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26 Nov 2003: 1. ,A. 2. ,. of subsets of N, define a new set A by the condition that n belongs to A if and only if n does not belong to A.

19 Dec 2003: 1. Reading to complement course material. 1. P. Petersen, Riemannian Geometry, Graduate Texts in Mathematics, Springer-Verlag,New York, 1998.

4 Mar 2003: symmetric rather than alternating. Lemma 5.2 does not apply. 6 A new example. ... Koblitz, Introduction to elliptic curves and modular forms, GTM 97.Springer-Verlag, New York, 1993.

26 Jun 2003: M. Pitts. New foundations for fix-point computations: FIX-hyperdoctrines and the FIX-logic. ... 20] R. Paterson. A new notation for arrows. In Proceed-ings of the International Conference on Functional Pro-gramming.

19 May 2003: If you invent a new proof, first check itagainst Example 4.12 and then get your supervisor to check it.

26 Mar 2003: Suppose some definition leads to a new and thriving branch of mathematics. ... Such results then form a new body of statements, one layer deeper than the original axioms.

8 May 2003: Each time we look at a new row or column, we have chosen only finitely many of the terms in it, so we can make the rest 1 (for a row) ... way that each time one arrives at a new object, one has not made one's task impossible.

20 Jan 2003: Department of Pure Mathematics and Mathematical StatisticsUniversity of Cambridge. FURTHER ANALYSIS. Notes Lent 2003. T. K. Carne.t.k.carne@dpmms.cam.ac.uk. c Copyright. Not for distribution outside Cambridge University. This PDF file should be

10 Sep 2003: In Appendix C, we present a new proof of Taimanov’s results usingGeometric Measure Theory. ... Ginzburg, New generalizations of Poincaré’s geometric theorem, Funct. Anal. Appl. 21 (1989).

21 Aug 2003: 3Lava now uses a modified version of Haskell with ‘observable sharing’: allowing new name. ... 28] R. Paterson. A new notation for arrows. In Proceedings of the International Conference onFunctional Programming.

2 Aug 2003: Two millennia later the new theory of mechanics and the new methodof mechanics enabled mathematicians to write down a model for a vibratingstring. ... rise to new setof questions and answers but for the moment let us take the most obviousinterpretation

9 Jun 2003: If it were, then the diagonal argument would produce a new definable real number - contradiction.). ... In other words, the axioms give us rules that allow us to create new vectors from old ones.

5 Nov 2003: definitions. A binary operation defined on a set A is something you can put in between two elements of A to make a new element of A.

19 Feb 2003: Each of these characterizations gives a new insight into geom-etry and dynamics. ... In fact, Theorem 1.10 gives a new, more geometric way of looking at thisquantity (cf.

3 Sep 2003: So if we ever want to define a new number by one of these arguments, we can. ... Doesn't that give a new, and defined, number? M. I told you we were getting into murky waters.

11 Mar 2003: THE ASYMPTOTIC MASLOV INDEXAND ITS APPLICATIONS. GONZALO CONTRERAS, JEAN-MARC GAMBAUDO,RENATO ITURRIAGA, AND GABRIEL P. PATERNAIN. Abstract. Let N be a 2n-dimensional manifold equipped with a symplecticstructure ω and Λ(N) be the Lagrangian