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  2. Analysis 1 (2008–09) Example Sheet 4 of 4 1. ...

    https://www.dpmms.cam.ac.uk/study/IA/AnalysisI/2008-2009/examples-An-09-4.pdf
    17 Feb 2009: Show thatIn =. 1/20. f (t/n) dt and hence that. |In| < 1/9n2. ... 7. Let In = π/20. cosn x. Prove thatnIn = (n 1)In2 , and hence 2n2n1 I2n1/I2n 1.
  3. 8 Dec 2009: Invent. Math., 20:249–266, 1973. [3] P. Deligne. Cohomologie étale. Lecture Notes in Mathematics, Vol.
  4. STATISTICS Part IB Example Sheet 2 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2008-2009/Example2.pdf
    4 Mar 2009: Improved No difference WorsePlacebo 18 17 15Half dose 20 10 20Full dose 25 13 12.
  5. STATISTICS Part IB Example Sheet 3 (of 3) RJS/Lent ...

    https://www.dpmms.cam.ac.uk/study/IB/Statistics/2008-2009/Example3.pdf
    4 Mar 2009: 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
  6. Numbers and Sets (2009–10) Example Sheet 3 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2009-2010/examples-NS-09-3.pdf
    17 Nov 2009: 7. Evaluate 20!2120 (mod 23) and 1710000 (mod 31). 8. By considering the n fractions 1n ,2n ,. ,. nn , or otherwise, prove that n =. d|n ϕ(d).
  7. Numbers and Sets (2009–10) Example Sheet 1 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2009-2010/examples-NS-09-1.pdf
    10 Oct 2009: 3. Between 0 and 10 there are four primes. The same is true between 10 and 20.
  8. Algebraic Geometry, Part II, Example Sheet 3,2009 Assume throughout…

    https://www.dpmms.cam.ac.uk/study/II/AlgebraicGeometry/2009-2010/ag2009_ex3.pdf
    20 Nov 2009: 20 is smooth ifchar(k) 6= 2, 3. Find the degree and ramification degrees for (i) the projectionφ = (X0 : X1) : V P1 (ii) theprojectionφ = (X0 : X2) : V P1.
  9. Michaelmas Term 2009 T.A. Fisher Linear Algebra: Example Sheet ...

    https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2009-2010/lin_alg-09-4.pdf
    27 Nov 2009: What is themaximum value of a1a2 a2a3 an1an ana1? 20. Let A be a 2n 2n alternating matrix over a field F.
  10. Michaelmas Term 2009 T.A. Fisher Linear Algebra: Example Sheet ...

    https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2009-2010/lin_alg-09-2.pdf
    30 Oct 2009: Which over R? 8. Find the eigenvalues and give bases for the eigenspaces of the following complex matrices: 1 1 00 3 20 1 0.
  11. How to Write a Part III Essay T. W. ...

    https://www.dpmms.cam.ac.uk/~twk/Essay.pdf
    11 Nov 2009: Of course this may be inaccurate by 10% or 20% butnobody cares about the exact length of your essay, your object is to providea rough guide for your own use. ... Sometimes first thoughts turn out to be better thansecond. 20. 5.4 What to do when you are

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