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Results tagged with big-list
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user 3308
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.
35
votes
Counterexamples in algebra?
In group theory, Lagrange's Theorem states that the order of a subgroup divides the order of the group, however the converse is false. The usual counterexample given is the alternating group $A_4$ of …
8
votes
Text for an introductory Real Analysis course.
I'm currently taking an introductory course in real analysis at the University of Glasgow. The set text is "Calculus" by Spivak. Totally deserving of its reputation. It's a great read with loads of ex …
6
votes
What is your favorite "strange" function?
A canonical example from elementary real analysis - the Blancmange function. Consider $f$ defined piecewise by
$f(x) = x - [x], \quad \text{if} \quad 0 \leq x- [x] \leq \frac{1}{2}$,
and
$f(x) = 1 …
4
votes
What out-of-print books would you like to see re-printed?
I've heard and read good things about "Mathematics, Form and Function" by Saunders Mac Lane which is sadly out of print. Second hand copies are scarce and prohibitively expensive.