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28 Apr 2004: I think this is the strongest argument yet for replacement, and it appears to be new--although Adrian Mathias tells me that he once showed that replacement is equivalent to the

4 May 2004: Probability. New: Is Cambridge biased against state-school applicants?. ... Topology. Watch this space. Miscellaneous. This is a talk I gave to the new Cambridge University Society for the Philosophy of Mathematics and Mathematical Sciences.).

22 Sep 2004: 3. B. Hasselblatt, A. Katok, A first course in dynamics. With a panorama of recent devel-opments, Cambridge University Press, New York, 2003.

16 Nov 2004: But see part (ii) of Remark 66 below.)No new phenomena emerge in higher dimensions (n 3) but the cal-culations become a bit more complicated.We make the following remarks

5 May 2004: Why would this phenomenon suddenly stop when you got to the last two (new) grades?

13 Nov 2004: Am as above and define a new sequence B1, B2,. ,

21 Oct 2004: Cesàro’s summation method takes a sequence c0, c1, c2,. and replaces it with a new sequence whose nth term. ... that if the old sequence converges to c so does the new one.(ii) Examine what happens when cj = (1).

20 Sep 2004: 3. ,. of subsets of N, and from those construct a new set A according to the rule. ... So we are not making new ontological commitments by introducing ordered pairs, or being asked to accept any new and unproved mathematical beliefs.

27 Jan 2004: is a new topological obstruction to the existenceof metrics with vanishing topological entropy. ... Thewhole idea is that z will represent the new (n 1)-cohomology class represented byD.

5 Oct 2004: p primepN. (. 1 1ps. )1. n=1. 1. ns. Using this result, we get a new proof of the existence of an infinity of primes. ... We now prove a new version of Euler’s formula. Theorem 81 (Euler-Dirichlet formula) With the notation of this sec-tion,.