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10 Jul 2011: Explicit n-descent on elliptic curves, II. Geometry (24 pages) The other papers in this series are Paper I.

12 Jan 2011: 23 5.9 9.24 5.8 9.24 6.1 9.61 6.3 9.60 6.4 9.61 6.2.

22 Jan 2011: ## This is the data set "Tourist Data". It gives the following table of ## prices, in pounds, for a three-course meal, bottle of beer, suntan ## lotion, taxi (5km), film (24 exposures)

23 Nov 2011: 1. Triangulating a ‘topological pretzel’: χ = 24 44 18 = 2, g = 2.

28 Oct 2011: Find all the subgroups of the cyclic group Cn. 7. Show that the symmetric group S4 has a subgroup of order d for each divisor d of 24, and find

26 Aug 2011: 7591 5126 350 297 324 299 Greater Manchester16. 906 734 55 34 38 24 Gwent17. ... 304 205 37 24 65 53 Warwickshire40. 948 1184 65 98 133 103 West Mercia41.

10 Mar 2011: qn1. (1 qn)24. Assuming this, let E2(τ) = 1 24.

10 Mar 2011: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(z) is not a modular form of weight 2.

18 Feb 2011: 13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21]. curr 9.01 8.97 9.05 9.23 9.24 9.24 9.61 9.6 9.61. ... 14] [,15] [,16] [,17] [,18] [,19] [,20] [,21]. x 8.97 9.05 9.23 9.24 9.24 9.61 9.6 9.61.

10 Jan 2011: 24 = g5.]. 1. 2 PART II REPRESENTATION THEORY SHEET 2. ... 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

1 Mar 2011: 35 30High Yes 9 12 19 19High No 24 25 28 29.

24 Nov 2011: 4.8. (i) What are the transitive subgroups of S4? Find a monic polynomial over Z of degree4 whose Galois group is V4 = {e, (12)(34), (13)(24), (14)(23)}. ... November 24, 2011t.yoshida@dpmms.cam.ac.uk.

10 Jan 2011: 8 Suppose we are given that H is a subgroup of order 24 in G.

2 Nov 2011: Find u, v Z with 76u 45v = 1. Does 3528x 966y = 24 have an integer solution?

24 Feb 2011: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

11 Feb 2011: i = 4, i! = 24. i = 5, i! = 120.

21 Nov 2011: 23, M2 hasprobability. 24, M3 has probability. 26 and M4 has probability.

4 Mar 2011: It gives a table ofprices, in pounds, for a three-course meal, bottle of beer, suntan lotion, taxi (5km), film(24 exposures) and car hire (per week) in 14 different popular

16 Mar 2011: Dispersion parameter for Gamma family taken to be 0.06801047). Null deviance: 7.7060 on 24 degrees of freedomResidual deviance: 1.5431 on 22 degrees of freedomAIC: 157.29.

16 Aug 2011: Here is a simple example which illustrates the main obstacle. Considerapplying a 12-compression to the family A = {13, 23, 24}. ... Only 24 moves,giving C12A = {13, 23, 14}. But now B = {23, 24} A is intersecting andmoves to {23, 14} which is not.

16 Oct 2011: hand side of (13) a small integer, and reducing as described in [24]. ... 24 = 3572860258x1 5569480730x2 953739600x3 2138046812x4 858145244x5φ′25 = 4674149266x1 943631490x2 6754488160x3 751535046x4 117685567x5φ′34 = 1851228934x1 5238146110x2

21 Dec 2011: Since c4 isprimitive it follows that c4 b22 (mod 24). Next putting x = b2 in an identity ofKraus [K],. ... 24 TOM FISHER. The Hessian, introduced in [F2], is an SL5 SL5-equivariant polynomial mapH : X5 X5 the.

9 May 2011: 24 T.A. FISHER. i.e. the ideal generated by the 44 minors of the Hessian matrix of F.

18 Jul 2011: STOLL. [L+ : K] = 4 quadrics from Q1 and [M+ : K] = 24 quadrics from Q2. ... 24 J.E. CREMONA, T.A. FISHER, C. O’NEIL, D. SIMON, AND M.

15 Aug 2011: E(. 2. ββT. )= XTWX. P.M.E.Altham, University of Cambridge 24. 2.3 Reminder: The Newton-Raphson algorithm.

29 Jul 2011: n} of order n2. 24 J. THORNE. (The point of this is that when.

12 Jul 2011: Examples Sheets. REPRESENTATION THEORY (D) 24 lectures, Lent term. Linear Algebra, and Groups, Rings and Modules are essential. ... χ5 d x y z w. Know: 24 = 1 1 9 9 d2 d = 2.