bio | website | |
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location | ||
age | ||
visits | member for | 3 years, 8 months |
seen | Apr 14 at 0:14 | |
stats | profile views | 164 |
Feb 13 |
awarded | Yearling |
Jan 12 |
revised |
About injective hull
now typed in TeX. |
Aug 17 |
awarded | Editor |
Aug 17 |
revised |
Why are noetherian rings such natural objects in algebraic geometry?
edited body |
Aug 16 |
answered | Why are noetherian rings such natural objects in algebraic geometry? |
Jul 1 |
answered | Textbook recommendations for undergraduate proof-writing class |
May 30 |
comment |
What has happened to Lang's Files and other political texts?
@Emerton - Maybe. I had a friend who was writing a thesis with Lang and got fed up with either Lang or his thesis, and told Lang off with some very choice words. Half the department was outraged, the other half cheered. Lang was not universally loved, I guess. Might have influenced Yale's decision. |
May 30 |
comment |
Old books still used
@Andreas - I have the English translation of the seventh edition with me. It has a condensed treatment of elimination. I use this book often as a reference, and have a couple of earlier editions. I especially like the section on factorization in a finite number of steps in the second edition, which is missing from later ones. van der Waerden presents a proof due to Kronecker for the case of polynomials with rational coefficients. From what he says in the preface to the second edition, I believe this is a concession to intuitionism. |
Aug 22 |
comment |
Is primary decomposition still important?
Very nicely done. I tried to give more than plus one, but the site is too smart. I would've given several more if I could. |
Mar 1 |
awarded | Necromancer |
Feb 29 |
answered | Do you find your students are less competent in basic algebra and arithmetic, and, if so, do you believe that this is due to overuse of calculators at an early level? |
Feb 29 |
awarded | Commentator |
Feb 29 |
comment |
Do names given to math concepts have a role in common mistakes by students?
Or my favorite from Lang's "Algebra": "a ring $R$ is said to be simple if it is semi-simple and ... ." |
Feb 10 |
comment |
minimal divisible group
Your $E$ is what would be called the divisible hull (or envelope) of $A$. Essentially by definition, $E$ is essential over $A$. This is the result of several equivalent conditions that are summarized in Section 4.2 of Lambek's "Lectures on Rings and Modules." For abelian groups, or modules over a PID, injective is equivalent to divisible. |
Jan 3 |
comment |
Books you would like to see translated into English.
I don't know how easy the French is in EGA or SGA, but the French in Grothendieck's "Sur quelques points d'algebre homologique", the Tohoku paper, is terribly opaque. I read French well, but that paper was an exceptional challenge. I would welcome an English translation. |
Jan 2 |
answered | Depressed graduate student. |
Jan 1 |
comment |
Demonstrating that rigour is important
If one wants to carry this to the extreme, any divergent series with the property that the n-th term goes to zero will converge on a calculator as the terms will eventually fall below the underflow value for the calculator, and hence be considered to be zero. |
Nov 9 |
comment |
Using slides in math classroom
In lower level math courses at a US university, most students do not want to be in the course to begin with. Providing slides, or even lecture notes, on-line would make it very tempting for them not to come to class. This is a consequence that must be weighed in any decision to use slides. If a student is physically present, you still have an opportunity to reach them. |
Nov 2 |
comment |
Does a notion of convex graph make sense?
This is an intriguing idea. I was wondering if non-planarity of the graph could be a complication. I could be wrong, but it seems that a lot depends on the number of edges, or, the length, of paths between vertices. If so, would it be of benefit to phrase the axioms or definitions in terms of this? |
Sep 14 |
comment |
Exact Value of a Series
The first thing that came to mind is that you might need Cesaro summability or something (cf. exercise 12-37 in Apostol, Mathematical Analysis), but I'm not sure that gets you where you where you want to go. It seems reasonable that this might be possible. Have you tried Hardy's Divergent Series? There may be a simple answer (one way or the other), but I'm not seeing it. |