bio | website | gmarks.org |
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location | ||
age | ||
visits | member for | 3 years, 10 months |
seen | yesterday | |
stats | profile views | 528 |
Note. I am less likely to respond to questions posed anonymously.
Oct 19 |
awarded | Necromancer |
Sep 13 |
comment |
What is the expected number of random numbers (generated uniformly) such that their sum of numbers exceeds one?
This question was Problem A3 of the 1958 Putnam Competition (and as such is not research-level mathematics). |
Sep 13 |
awarded | Informed |
Aug 20 |
answered | Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring |
Jul 29 |
answered | Subgroups of finite index of fields |
Jun 25 |
awarded | Revival |
Jun 2 |
awarded | Yearling |
Jul 6 |
comment |
How do you present a non-existence theorem?
This story implicitly answers the problem of the student who shrugs upon hearing the theorem on bounded entire functions. By the time it occurs in a class it's very natural, but presented with it cold, the reaction of any student of normal inquisitiveness would be astonishment and an attempt at a counterexample. A student who isn't excited about celebrated classical results is perhaps best advised to find a field of study more to his liking. Incidentally, a result that has allured many a student into mathematics is, so to speak, a non-existence non-theorem: the continuum hypothesis. |
Jul 6 |
comment |
How do you present a non-existence theorem?
My first reaction on seeing the title of this question was to recall Rota's "Ten Lessons I Wish I Had Been Taught": completely erase the blackboard, begin writing in the upper left corner, .... |
Jun 17 |
awarded | Nice Answer |
Jun 13 |
answered | When is a topological group Hausdorff (separated)? |
Jun 2 |
awarded | Yearling |
Feb 17 |
awarded | Nice Answer |
Aug 27 |
comment |
When a group ring is a local ring
For the general problem, can you see why the augmentation ideal is nilpotent? |
Jul 30 |
comment |
How do you pronounce “Hartshorne”?
The poor devils could follow Kiran Kedlaya's example: mit.edu/~kedlaya/about-my-name.html |
Jun 3 |
awarded | Yearling |
Apr 4 |
comment |
The multiplicative order of 2 modulo primes
Simple but amusing application: that multiplicative order is the minimal number of perfect shuffles required to restore a deck of $p \pm 1$ cards (the $\pm$ depending on which of the two ways of perfectly shuffling we're talking about). |
Mar 28 |
answered | Why is it a good idea to study a ring by studying its modules? |
Mar 14 |
comment |
Group ring and left zero divisor.
You are very kind to credit me, but I doubt I deserve it. I am embarrassed to say that the very interesting paper of Gutan and Kisielewicz had slipped my mind. Gutan and Kisielewicz completely resolve the group algebra reversibility question for the case of torsion groups. They remark that the torsion-free case is connected with the zero divisor problem, in the sense that it will be very difficult to produce a non-reversible group algebra with a torsion-free group, since this will of course resolve the zero divisor problem in the negative. |
Mar 12 |
revised |
Group ring and left zero divisor.
added 7 characters in body |