user avatar
user avatar
user avatar
math.n00b
  • Member for 8 years, 3 months
  • Last seen more than 5 years ago
18 votes
5 answers
2k views

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

12 votes
2 answers
454 views

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

10 votes
1 answer
530 views

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

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?

8 votes
3 answers
536 views

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

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 $R$?

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 $n_{k+1}/n_k\in \{2,3,4\}$

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

7 votes
2 answers
2k views

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

6 votes
1 answer
2k views

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

5 votes
2 answers
903 views

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

5 votes
2 answers
660 views

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

5 votes
3 answers
1k views

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

4 votes
0 answers
136 views

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

4 votes
2 answers
208 views

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

4 votes
3 answers
470 views

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

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.

3 votes
1 answer
316 views

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

3 votes
1 answer
135 views

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

3 votes
1 answer
2k views

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

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 $\ell^2$

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?

2 votes
0 answers
859 views

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

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

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 $A,B \subseteq \mathbb{R}$?

2 votes
1 answer
166 views

Differentiation of scalar fields using tensor notation

2 votes
1 answer
245 views

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

2 votes
5 answers
140 views

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

2 votes
2 answers
873 views

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

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