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18 Nov 2019: Graph Theory (2019–20) Example Sheet 3 of 4. 1. Let G = Ks,t.

28 Oct 2019: Graph Theory (2019–20) Example Sheet 2 of 4. 1. For which n and m is Kn,m Hamiltonian?

9 Oct 2019: Graph Theory (2019–20) Example Sheet 1 of 4. 1. Show that every graph (of order at least two) has two vertices of the same degree.

15 Oct 2019: Example sheet 2 (updated 15 Aug, 2012). 2010 - 2011. updated 20 May, 2011.

18 Nov 2019: Graph Theory (2019–20) Example Sheet 4 of 4. 1. Prove that R(3,3) = 6 and R(3,4) = 9.

9 Oct 2019: Graph Theory (2019–20) Example Sheet 1 of 4. 1. Show that every graph (of order at least two) has two vertices of the same degree.

15 Oct 2019: 2011 - 2012. 2010 - 2011. update 20 Nov 2010).

11 Oct 2019: lecture Monday 27 November - replacement lecture Wednesday 20 November, 2pm, MR3.

12 Nov 2019: Use these to reconstruct thecharacter table of S5. Then repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of S5 of order 20.

8 Feb 2019: Theorem 2.20 (Principle of isolated zeros). Assume that f : D(w,R) C is a holomorphicfunction which is not identically zero. ... Here is another important consequence of Theorem 2.20. Corollary 2.21 (‘Identity Theorem’).

6 Oct 2019: Figure 1: Hd(Γg,1, Γg1,1; Q);? means unknown,? means not zero. Non-zero groups: use results of Faber, Kontsevich, Morita.20.

7 Sep 2019: Aux LazaristesPCSI. Colle 20Matrices – Dimension finie. Alexis Marchand02/05/2019. Questions de cours.1. Énoncer et démontrer la Formule de Grassmann.2. Énoncer et démontrer le Théorème du rang.3. Énoncer et démontrer le Théorème de la

8 Nov 2019: Show that I is contained in some Qi. 20. Let R be a Noetherian ring and P1 < P2 be prime ideals of R.

27 Nov 2019: 20. Write cos(2π/17) explicitly in terms of radicals. 21. Show that for any n > 1 the polynomial xn x 3 is irreducible over Q.

8 Feb 2019: Estimate v from the following independentobservations made on 9 shells. α (deg) 5 10 15 20 25 30 35 40 45sin 2α 0.1736 0.3420 0.5 0.6428

28 Feb 2019: fixed). Improved No difference WorsePlacebo 18 17 15. Half dose 20 10 20Full dose 25 13 12.

16 Oct 2019: 2. Between 10 and 20 there are 4 primes; does it ever happen again that there are 4 primesbetween two consecutive multiples of 10 (apart from between 0 and 10)?

28 Feb 2019: α (deg) 5 10 15 20 25 30 35 40 45sin 2α 0.1736 0.3420 0.5 0.6428 0.7660 0.8660 0.9397 0.9848 1range (m) 4860

12 Nov 2019: Use these to reconstruct thecharacter table of S5. Then repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of S5 of order 20.

11 Nov 2019: 20. differential geometry 21. more generally, the bundle of differential p-forms ΛpTM are real vector bundles of rank(np. ... Corollary 2.20. The curvature form F(A) of an orthogonal (resp. unitary) connection Ais skew-symmetric (resp.