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 935
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.
142
votes
Examples of theorems misapplied to non-mathematical contexts
A tragic example of this is the case People v. Collins, in which a prosecutor asked a mathematician (as an expert witness) a question of the form, "assuming these events are independent, what is the p …
59
votes
Fundamental problems whose solution seems completely out of reach
A proof of this conjecture of Erdos would certainly turn heads, raise eyebrows, and garner the attention of the Fields Medal committee.
If $\sum_{a \in A} \frac 1a$ diverges and $A\subseteq {\mathbb …
59
votes
Examples of eventual counterexamples
Freeman Dyson observed in my presence that the sequence with initial condition $a_0=3,a_1=0,a_2=2$, and recurrence $a_{n+3}=a_{n+1}+a_{n}$ almost has the property that $n\mid a_n$ if and only if $n$ i …
55
votes
Interesting Calculus Questions/Exercises
The theorems of calculus that you mention are all obviously true, and so a proper bed must be made for their discussion to not seem pedantic. Counterexamples are crucial, of course. Three of my favori …
53
votes
Why linear algebra is fun!(or ?)
An example that my last class loved was lossy image compression using the singular value decomposition.
The SVD says that the transformation corresponding to any real matrix (not necessarily square) …
43
votes
Fundamental problems whose solution seems completely out of reach
This comes up in Waring's Problem, but it is so freakishly simple that it has taken on a life of its own. Let $\{ x \} = x \mod 1 = x-\lfloor x \rfloor$ be the fractional part of $x$.
Say anything ab …
37
votes
Accepted
What are some results in mathematics that have snappy proofs using model theory?
Hilbert's Nullstellensatz is a consequence of the model completeness of algebraically closed fields.
Edit: I don't have a reference, but I can sketch the proof. Suppose you have some polynomial equati …
- 9,756
22
votes
Fundamental problems whose solution seems completely out of reach
Artin's Conjecture: There are infinitely many primes $p$ for which 2 is a primitive root, i.e., 2 generates the multiplicative group of ${\mathbb Z}/p{\mathbb Z}$.
The conjecture is actually a bit mo …
18
votes
How helpful is non-standard analysis?
Freiman conjectured a classification of finite sets $A$ of integers that have
$$\lvert A+A\rvert = 3\lvert A\rvert-3+b$$
for some $0\leq b \leq \lvert A\rvert/3-2$. Renling Jin recently resolved this …
- 9,756
13
votes
Computer algebra errors
In Mathematica 7, the command
Table[DirichletCharacter[4, 2, n], {n, 0, 8}]
should return a list of values of the character with modulus 4 and index 2, evaluated at 0, 1, 2, ..., 8. Instead, it retu …
11
votes
Papers that debunk common myths in the history of mathematics
There have been recent articles in The Mathematical Intelligencer about the well-known rivalry/animosity between Erdős and Selberg. Didier adds this link, pointing to an article of Graham and Spencer …
8
votes
Compilation of strategies to show that some constant is irrational
Don't forget the obvious: If the digits of $\alpha$ in any base are not eventually periodic, then $\alpha$ is irrational.
Mel Nathanson and I (Integers 14 (2014), A40, pp. 1--11) used this to prove th …
- 9,756
8
votes
Which journals publish expository work?
The front page of the Notices (Jan 2011) is an advertisement for the "Bulletin of Mathematical Sciences". The "Aims and Scope" are:
The Bulletin of Mathematical Sciences, a peer-reviewed free acce …
7
votes
nonstandard analysis book recommendation
I loved Goldblatt's book, "Lectures on the Hyperreals".
For a more sophisticated treatment, don't overlook "Nonstandard Analysis: Theory and Applications", edited by Henson (first chapter available t …
7
votes
Computer algebra errors
Just found this in Mathematica 7.0 for Mac OS X x86 (64-bit) (November 11, 2008):
x=Exp[Pi Sqrt[163] ];
N[x-Round[x] ]
N[x-Floor[x] ]
N[x-Ceiling[x] ]
N[x - Round[x], 2]
N[x - Floor[x], 2]
N[x - Ceil …