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 17 If $A^2 = I$ (Identity Matrix) then $A = \pm I$ 15 Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous? 7 Memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$ 7 Is the Look and Say Sequence a “proper” maths problem? 7 If $\omega$ is an $n$-form on a compact $n$-manifold $M$ without boundary, then $\omega$ is exact if and only if $\int\limits_{M}\omega=0$

### Reputation (3,429)

 +15 Show $(⊕M_α)/I(⊕M_α)\simeq ⊕(M_α/IM_α)$ for ${M_α}$ $R$-modules, and $I$ is an ideal of the commutative ring $R$ +20 How do I show $SO(n)$ is open and closed in $O(n)$? +40 If $f$ is a increasing function in $[a,b]$, then is it true that $\text{Img}(f) = [f(a),f(b)]$? +10 How to show that a map $F:M\to N$ between manifolds is smooth if $f\circ F$ is smooth for smooth $f:N\to R$.

### Questions (2)

 2 Extension of smooth maps at a cusp 2 Does the sum generate the field compositum when degrees are prime?

### Tags (116)

 49 differential-geometry × 20 20 ring-theory × 11 34 linear-algebra × 20 17 riemannian-geometry × 7 31 matrices × 9 16 calculus × 11 26 abstract-algebra × 21 12 general-topology × 7 26 real-analysis × 7 12 ideals × 6

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 Mathematics 3,429 rep 514