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 17 Prove $|e^{i\theta} -1| \leq |\theta|$ 14 What does the notation $f\colon A\to B$ mean? 12 $f: \mathbb{R} \to \mathbb{R}$ satisfies $(x-2)f(x)-(x+1)f(x-1) = 3$. Evaluate $f(2013)$, given that $f(2)=5$ 10 How to find the determinant of this matrix? 10 Prove that if a is a root of $f(x)$ then $\overline{a}$ is also a root

### Reputation (5,834)

 +10 What does the notation $f\colon A\to B$ mean? +10 An exercise to understand free group +10 Prove $|e^{i\theta} -1| \leq |\theta|$ +10 An abelian group is not isomorphic to an non-abelian group.

### Questions (12)

 15 When does it hold that $\int_{0}^{x} fg=\left(\int_{0}^{x} f\right)\left(\int_0^x g\right)$ 8 Is there a ring so that any two distinct non-zero elements do not commute? 5 Terminal objects of the category of morphisms 4 How do we find specific values of sin and cos given the series definition 4 Can all linear code be adapted so that the first bits of the encoded message are the bits from the original message?

### Tags (105)

 123 linear-algebra × 53 36 calculus × 16 49 real-analysis × 26 26 sequences-and-series × 15 47 functions × 17 26 abstract-algebra × 11 46 matrices × 22 25 notation × 5 38 elementary-set-theory × 14 24 algebra-precalculus × 14

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