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  2. ANALYSIS I EXAMPLES 4 G.P. Paternain Lent 2010 Comments ...

    https://www.dpmms.cam.ac.uk/~gpp24/aI4.pdf
    15 Feb 2010: dx log n for n N. Show that In =. 1/20. f (t/n) dt and hence that|In| < 1/9n2. By considering. ... 7. Let In = π/20. cosn x. Prove that nIn = (n 1)In2, and hence 2n2n1 I2n1/I2n 1.
  3. Hypersurfaces and the Weil conjectures

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/bogaz.pdf
    29 Jan 2010: 20 / 21. Conclusions. The proof is complicated but is mostly rather formal.
  4. STATISTICS Part IB Example Sheet 3 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example3.pdf
    24 Feb 2010: α (deg) 5 10 15 20 25 30 35 40 45sin 2α 0.1736 0.3420 0.5 0.6428 0.7660 0.8660 0.9397 0.9848 1range (m) 4860
  5. STATISTICS Part IB Example Sheet 2 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example2.pdf
    8 Feb 2010: Improved No difference WorsePlacebo 18 17 15Half dose 20 10 20Full dose 25 13 12.
  6. MODULAR FORMS AND ALGEBRAIC K-THEORY A. J. SCHOLL In ...

    https://www.dpmms.cam.ac.uk/~ajs1005/preprints/gen.pdf
    29 Jan 2010: Soulé. 20–1–1985[8] P. Deligne, M. Rapoport, Les schémas de modules des courbes elliptiques. ... In [18].[20] A. J. Scholl, The -adic representations attached to a certain noncongruence.
  7. Numbers and Sets (2010–11) Example Sheet 1 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2010-2011/examples-NS-10-1.pdf
    19 Oct 2010: 2. Between0 and 10 there are four primes. The same is true between10 and 20.
  8. EXAMPLE SHEET 3 (LECTURES 13–18) GALOIS THEORY MICHAELMAS 2009 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2009-2010/ex3.pdf
    28 Mar 2010: See Example Sheet 2, Problem 10.). 20. (i) Let p be prime.
  9. PART II REPRESENTATION THEORYSHEET 3 Unless otherwise stated, all ...

    https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2009-2010/repex3.pdf
    30 Mar 2010: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5.
  10. Example Sheet 3. Lectures 13–18, Galois Theory Michaelmas 2010 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2010-2011/2010_Galois_Ex3.pdf
    9 Nov 2010: group. 3.13. Use (1) the structure of (Z/(m)) (Problem 2.20), (2) the Dirichlet’s theorem onprimes in arithmetic progressions, stating that if a and b are coprime positive ... Write cos(2π/17) explicitly in terms of radicals. 3.20. (i) Let G be a
  11. Numbers and Sets (2010–11) Example Sheet 3 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2010-2011/examples-NS-10-3.pdf
    9 Nov 2010: Evaluate 1000! (mod 10249). 6. Without using a calculator, evaluate 20!2120 (mod 23) and 1710000 (mod 30).

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