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14 Oct 2014: 2. Between 0 and 10 there are four primes. Another example of two consecutive multiples often, between which there are four primes, is 10 and 20.

11 Nov 2014: Evaluate 1000! (mod 10249). 7. Without using a calculator, evaluate 20!2120 (mod 23) and 1710000 (mod 30).

27 Oct 2014: 5. Find the eigenvalues and give bases for the eigenspaces of the following complex matrices: 1 1 00 3 20 1 0.

12 Feb 2014: 20 and σ. 21 (> σ. 20). Show. that this test is a size α uniformly most powerful test for testing H′0 : σ2 σ20 against. ... Improved No difference WorsePlacebo 18 17 15. Half dose 20 10 20Full dose 25 13 12.

28 Feb 2014: 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

29 Apr 2014: γV θ = µ λS0, (1.20). which is solved by takingθ = γ1V 1(µ λS0). ... If one unit of time corresponds to one year, then typical values for α would be of theorder of 10% 30% and for σ of the order of 20% 80%.

20 Oct 2014: Show that|HomF (L,E)| 1 for every extension F E. (20) Let K L be a finite field extension inside C.

15 Jan 2014: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5.

20 Oct 2014: 20 W. T. GOWERS. From this it follows that there exist vertices x′ X and y′ Y such that.

19 Dec 2014: M[H] such that M[H] |= (20 = λ and there is a Suslin tree).(iv) Suppose that M |= (P is a c.c.c. ... MM requires a large cardinal axiomfor its consistency. 20 Optional. Normal Functions and Mahlo Cardinals.