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 19 Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous? 18 If $A^2 = I$ (Identity Matrix) then $A = \pm I$ 9 If $\omega$ is an $n$-form on a compact $n$-manifold $M$ without boundary, then $\omega$ is exact if and only if $\int\limits_{M}\omega=0$ 8 Prove: The pre-image of an ideal is an ideal. 7 Memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$

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 +10 When to give up on a hard math problem? +10 If $\omega$ is an $n$-form on a compact $n$-manifold $M$ without boundary, then $\omega$ is exact if and only if $\int\limits_{M}\omega=0$ +10 Prove: The pre-image of an ideal is an ideal. -2 Rank Theorem question

### Questions (2)

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

### Tags (114)

 54 differential-geometry × 20 22 ring-theory × 11 39 linear-algebra × 20 18 examples-counterexamples 33 matrices × 9 17 riemannian-geometry × 7 30 real-analysis × 7 16 calculus × 11 29 abstract-algebra × 21 14 general-topology × 7

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 Mathematics 3,667 rep 614