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4 Feb 2008: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.

19 Mar 2008: 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

4 Feb 2008: 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

19 Mar 2008: 24. Let f : R2 R be a continuous function satisfying a Lipschitz condition.

1 Nov 2008: suggested in lectures.]. 24. Find a maximal flow and a minimal cut for the network pictured with a source at node1 and a sink at node n.

19 Aug 2008: The following result is a restatement of the first main result of [24]. ... 1–24, Berlin: Springer-Verlag, 2001. 23. G. D. Plotkin and A. J.

17 Nov 2008: 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

27 Aug 2008: These 100 cases of cuts we will consider as follows: 40 casesof cuts the form (R;D) as we have 4 right rules and 10 others; 24 cases of cuts ofthe ... There are hence 24 remaining cutsof interest.We now summarize the cuts of which we need to take some

3 Feb 2008: 35 30High Yes 9 12 19 19High No 24 25 28 29.

6 Mar 2008: V = {1, (12)(34), (13)(24), (14)(23)}. is a subgroup of A4 and that A4 is not simple.(ii) Describe V in terms of modules.(iii) Write the product

27 Aug 2008: These 100 cases of cuts we will consider as follows: 40 casesof cuts the form (R;D) as we have 4 right rules and 10 others; 24 cases of cuts ofthe ... There are hence 24 remaining cutsof interest.We now summarize the cuts of which we need to take some

19 Aug 2008: Each of these corresponds tothe composition of associated formal power series (see, e.g., [23, 24, 40, 6, 38,37, 7]). ... 1981), 1–82. 24. , Foncteurs analytiques et espèces de structures, Combinatoire Énumérative,Lecture Notes in Mathematics, vol

2 Feb 2008: 2, 304315. 2. J.W.S. Cassels, Lectures on elliptic curves, LMS Student Texts, 24, CUP, Cam-bridge, 1991. ... Symbolic Comput. 24 (1997), no. 3-4, 235265. TheMagma home page is at http://magma.maths.usyd.edu.au/magma/.

22 Aug 2008: R x if and only if ju xj 1.Girard's Coheren e spa es [24,28 are essentially G?(Rel) for this orthogona-17. ... Springer Verlag, 1993.[16 G.M. Bierman. On intuitionisti linear logi. Te hni al Report 346, Universityof Cambridge Computer Laboratory, August

22 Aug 2008: R x if and only if ju xj 1.Girard's Coheren e spa es [24,28 are essentially G?(Rel) for this orthogona-17. ... Springer Verlag, 1993.[16 G.M. Bierman. On intuitionisti linear logi. Te hni al Report 346, Universityof Cambridge Computer Laboratory, August

19 Aug 2008: 24]. So we are keen to define the notion of Kleisli bicategoryin a way that includes such variants. ... Diff. 21 (1980)111–160. [24] Winskel, G., Linearity and non-linearity in distributed computation, (bookchapter, to appear).

13 Aug 2008: 18The treatment of quotients in Jacobs [24] should make clear what is intended. ... Myhill. Choice implies excluded middle. Zeitschriftfür mathematische Logik und Grundlagen der Mathematik, 24:461, 1978.

20 Feb 2008: Proof. When N = G this is follows from [13, Theorem 7.24]; see also [1, Lemma3.11]. ... Lemma. The quotient category Fd/Fd1 is equivalent to M(Q(kG)). Proof. This follows from [24, Propositions XI.3.4(a) and XI.6.4], with appropriatemodifications to

8 Mar 2008: 24. 12 The inversion theorem. Before proving Bochner’s theorem we need some simple results on positivedefinite functions.

18 Aug 2008: normalforms to which a proof in the sequent calculus can reduce (seefor example [24, Page127]). ... The project on which we report here was motivated by Urban’s strong normalisationresult ([25] and [24]) for a formulation of classical proof.In [11],

27 Aug 2008: These 100 cases of cuts we will consider as follows: 40 casesof cuts the form (R; D) as we have 4 right rules and 10 others; 24 cases of cuts ofthe ... There are 24 remainingcuts of interest.We now summarize the cuts of which we need to take some note.

27 Aug 2008: These 100 cases of cuts we will consider as follows: 40 casesof cuts the form (R; D) as we have 4 right rules and 10 others; 24 cases of cuts ofthe ... There are 24 remainingcuts of interest.We now summarize the cuts of which we need to take some note.

7 May 2008: DEFINITION 24 The things that are are values of k are either:. ... PROPOSITION 25 The clauses of definition 24 give a model in which every lowset x has a cardinal: {y : |y| = |x|}.

18 Aug 2008: Longo, Set-Theoretical Models of λ-Calculus: Theories, Expansions, Isomorphisms, Ann. Pure Appl.Logic 24 (1983) 153–188.

27 Aug 2008: Term Assignment for Intuitionistic Linear Logic(Preliminary Report)Nick Benton Gavin Bierman Valeria de PaivaComputer LaboratoryUniversity of Cambridgefpnb,gmb,vcvpg@cl.cam.ac.ukMartin HylandDepartment of Pure Mathematics and Mathematical

27 Aug 2008: Term Assignment for Intuitionistic Linear Logic(Preliminary Report)Nick Benton Gavin Bierman Valeria de PaivaComputer LaboratoryUniversity of Cambridgefpnb,gmb,vcvpg@cl.cam.ac.ukMartin HylandDepartment of Pure Mathematics and Mathematical

7 Aug 2008: Proof. The correspondences between the first two are in [21, 24]: for any T -algebra r : T R R, the monad map is given by dX (γ) = κ RX 7 ... Proof. To give a T -action on x is equivalent to giving a monad map from T to amodified form of xA(,x) with

13 Aug 2008: A precise connection was given by Hofmann andStreicher [24]. As explained in detail by Selinger [37], RC corresponds to thecall-by-name λµ-calculus, and CR to the call by value. ... 24. 5 Classical Proof. In the previous section I discussed approaches

15 Oct 2008: 1.24 DefinitionLet M be a smooth manifold. The tangent bundle of M is the disjoint union of the tangentspaces;.

8 Jan 2008: 24. Theorem 10.6. [Bessel’s inequality] Consider an inner product space V.

1 Feb 2008: 24. 3.3 Singularities and the Laurent expansion; the residuetheorem. Just as a holomorphic function on a disc D(a,r) can be expanded as a series inpowers of (z a),

7 Aug 2008: Example 10. Probabilistic Nondeterminism A computationally natural pre-sentation of a countable Lawvere ω-Cpo-theory for probabilistic nondetermin-ism combined with nontermination [16,22,24,47] can be obtained by

22 Aug 2008: Thus, Berryand Curien introdu ed sequential algorithms over dss [10 (see also Curien's book[24 for a omprehensive introdu tion). ... 11, 23, 57. Curien's book (se ond edition) [24 provides an ex ellent a ountof the main body of resear h inspired by the

22 Aug 2008: Thus, Berryand Curien introdu ed sequential algorithms over dss [10 (see also Curien's book[24 for a omprehensive introdu tion). ... 11, 23, 57. Curien's book (se ond edition) [24 provides an ex ellent a ountof the main body of resear h inspired by the