User math.n00b

18 votes

5 answers

2k views

How did Euler realize $x^4-4x^3+2x^2+4x+4=(x^2-(2+\alpha)x+1+\sqrt{7}+\alpha)(x^2-(2-\alpha)x+1+\sqrt{7}-\alpha)$?

asked May 6, 2014 at 12:36

12 votes

2 answers

454 views

Is it normal that a pure math student doesn't know vector analysis?

reference-request soft-question

asked Jul 19, 2014 at 14:00

10 votes

1 answer

530 views

How do people on MSE find closed-form expressions for integrals, infinite products, etc?

reference-request soft-question special-functions closed-form

asked Jul 22, 2014 at 19:33

10 votes

2 answers

4k views

If $R$ is a local ring, is $R[[x]]$ (the ring of formal power series) also a local ring?

abstract-algebra ring-theory

asked Oct 25, 2014 at 1:08

8 votes

3 answers

536 views

Is $R^n$ projective as a $M_n(R)$-module?

abstract-algebra modules projective-module

asked Dec 9, 2016 at 15:39

7 votes

2 answers

810 views

Why $J(M_n(R))=M_n(J(R))$ for any ring, where $J$ is the Jacobson radical of $R$?

abstract-algebra noncommutative-algebra

asked Dec 1, 2014 at 20:54

7 votes

2 answers

237 views

Every $x \in (0,1]$ can be represented as $x = \sum_{k=1}^{\infty} 1/{n_k}$, such that $n_{k+1}/n_k\in \{2,3,4\}$

real-analysis analysis problem-solving

asked Mar 14, 2014 at 7:32

7 votes

1 answer

265 views

If $(n_k)$ is strictly increasing and $\lim_{n \to \infty} n_k^{1/2^k} = \infty$ show that $\sum_{k=1}^{\infty} 1/n_k$ is irrational

sequences-and-series analysis problem-solving irrational-numbers

asked Mar 14, 2014 at 18:33

7 votes

2 answers

2k views

A real continuous periodic function with two incommensurate periods is constant.

calculus real-analysis proof-verification examples-counterexamples

asked Apr 30, 2014 at 14:22

6 votes

1 answer

2k views

When are two simple tensors $m' \otimes n'$ and $m \otimes n$ equal? (tensor product over modules)

abstract-algebra modules tensor-products multilinear-algebra

asked Nov 30, 2014 at 13:05

5 votes

2 answers

903 views

How does the representation of co-vectors change if we change the basis of a vector space $V$?

linear-algebra differential-geometry tensors multilinear-algebra

asked Nov 4, 2014 at 15:11

5 votes

2 answers

660 views

How to show that $\displaystyle [a,b,c] = \frac{abc}{(ab,bc,ca)}$ without prime factorization?

elementary-number-theory least-common-multiple gcd-and-lcm

asked May 17, 2014 at 13:35

5 votes

3 answers

1k views

Find the number of $2$-element subsets $\{a,b\}$ of $\{1,\cdots,1000\}$ such that $5 \mid a\cdot b$

combinatorics

asked Jun 10, 2014 at 22:40

4 votes

0 answers

136 views

Is it possible to find $\int \frac{1}{\sqrt[4]{1+x^4}} dx$ by parametrizing the curve $y^4-x^4=1$?

calculus real-analysis integration alternative-proof

asked Aug 10, 2014 at 17:57

4 votes

2 answers

208 views

Accumulation points of $\{ \sqrt{n} - \sqrt{m}: m,n \in \mathbb{N} \}$

analysis problem-solving

asked Mar 13, 2014 at 16:59

4 votes

3 answers

470 views

A group theoretical game: Is it possible to reach a state when only blue marbles are left?

group-theory contest-math

asked May 9, 2014 at 14:23

4 votes

1 answer

826 views

$f: [0,\infty) \to \mathbb{R}$ is continuous and $\displaystyle \lim_{x \to \infty}f(x) = L < \infty$. Prove that $f$ is uniformly continuous.

analysis

asked May 10, 2014 at 19:16

3 votes

1 answer

316 views

Does a maximal ideal in a unital commutative ring contain the set of zero-divisors?

abstract-algebra

asked May 14, 2014 at 16:05

3 votes

1 answer

135 views

Does $Ext^n(A,C)=0$ imply $Ext^{n+1}(A,C)=0$

homological-algebra

asked Nov 16, 2014 at 12:26

3 votes

1 answer

2k views

How to calculate differential forms on $S^2$ parameterized by stereographic projection?

differential-geometry manifolds smooth-manifolds

asked Nov 1, 2014 at 14:30

3 votes

1 answer

158 views

How to find the norm of $ \Lambda x = \sum_{n=1}^{\infty} \frac{x_n}{n\sqrt{6}}$ in $\ell^2$

real-analysis analysis functional-analysis lp-spaces

asked Jan 30, 2015 at 16:42

2 votes

0 answers

188 views

How to find the tangent space of $O(n)$ by considering $O(n)$ as the pre-image of the map $A \mapsto AA^T$ at identity?

manifolds

asked Feb 12, 2015 at 16:58

2 votes

0 answers

859 views

How to show that restricted Lorentz group (orthochoronous proper Lorentz transformations) is a normal subgroup?

linear-algebra abstract-algebra group-theory mathematical-physics

asked Jun 17, 2015 at 18:11

2 votes

1 answer

58 views

$A$ is a $K$-algebra and $x$ is an indeterminate. $K[x] \otimes A \cong A[x]$ as $K$-algebras

abstract-algebra modules tensors

asked Dec 26, 2016 at 16:45

2 votes

1 answer

184 views

How to show that $m^(A \cup B) + m^(A \cap B) \leq m^(A)+m^(B)$ for any $A,B \subseteq \mathbb{R}$?

real-analysis analysis measure-theory

asked May 8, 2016 at 11:34

2 votes

1 answer

166 views

Differentiation of scalar fields using tensor notation

differential-geometry vector-analysis tensors

asked Jul 31, 2014 at 9:57

2 votes

1 answer

245 views

Levi-Cevita symbols: Why is $\epsilon_{ijk}\epsilon_{pjk}$ equal to $2\delta_{ip}$, but not $0$?

differential-geometry vector-analysis

asked Jul 20, 2014 at 8:23

2 votes

5 answers

140 views

How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?

linear-algebra

asked Oct 1, 2014 at 16:22

2 votes

2 answers

873 views

A concrete example of a unital noncommutative ring without maximal two-sided ideals

abstract-algebra ring-theory ideals noncommutative-algebra

asked Oct 25, 2014 at 7:01

2 votes

1 answer

1k views

Example of a homomorphism with a right or left inverse function that its right or left inverse is not a homomorphism

abstract-algebra category-theory

asked Oct 28, 2014 at 20:13

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53 Questions

How did Euler realize $x^4-4x^3+2x^2+4x+4=(x^2-(2+\alpha)x+1+\sqrt{7}+\alpha)(x^2-(2-\alpha)x+1+\sqrt{7}-\alpha)$?

Is it normal that a pure math student doesn't know vector analysis?

How do people on MSE find closed-form expressions for integrals, infinite products, etc?

If $R$ is a local ring, is $R[[x]]$ (the ring of formal power series) also a local ring?

Is $R^n$ projective as a $M_n(R)$-module?

Why $J(M_n(R))=M_n(J(R))$ for any ring, where $J$ is the Jacobson radical of $R$?

Every $x \in (0,1]$ can be represented as $x = \sum_{k=1}^{\infty} 1/{n_k}$, such that $n_{k+1}/n_k\in \{2,3,4\}$

If $(n_k)$ is strictly increasing and $\lim_{n \to \infty} n_k^{1/2^k} = \infty$ show that $\sum_{k=1}^{\infty} 1/n_k$ is irrational

A real continuous periodic function with two incommensurate periods is constant.

When are two simple tensors $m' \otimes n'$ and $m \otimes n$ equal? (tensor product over modules)

How does the representation of co-vectors change if we change the basis of a vector space $V$?

How to show that $\displaystyle [a,b,c] = \frac{abc}{(ab,bc,ca)}$ without prime factorization?

Find the number of $2$-element subsets $\{a,b\}$ of $\{1,\cdots,1000\}$ such that $5 \mid a\cdot b$

Is it possible to find $\int \frac{1}{\sqrt[4]{1+x^4}} dx$ by parametrizing the curve $y^4-x^4=1$?

Accumulation points of $\{ \sqrt{n} - \sqrt{m}: m,n \in \mathbb{N} \}$

A group theoretical game: Is it possible to reach a state when only blue marbles are left?

$f: [0,\infty) \to \mathbb{R}$ is continuous and $\displaystyle \lim_{x \to \infty}f(x) = L < \infty$. Prove that $f$ is uniformly continuous.

Does a maximal ideal in a unital commutative ring contain the set of zero-divisors?

Does $Ext^n(A,C)=0$ imply $Ext^{n+1}(A,C)=0$

How to calculate differential forms on $S^2$ parameterized by stereographic projection?

How to find the norm of $ \Lambda x = \sum_{n=1}^{\infty} \frac{x_n}{n\sqrt{6}}$ in $\ell^2$

How to find the tangent space of $O(n)$ by considering $O(n)$ as the pre-image of the map $A \mapsto AA^T$ at identity?

How to show that restricted Lorentz group (orthochoronous proper Lorentz transformations) is a normal subgroup?

$A$ is a $K$-algebra and $x$ is an indeterminate. $K[x] \otimes A \cong A[x]$ as $K$-algebras

How to show that $m^(A \cup B) + m^(A \cap B) \leq m^(A)+m^(B)$ for any $A,B \subseteq \mathbb{R}$?

Differentiation of scalar fields using tensor notation

Levi-Cevita symbols: Why is $\epsilon_{ijk}\epsilon_{pjk}$ equal to $2\delta_{ip}$, but not $0$?

How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?

A concrete example of a unital noncommutative ring without maximal two-sided ideals

Example of a homomorphism with a right or left inverse function that its right or left inverse is not a homomorphism