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21 May 2005: ANALYSIS II EXAMPLES 1. Michaelmas 2004 J. M. E. Hyland. This sheet contains Basic Questions, which focus on the examinable component of the course, to-gether with Additional Questions for those wishing to take things further. The questions are not

21 May 2005: A.G.Thomason@dpmms.cam.ac.uk - 1 - 24 January 2005. 13) Prove that a graph G is k-connected iff |G| k 1 and for any U V (G) ... A.G.Thomason@dpmms.cam.ac.uk - 2 - 24 January 2005.

18 Oct 2005: ANALYSIS II EXAMPLES 1. Michaelmas 2005 J. M. E. Hyland. The Basic Questions are cover examinable material from the course. The Additional Questions arefor those wishing to take things a bit further. The questions are not all equally difficult; I

21 May 2005: 3. (i) Show that X4 2X 2 and X4 18X2 24 are irreducible in Q[X].(ii) Are X3 9 and X4 8 irreducible in Q[X]?(iii) Show that X4

21 May 2005: 4n 3} then G contains a cycle of length 4. 24) Let G be a graph of order n and let G1,.

22 Nov 2005: 24. Let f : R2 R be a continuous function satisfying a Lipschitz condition|f(x,y1) f(x,y2)| K|y1 y2|.

21 May 2005: 24. Let f : R2 R be a continuous function satisfying a Lipschitz condition|f(x,y1) f(x,y2)| K|y1 y2|.

17 Jun 2005: J. Baues, S. Halperin and J.-M. Lemaire. DMV Seminar, 24, Birkhuser Verlag, Basel,1995.

30 Jun 2005: Green [25].The method is still paying dividends, cf. [3, 24]. Let be an arbitrary smooth 2-form. ... Math. 246, Amer. Math. Soc., Providence, RI, 1999. [24] N. Gouda, A theorem of E.

27 Oct 2005: 24) (i) Show that H(X|Y ) 0 with equality if and only if X is a function of Y.