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ANALYSIS I EXAMPLES 4 G.P. Paternain Lent 2010 Comments ...
https://www.dpmms.cam.ac.uk/~gpp24/aI4.pdf15 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. -
Hypersurfaces and the Weil conjectures
https://www.dpmms.cam.ac.uk/~ajs1005/preprints/bogaz.pdf29 Jan 2010: 20 / 21. Conclusions. The proof is complicated but is mostly rather formal. -
STATISTICS Part IB Example Sheet 3 (of 3) RJS/Lent ...
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example3.pdf24 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 -
STATISTICS Part IB Example Sheet 2 (of 3) RJS/Lent ...
https://www.dpmms.cam.ac.uk/study/IB/Statistics/2009-2010/Example2.pdf8 Feb 2010: Improved No difference WorsePlacebo 18 17 15Half dose 20 10 20Full dose 25 13 12. -
MODULAR FORMS AND ALGEBRAIC K-THEORY A. J. SCHOLL In ...
https://www.dpmms.cam.ac.uk/~ajs1005/preprints/gen.pdf29 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. -
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.pdf19 Oct 2010: 2. Between0 and 10 there are four primes. The same is true between10 and 20. -
EXAMPLE SHEET 3 (LECTURES 13–18) GALOIS THEORY MICHAELMAS 2009 ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2009-2010/ex3.pdf28 Mar 2010: See Example Sheet 2, Problem 10.). 20. (i) Let p be prime. -
PART II REPRESENTATION THEORYSHEET 3 Unless otherwise stated, all ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2009-2010/repex3.pdf30 Mar 2010: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5. -
Example Sheet 3. Lectures 13–18, Galois Theory Michaelmas 2010 ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2010-2011/2010_Galois_Ex3.pdf9 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 -
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.pdf9 Nov 2010: Evaluate 1000! (mod 10249). 6. Without using a calculator, evaluate 20!2120 (mod 23) and 1710000 (mod 30).
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