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Jeroen

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combinatorics

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38	Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
11	Let $G$ be a finite group with $\|G\|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
10	Show that $h \equiv 1 \pmod p$, where $h$ is the number of subgroups of order $p$ and $p$ divides the group order. [duplicate]
8	Let $G$ be a group of order $pq$, with $p$ and $q$ prime. Prove that the order of the center of $G$ is 1 or $pq$.
6	Calculate $\int_{0}^{2\pi} \frac{\cos((2n+1)t)}{\cos(t)}dt$

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2	Students in class

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2 combinatorics × 3	0 analysis × 3
0 real-analysis × 5	0 matrices × 3
0 linear-algebra × 4	0 logic × 2
0 abstract-algebra × 4	0 ordinary-differential-equations × 2
0 group-theory × 4	0 asymptotics × 2

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