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8 Jan 2015: Read about Nick's new book Escape from Tibet', available from March 29, 2012..

23 Feb 2015: If the answer is ‘yes’ this can only be because P ′ gets into a new,artificial loop of the kind not experienced by P.

15 Oct 2015: Show that G is a tree if and only if theaddition of any edge to G produces exactly 1 new cycle.

8 Dec 2015: jk by deforming the embedding ei does not create new intersection points.

7 Mar 2015: Itherefore find a new pair of primes and announce that I shall be using the Rabin code with modulusN′ > N. ... Alice uses the Elgamal signature scheme to sign a sequence of messages, incrementing the value ofk by 2 for each new message.

29 Nov 2015: I’d never thought of coding tricks as many-onereductions (that is Chiodo’s idea) but one learns something new every day.

22 Jan 2015: Find an injective function h on (0,) such that, writ-ing ψ = h(θ), the maximum likelihood estimator ψ̂ of the new parameter ψ isunbiased.

23 Dec 2015: 3. The action of diffeomorphisms. If f : M M is a diffeomorphism and ξ isa stable framing, we obtain a new stable framing fξ by. ... Similarly, if ζ = (E,b) is a stable almost complex structure, we obtain a new onefζ = (fE,fb) where fb is given by.

25 Feb 2015: A new code is formed by adding a single parity check bit to the end of the Hamming code, showthat this is linear and repeat the exercise above for this code.

19 Feb 2015: A new code is formed by adding a single parity check bit to the end of the Hamming code, showthat this is linear and repeat the exercise above for this code.

12 Feb 2015: fn gn = hn. Use unique factorisation in C[X] to construct a new solution tothis equation involving polynomials of smaller degree.

21 Oct 2015: Illinois J. Math 46, 885-891 2002. [Gor68] D. Gorenstein. Finite Groups Harper and Row, New York, 1968.

9 Jan 2015: Finally, we fix an isomorphism ι : Ql = C. For each irreducible algebraic representation ξ of the semi-simplegroup G, we can define a new lisse sheaf F0,ξ on U0, which

2 Jun 2015: 1)2, respectively 1, 3. , ( 3. )2. We. then eliminate t, and homogenise (introducing a new variable s) to give. ... Silverman. and G. Stevens (eds.), Springer-Verlag, New York, (1997), 447–461. University of Cambridge, DPMMS, Centre for Mathematical

15 Sep 2015: In particular, we obtain a new recursive proof of the well-known factthat every n-ary quadratic form over Qp is isotropic when n 5. ... We note that our general argument shows in particular thatquadratic forms in n 5 variables over Qp are always isotropic

7 Feb 2015: And for a bonus point, formalise “x is the doublecousin of y”.1 Hint: might need new variables! ... The new clause isthen:. if t is a formula of the form 2s and v is a state then SAT(v,t) = 1iff for all states v′ such that v′ R

22 Oct 2015: on the tape that is marked with "end" the following isa heuristic description of what the new Turing Machine does:. ... iv) in the new data, rend the original position and instruction, con-tinue computation.

10 Jul 2015: If Q is a quasi-ordered set or class, construct a new QO Q. ... Define a new labelling l1 : E Ñ R : x ÞÑ 1lpxq and let χ1 xPE 1l1pxq.

29 Nov 2015: Karatuba’s algorithm takes a pair ofn-bit integers and views them as two-digitvalues where each new digit hasn/2 bits. ... are just fromthe TMs alphabet (I will useai as such a symbol) and a new symbol$ that I willuse as a delimiter.

11 Sep 2015: Lemma 4.2 shows that thereexists ξ S satisfying the condition on line 14, and that after modifying αk online 15, the new αk satisfies (6) with j = k. ... We also found 10 new examples of ellipticcurves E/Q with E(Q) = Z/2ZZ/8ZZ3, including one where