Topology
How many holes does a pair of pants have?
2 holes
What is the factorization of x^2-1?
(x+1)(x-1)
What came first? The intermediate value theorem or the mean value theorem?
The intermediate value theorem.
What does NFA stand for?
Non-deterministic finite automata.
Who is the president of the Math Club?
Adam Muhlaney
How many holes (and of what dimension) does a sphere have?
One 2-dimensional hole.
Groups embody what concept?
Symmetry
Are the real numbers closed or open?
Both
Is the language composed of odd-length strings regular?
Yes.
Cycle between two states, the latter accepts any character.
I don't know.
The klein bottle is the gluing together of what surface with itself?
The mobius band.
CRT stands for what?
Chinese Remainder Theorem
If a subsequence of a sequence converges, does the sequence also converge?
No
What form can every context-free grammar be transformed into?
Chomsky Normal Form
Who was the first to prove that some concepts in math are unprovable?
Kurt Godel
What set must be in every topology?
The empty set.
What is the sum of all positive integers?
-1/12
Is the function f(x)=x^2 uniformly continuous?
No
What is unique about a turing-decidable language compared to a turing-recognizable one?
A turing-decidable language has a turing machine that always halts.
Turing-recognizable languages permit infinite loops.
Where is Jack Curtis?
Ecuador
Define continuity topologically.
For topological spaces X and Y, f: X->Y is continuous if for each open subset V of Y, f^(-1)(V) is an open subset of X.
If p(x) is irreducible over some ring F[x], and a is a zero of p(x) in some extension, what is F(a) isomorphic to?
F[x]/<p(x)>
What is the measure of the rationals?
0
Is the graph isomorphism problem in P or NP?
Currently no algorithm exists; we don't know.
What argument was the first Math Club Swordfight over?
Condiments used on chicken tenders.