Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with big-list
Search options answers only
not deleted
user 3272
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
17
votes
Different ways of thinking about the derivative
Algebraic: a derivation on a ring $R$ is an additive map $R \rightarrow R$ that satisfies the product rule (with suitable generalizations allowing modules, etc.)
This is related to the Symbolic way o …
22
votes
Notable mathematics during World War II
Eilenberg and Mac Lane's papers on category theory started appearing: "Natural Isomorphisms in Group Theory" in the Proc. National Acad. Sci. USA in 1942 and "General Theory of Natural Equivalences" i …
35
votes
Fields of mathematics that were dormant for a long time until someone revitalized them
Modular forms were actively studied by number theorists Hecke and Siegel in the 1930s, but it was not widely appreciated. Around the same time Hardy, in a series of lectures on Ramanujan's work deliv …
32
votes
What are the worst notations, in your opinion?
Writing a finite field of size $q$ as $\mathrm{GF}(q)$ instead of as $\mathbf{F}_q$ always rubbed me the wrong way. I know where it comes from (Galois Field), and I think it is still widely used in c …
29
votes
Demonstrating that rigour is important
Nonexistence theorems can not be demonstrated with numerical evidence. For example, the impossibility of classical geometric construction problems (trisecting the angle, doubling the cube) could only …
17
votes
Special rational numbers that appear as answers to natural questions
For a prime number $p$, the number of nonisomorphic groups of order $p^n$ is $p^{(2/27)n^3 + O(n^{8/3})}$. I was surprised when I first saw this formula with leading coefficient $2/27$ in the exponent …
33
votes
Examples of common false beliefs in mathematics
After learning that the Witt vectors of a finite field of size $p^n$ is the ring of integers of the unramified extension of ${\mathbf Q}_p$ of degree $n$, I think lots of people then think that the Wi …
11
votes
Magic trick based on deep mathematics
Here is a card trick from Edwin Connell's Elements of Abstract and Linear Algebra, page 18 (it can be found online). I always do this trick to my undergraduate number theory class in the first minute …
9
votes
Ways to prove the fundamental theorem of algebra
Here is the proof by Pukhlikov (1997) at
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mp&paperid=6&option_lang=eng
which Ilya mentioned as being only in Russian so far. What I present …
12
votes
Applications of Group Theory Which Motivate Theoretical Questions?
I had the same question before I taught a course that was largely group theory.
Here is the webpage I created to address the issue:
http://www.math.uconn.edu/~kconrad/math216/whygroups.html
15
votes
What would you want to see at the Museum of Mathematics?
There are many interesting films at the site http://www.etudes.ru/ (not in English): curves of constant width, Pick's theorem, geometry of polyhedra, an infinite staircase with the harmonic series, me …
6
votes
What well known results with countability assumptions can be naturally extended to uncountab...
Here are some examples from algebra where finiteness assumptions can be removed. In the first two, the statement of the more general result is unchanged, but the third result has to be expressed in a …
14
votes
Algebraic number theory and applications to properties of the natural numbers.
The truncated exponential polynomial $1 + x + x^2/2! + ... + x^n/n!$ is irreducible for all positive integers $n$. This result is due to Schur and the proof uses prime ideal factorizations in the numb …
13
votes
Counterexamples in algebra?
If $f$ and $g$ are relatively prime in ${\mathbf Q}[X]$ then the mapping ${\mathbf Q}[X]/(fg) \rightarrow {\mathbf Q}[X]/(f) \times {\mathbf Q}[X]/(g)$ given by $h \bmod fg \mapsto (h \bmod f, h \bmod …
15
votes
Ways to prove the fundamental theorem of algebra
Here is a translation into English of a second "real" proof from the journal Ilya mentioned in his answer. This proof is due to Petya Pushkar', in the 1997 paper titled О некоторых топологических док …