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Mathematics professor at Cambridge
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. |
Dec
5 |
answered | Why is it useful to study vector bundles? |
Dec
1 |
comment |
k-pseudorandom measures
The problem there is that the sets we are looking at are so sparse that the U^k norm of any function is dominated by the degenerate cubes and so tells you nothing. Also, the control of one norm by another is often OK in the dense case but breaks down if you are sitting inside a sparse random set (because the constant depends on the sparsity of the random set). |
Nov
30 |
awarded | Nice Answer |
Nov
29 |
comment |
k-pseudorandom measures
It's not true that we removed the correlation condition -- that question is still open. What we did was look at functions bounded by random as opposed to pseudorandom measures, and we obtained best possible results by considering a specially constructued norm rather than the $U^k$ norm. The paper will be posted on the arXiv soon. |
Nov
29 |
awarded | Nice Answer |
Nov
29 |
revised |
Typical value of totient function
added 468 characters in body |
Nov
28 |
awarded | Popular Question |
Nov
28 |
awarded | Self-Learner |
Nov
28 |
answered | Typical value of totient function |
Nov
28 |
awarded | Editor |
Nov
28 |
answered | What is the first interesting theorem in (insert subject here)? |
Nov
28 |
asked | Typical value of totient function |
Nov
28 |
revised |
Intuitive explanation to Probability question
added 42 characters in body |
Nov
28 |
answered | Intuitive explanation to Probability question |
Nov
26 |
answered | A random walk matrix has eigenvalue 1 with multiplicty 1 - why? |
Nov
23 |
answered | Finding the new zeros of a “perturbed” polynomial |
Nov
23 |
awarded | Nice Answer |