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  2. GEOMETRY AND GROUPS – Example Sheet 1TKC Michaelmas 2012 ...

    https://www.dpmms.cam.ac.uk/~tkc10/GeometryandGroups/Exercise1.pdf
    13 Oct 2012: Let u =(. ac. ), v =. (bd. )for some integers a, b, c, d with ad bc = 1. ... Show that every vector. w Z Z can be written as mu nv for some integers m and n.
  3. Mathematical Tripos: Part IB DJS/Lent 2015 Statistics: Example Sheet…

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2014-2015/ex1.pdf
    22 Jan 2015: Xn be independent Poisson random variables, with Xi having meaniθ, for some θ > 0. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).
  4. Abstract set theory

    https://www.dpmms.cam.ac.uk/~wtg10/settheory.html
    9 Jun 2003: b. 3. for some pair of positive integers a,b}. (vi) X. ... n. , but for a general proof, we must specify some method that always works.
  5. Publications | Department of Pure Mathematics and Mathematical…

    https://www.dpmms.cam.ac.uk/publications?page=187
    30 Jun 2024: JME Hyland. (1979). 753,. 442. SOME MISLEADING ARGUMENTS INVOLVING CONDITIONAL INDEPENDENCE. ... 1979). 41,. 1. (link to publication). Set colourings of graphs. B BOLLOBAS, A THOMASON. –
  6. Publications | Department of Pure Mathematics and Mathematical…

    https://www.dpmms.cam.ac.uk/publications?page=124
    30 Jun 2024: 2006). 10,. 553. Some notes on approximations for the deficit at ruin in the compound Poisson model. ... doi: 10.1086/505480). Mutual information, synergy and some curious phenomena for simple channels.
  7. Mapping class groupsProblem sheet 2 Lent 2021 1. What ...

    https://www.dpmms.cam.ac.uk/study/III/MappingClassGroups/2020-2021/MCGs%20Sheet%202.pdf
    19 Jan 2021: a) Show that there is a surjection π1Sg G, for some g.(b) Show that G is a subgroup of Mod(Sh), for some h. ... a) Prove that TαTβ(α) = β. (b) Prove the braid relation: TαTβTα = TβTαTβ.
  8. Mich. 2012 ANALYSIS II—EXAMPLES 4 PAR 1. Use the ...

    https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2012-2013/12sheet4.pdf
    26 Nov 2012: a) Suppose that D1f exists and is continuous in some open ball around (a, b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and.
  9. Mich. 2013 ANALYSIS II—EXAMPLES 4 PAR 1. (a) Let ...

    https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2013-2014/13sheet4.pdf
    29 Nov 2013: 7. Let f: R2 R and (a,b) R2.(a) Suppose that D1f exists and is continuous in some open ball around (a,b), and that. ... b) Suppose instead that D1f exists and is bounded on some open ball around (a,b), and.
  10. Mapping class groupsProblem sheet 2 Michaelmas 2019 1. What ...

    https://www.dpmms.cam.ac.uk/study/III/MappingClassGroups/2019-2020/MCGs%20Sheet%202.pdf
    12 Nov 2019: 1. 5. Let G be any finite group. (a) Show that there is a surjection π1Sg G, for some g.(b) Show that G is a subgroup of Mod(Sh), for
  11. Mich. 2013 ANALYSIS II—EXAMPLES 1 PAR 1. Which of ...

    https://www.dpmms.cam.ac.uk/study/IB/AnalysisII/2013-2014/13sheet1.pdf
    23 Oct 2013: 4. Let (fn) be a sequence of real-valued continuous functions on a closed, bounded interval [a,b], and. ... f. Prove that there is some subinterval [a,b] of [0, 1] with a < b on which f is bounded.

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