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21 Jan 2009: B[p] := {bp : b B}. in B provided that B is reduced.Let t be a positive integer. ... r. for all v V.Let B = Sym(V k) and let P be a graded prime ideal of B.

5 Nov 2009: 1. (Reduced homology) Let X be a space, and recall that C0(X) = 〈ex | x X〉. ... b) Suppose f : X X is a homeomorphism, and let Y = X [0, 1]/ , where(x, 1) (f (x), 0).

28 Jan 2009: to. 4. Let A, B be two distinct points in the Euclidean plane. ... Let be a spherical triangle with sides of length a,b,c and angles α,β,γ.

24 Jun 2009: Let A K be a finite setof sources, and let B B, G F. ... Let B B, G F, let A Kbe a finite set of sources, and write ψA = ψA(B,G) for the colouringgiven in the last section.

30 Jan 2009: to. 4. Let A, B be two distinct points in the Euclidean plane. ... Let be a spherical triangle with sides of length a,b,c and angles α,β,γ.

18 Nov 2009: 4) And here a really hard one: Two logicians meet, let us call them A and B. ... B: I do not know the numbers. A: I do not know the numbers.

23 Oct 2009: What if we replace ‘injective’ by ‘surjective’ passim? 5. Let A = {1, 2, 3} and B = {1, 2, 3, 4, 5}? ... Let R be the relation on Z‘ aRb if b = a 3 ’. How many equivalence relations on Z contain R? 8. Let A be a set of n positive integers.

21 Apr 2009: b) Let π be the true probability that a one-litre water sample fromthis type of site contains pathogenic material. ... Show thatv is also an eigenvector of A1. (b) Let.  =. [2 11 2. ]. i. Find the eigenvalues of  and derive an eigenvector

18 Feb 2009: This curve is called the longitudeof K. 13. Let X = S1 D2, and let a = S1 1 and b = 1 D2 be curves on X = T 2. ... 14. In the notation of problems 7 and 8, let M = Y f X, where f : X Y is anorientation reversing diffeomorphism with f([b]) = p[m] q[].

13 Oct 2009: a) How do we know that R(G) exists? (b) Let Ik be a set of k independent edges (so |Ik| = 2k). ... b) Let A be a collection of subsets of [s 1].