# math.n00b

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# 41 Questions

 11 Is it normal that a pure math student doesn't know vector analysis? 7 Every $x \in (0,1]$ can be represented as $x = \sum_{k=1}^{\infty} 1/{n_k}$, such that $n_{k+1}/n_k\in \{2,3,4\}$ 6 How do people on MSE find closed-form expressions for integrals, infinite products, etc? 5 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 4 Is it possible to find $\int \frac{1}{\sqrt[4]{1+x^4}} dx$ by parametrizing the curve $y^4-x^4=1$?

# 1,484 Reputation

 +15 Why $J(M_n(R))=M_n(J(R))$ for any ring, where $J$ is the Jacobson radical of $R$? -2 If $a_n>0$ and $\displaystyle \frac{a_{n+1}}{a_n} \leq 1 + \frac{1}{n^2}$ and $\displaystyle \{\frac{a_{n+1}}{a_n} \} \not\to 1$ then $a_n \to 0$ +10 When are two simple tensors $m' \otimes n'$ and $m \otimes n$ equal? (tensor product over modules) +5 Does $Ext^n(A,C)=0$ imply $Ext^{n+1}(A,C)=0$

 8 How to prove the inequality $\det (AA^T) \ge 0$? 5 Exercise on inner products 4 How do I prove $\sec^2 \frac{a}{2}=\frac{2\sec a}{1+\sec a}$? 4 What is the upper bound for $\frac1n$ where $n$ is a prime? 4 Existence of isomorphism between groups of upper triangular matrices.

# 71 Tags

 29 linear-algebra × 18 6 elementary-number-theory × 4 18 matrices × 6 5 finite-groups × 2 13 calculus × 12 4 power-series × 2 9 group-theory × 6 4 complex-analysis × 2 8 determinant 4 number-theory

# 4 Accounts

 Mathematics 1,484 rep 224 Physics 106 rep 2 Information Security 103 rep 1 English Language & Usage 101 rep