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Mathematics professor at Cambridge

Jan
15
revised Improving a sequence of 1s and -1s
deleted 6 characters in body
Jan
15
revised Partial sums of multiplicative functions
edited tags
Jan
15
asked Improving a sequence of 1s and -1s
Jan
9
comment Undecidable graph problems?
Yes, I was using it as a synonym for "independent", as the sometimes is used that way.
Jan
8
revised Undecidable graph problems?
Corrected typo
Jan
8
answered Undecidable graph problems?
Jan
8
awarded  Nice Question
Jan
7
comment Partial sums of multiplicative functions
I was fairly sure that partial sums of mu were not better than the square root of n, but I didn't in fact know this argument, so thanks for giving it. I'll think about whether it can be adapted to work for the Liouville function.
Jan
7
asked Partial sums of multiplicative functions
Dec
20
awarded  Nice Answer
Dec
20
answered Pedagogical question about linear algebra
Dec
19
awarded  Good Answer
Dec
17
awarded  Nice Answer
Dec
17
awarded  Nice Answer
Dec
15
awarded  Enthusiast
Dec
8
answered Cardinality of Equivalence Classes of Cauchy Sequences
Dec
6
comment Why is it useful to study vector bundles?
OK, in that case I think one has to turn to more sophisticated answers such as that you can use them to form K groups. If you'll excuse the indirect self-promotion, I'd recommend Burt Totaro's article on algebraic topology in the Princeton Companion to Mathematics, where he has quite a lot to say about bundles and why they are important.
Dec
5
comment What are the most misleading alternate definitions in taught mathematics?
I would almost prefer not even to say what a function is at all. I'd just say that if f is a function from A to B and x is an element of A then f(x) is an element of B. And that's all you need to know. Of course, I'm exaggerating a bit, and this point of view is not sufficient after a while (e.g. how would you decide whether the set of functions from A to B is countable, how would you define function spaces, etc.?) but in some situations this is the most important fact that you need from the basic definition of functions. Of course, one would also give examples, including artificial ones.
Dec
5
answered What are the most misleading alternate definitions in taught mathematics?
Dec
5
comment What are the most misleading alternate definitions in taught mathematics?
I totally agree with this and always tell students to think of "kernel of some homomorphism" as the definition and "closed under conjugation by any element of G" as a fact that can be shown to be equivalent to it.