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19 Jan 2021: a) Show that there is a surjection π1Sg G, for some g.(b) Show that G is a subgroup of Mod(Sh), for some h. ... a) Prove that TαTβ(α) = β. (b) Prove the braid relation: TαTβTα = TβTαTβ.

3 Oct 2021: To see (b), note that every A G takes the form A = {U B}, for some Borel set B. ... To see this, consider first the case where Y = 1B for some B G.

26 Jan 2021: Some of these terminals were from the traditional VT100 series, and others were BBC model B microcomputers with suitable ROMs in their expansion slots. ... The national facility to which some in TCM had access had a T3D.

27 Jul 2021: 9. EITHER: (A) ‘In absolutely indifferent things there is no choice, and consequently no election or will, since choice must be founded in some reason or principle.’ (LEIBNIZ) Discuss. ... voluntarily do: which, because they proceed from their will,

6 Feb 2021: Prove that f is continuous on (a,b). Must it be continuous at a andb too? ... 13. Let f : R R be a function which has the intermediate value property: Iff(a) < c < f(b), then f(x) = c for some x between a and b.

5 Oct 2021: Ratings for some crimes e.g. ‘drive dangerously’ overall higher and with broader spread than others e.g. ... Specific crimes: SSBE least likely to commit some crimes – ‘physical assault’, ‘shoplift’ and ‘vandalise a shop front’. •

20 Jul 2021: n. 1. ) ck. for some integers c0,. ,ck. (b) State the binomial theorem. ... x a (mod n) ,x b (mod m). have the same set of solutions as x c (mod mn) for some c N.

28 May 2021: researchers, (b) he felt a desire to repay to society some of the remarkable gains he had made by introducing innovative approaches to hedge-fund management, in the process hoping to ... 6-10 MeV/c2 and the world’s best B hadron mass measurements, and

16 Mar 2021: F i //. Ep //. p. B. {b0} // B B. ... for some monic polynomial p(x) H(B; Z)[x]. Homotopy Theory Example sheet 3.

15 Jan 2021: some a,b 0. Hence prove that the class group of K is cyclic and find itsorder.