algebra group-theory ring-theory

answered Nov 24, 2014 at 4:41

6 votes

Absolute convergence to zero imply convergence to zero?

sequences-and-series convergence-divergence absolute-convergence

answered Apr 13, 2015 at 3:34

6 votes

A well defined homomorphism from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/{36}$

group-theory cyclic-groups

answered Mar 6, 2015 at 10:36

6 votes

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Group Theory : What is $Ha \ne Hb$?

group-theory normal-subgroups

answered Dec 28, 2015 at 5:39

6 votes

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Suggestions for research in Group Theory

group-theory soft-question recreational-mathematics education research

answered Dec 31, 2015 at 16:32

6 votes

Prove that the function $x\mapsto\sin(x^{2})$ is not periodic

real-analysis functions trigonometry proof-writing periodic-functions

answered Nov 19, 2016 at 15:24

6 votes

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Book recommendation for Lebesgue integration and Fourier Analysis

reference-request soft-question fourier-analysis lebesgue-measure book-recommendation

answered Feb 9, 2017 at 17:11

6 votes

Prove that the normalizer of the subgroup is the subgroup is itself

abstract-algebra group-theory finite-groups sylow-theory

answered Jan 8, 2017 at 7:24

6 votes

Prove that $a_n=1+\frac{1}{1!} + \frac{1}{2!} +...+ \frac{1}{n!}$ converges using the Cauchy criterion

calculus real-analysis limits convergence-divergence cauchy-sequences

answered Dec 7, 2016 at 12:14

6 votes

Accepted

Number of nonsingular $2\times2$ matrices over $GF(3)$

linear-algebra matrices group-theory discrete-mathematics

answered Dec 13, 2016 at 16:28

6 votes

If a group has order $100$ and every subgroup of $G$ is normal why can't it be non-abelian?

abstract-algebra group-theory finite-groups

answered Dec 14, 2016 at 17:32

5 votes

Is the image of a compact set under a bounded continuous function compact?

general-topology proof-verification

answered Nov 4, 2016 at 15:16

5 votes

Analysis problem: Show that$ f(x)$ is less or equal than$ g(x)$

real-analysis proof-writing

answered Nov 10, 2016 at 3:14

5 votes

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Is $T$, the set of all polynomials with integer coefficients, countable?

elementary-set-theory

answered Nov 13, 2016 at 3:20

5 votes

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Book for Functional Analysis

functional-analysis soft-question book-recommendation

answered Nov 14, 2015 at 13:19

5 votes

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Prove/disprove: $I \cup J$ is (always) an Ideal of $R$.

abstract-algebra ring-theory ideals

answered Mar 8, 2015 at 16:17

5 votes

Good abstract algebra books for self study

abstract-algebra reference-request self-learning book-recommendation

answered Oct 8, 2014 at 15:40

5 votes

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$G/Z(G)$ is cyclic useful for proving groups abelian?

abstract-algebra group-theory abelian-groups

answered Dec 7, 2014 at 5:01

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557 Answers

Suppose that $f ' (x)$ exists and $f(x)$ has two roots $x_1$ and $x_2$. Try to prove that:

Prove that the center of G has order divisible by p

Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

Is there an elegant way to prove a function is linear?

Metric is continuous function

A function continuous and bounded on a closed and bounded set but not uniformly continuous there

How many matrices are there in the vector space $M_{m \times n} (\mathbb{Z}_2)$?

Difference between homomorphisms and homomorphic images

Sum $\frac{1}{6} + \frac{5}{6\cdot 12} + \frac{5\cdot 8}{6\cdot 12\cdot 18} + \frac{5\cdot 8\cdot 11}{6\cdot 12\cdot 18\cdot 24}+\ldots$

Give $[0,1]^{\omega}$ the uniform topology. Find an infinite subset of this space that has no limit point.

A subspace $X$ is closed iff $X =( X^\perp)^\perp$

Is a continuous bijection function from a hausdorff space to a compact space a homeomorphism?

Is that Ring a field?

Absolute convergence to zero imply convergence to zero?

A well defined homomorphism from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/{36}$

Group Theory : What is $Ha \ne Hb$?

Suggestions for research in Group Theory

Prove that the function $x\mapsto\sin(x^{2})$ is not periodic

Book recommendation for Lebesgue integration and Fourier Analysis

Prove that the normalizer of the subgroup is the subgroup is itself

Prove that $a_n=1+\frac{1}{1!} + \frac{1}{2!} +...+ \frac{1}{n!}$ converges using the Cauchy criterion

Number of nonsingular $2\times2$ matrices over $GF(3)$

If a group has order $100$ and every subgroup of $G$ is normal why can't it be non-abelian?

Is the image of a compact set under a bounded continuous function compact?

Analysis problem: Show that$ f(x)$ is less or equal than$ g(x)$

Is $T$, the set of all polynomials with integer coefficients, countable?

Book for Functional Analysis

Prove/disprove: $I \cup J$ is (always) an Ideal of $R$.

Good abstract algebra books for self study

$G/Z(G)$ is cyclic useful for proving groups abelian?