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  2. Elements of order 5 in the Tate-Shafarevich group

    https://www.dpmms.cam.ac.uk/~taf1000/g1data/order5.html
    16 Feb 2015: This left a comparatively small number of examples where we needed to compute the S-units in a degree 24 number field. ... 24, 235--265 (1997). The MAGMA home page is at.
  3. PART II REPRESENTATION THEORYSHEET 2 Unless otherwise stated, all ...

    https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2014-2015/repex2.pdf
    19 Jan 2015: 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2. ... 24 = g5.]. 11 Let a finite group G act on itself by conjugation.
  4. CODES AND CRYPTOGRAPHY – Example Sheet 3TKC Lent 2015 ...

    https://www.dpmms.cam.ac.uk/study/II/Coding/2014-2015/CC3.pdf
    25 Feb 2015: Show by direct calculation that K = K{0}is a cyclic group and deduce that K is finite field with 24 elements.
  5. Groups Example Sheet 2Michaelmas 2015 Julia Goedecke Please send ...

    https://www.dpmms.cam.ac.uk/study/IA/Groups/2015-2016/GroupsSheet2-2015.pdf
    21 Oct 2015: 4. (a) Show that the symmetric group S4 has a subgroup of order d for each divisor d of 24,and find two non-isomorphic subgroups of order 4.
  6. CODES AND CRYPTOGRAPHY – Example Sheet 3TKC Lent 2015 ...

    https://www.dpmms.cam.ac.uk/~tkc10/CodesandCryptography/Exercise_3.pdf
    19 Feb 2015: Show by direct calculation that K = K{0}is a cyclic group and deduce that K is finite field with 24 elements.
  7. Lent Term 2015 R. Camina IB Groups, Rings and ...

    https://www.dpmms.cam.ac.uk/study/IB/GroupsRings%2BModules/2014-2015/grm20153.pdf
    26 Feb 2015: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.
  8. ON FAMILIES OF 9-CONGRUENT ELLIPTIC CURVES TOM FISHER Abstract. ...

    https://www.dpmms.cam.ac.uk/~taf1000/papers/congr9.pdf
    2 Jun 2015: J. Symb. Comb. 24, 235–265 (1997). See also http://magma.maths.usyd.edu.au/magma/. ON FAMILIES OF 9-CONGRUENT ELLIPTIC CURVES 17. ... 24, Cambridge University Press, Cambridge, 1991. [6] Z. Chen, Families of elliptic curves with the same mod 8
  9. Mirror symmetry

    https://www.dpmms.cam.ac.uk/~mg475/utah.pdf
    10 Aug 2015: Mirror symmetry. Mark Gross. University of Cambridge. July 24, 2015. Mark Gross Mirror symmetry.
  10. Starred exercises have model answers. The following relevant tripos…

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/discex.pdf
    7 Feb 2015: 24. You know that lists can be thought of as ordered pair of head and tail.By using the pairing function 〈x,y〉 = 2x (2y 1) show how to encode alist ... 24. Let X be a set, and R the refinement relation on partitions of X.
  11. INTRODUCTION TO STATISTICALMODELLING IN R P.M.E.Altham, Statistical…

    https://www.dpmms.cam.ac.uk/~pmea/redwsheets.pdf
    8 Jan 2015: P.M.E.Altham, University of Cambridge 24. "New Orleans" 9 68.3 204 361 8.4 56.77 113. ... rolling tobacco. 24 X 440 cans Stella Artois 11.95 20.80 23.96 9.25 9.67.
  12. INTRODUCTION TO PLECTIC COHOMOLOGY J. NEKOVÁŘ AND A. J. ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/introplec.pdf
    18 Feb 2015: Hint 'f. V rfm(f)ΓQ. ,. where Vf is the two-dimensional -adic representation of ΓF attached [18, 24, 22]to f. ... 24] A. Wiles: On ordinary λ-adic representations associated to modular forms.
  13. Multivariate and other worksheets for R (or S-Plus): a ...

    https://www.dpmms.cam.ac.uk/~pmea/misc.pdf
    9 Jan 2015: 9 CorpusC 65.24 24.1. 10 Pembroke 64.96 24.5. 11 StCaths 64.63 23.5. ... 24 24 3.9 5.2 13.9 1093 356 88.2 71.3 61.9 688.
  14. HIGHER DESCENTS ON AN ELLIPTIC CURVEWITH A RATIONAL 2-TORSION ...

    https://www.dpmms.cam.ac.uk/~taf1000/papers/higherdesc.pdf
    11 Sep 2015: Then t = (u βv)(u βv) K[x,y,u,v] is a quadratic form with(24) f(r1,. ... Thequadratic form t computed in (24) is an example of an odd form.
  15. What is the probability that a random integral quadraticform ...

    https://www.dpmms.cam.ac.uk/~taf1000/papers/isotropic.pdf
    15 Sep 2015: P(λ(M) [λ dλ). )=. 1. ZGOEn|(λ)|. ni=1. e14λ2i dλi; (24). here(λ) :=. 1i<jn. (λj λi) = det(ϕi(λj)),. where (ϕi(λj)) = (λi1j ) is a Vandermonde matrix, and
  16. University of Cambridge Mathematical Tripos Computability and Logic…

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/comp.pdf
    22 Oct 2015: 4.2 Curry-Howard Correspondence in Proofs. 22. 5 Tennenbaum's Theorem 24. 6 Incompleteness 26. ... 24. CHAPTER 5. TENNENBAUM'S THEOREM. Theorem 5.2 (Tennenbaum's Theorem). PA has no non-standardmodel in which the graphs of and are decidable.
  17. Holmes.dvi

    https://www.dpmms.cam.ac.uk/~twk10/Holmes.pdf
    22 Sep 2015: so b = 1. 24. Exercise 1.5.1. There are many ways of explaining this. ... By inspection m = 1 is not asolution, but m = 2 is a solution (24 = 42).
  18. On Laver’s proof of Fräıssé’s order typeconjecture Philipp…

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/kleppmann-essay.pdf
    10 Jul 2015: 24. If L consists of one equivalence class, we’re done. So suppose pDx,y P Lqx y.
  19. hyp.dvi

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/batty.pdf
    7 Oct 2015: Note that Gromov has given an equivalent formulation of quasi-isometry via Hausdorff and Lipschitzequivalence (see [24]). ... Theorem 2.24 Let x1 and y1 be points of a hyperbolic metric space X.
  20. Automorphy of some residually dihedral Galois representations Jack A. …

    https://www.dpmms.cam.ac.uk/~jat58/version_over_F.pdf
    3 Apr 2015: Automorphy of some residually dihedral Galois representations. Jack A. Thorne. April 3, 2015. Abstract. We establish the automorphy of some families of 2-dimensional representations of the absolute Galoisgroup of a totally real field, which do not
  21. INTRODUCTION TO HYPERBOLIC AND AUTOMATIC GROUPS S. M. Gersten ...

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/baumslag.pdf
    28 Jul 2015: INTRODUCTION TO HYPERBOLIC. AND AUTOMATIC GROUPS. S. M. Gersten. 1.0. Introduction. These notes comprise the revised and edited text of two hourlectures I delivered at the CRM Summer School on Groups held at Banff in August1996. I made no attempt at

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