Cat Theory
What an arrow points to in a category
What is the codomain?
This algorithm says that for a given d and n, there are integers q,r with 0<= r < d such that n = dq + r.
What is the division algorithm?
The type of group where objects commute? (NOT commutative)
What is an Abelian group?
The number of elements in the symmetric group on 6 elements.
What is 6! (or 720)?
You can define this type of function on a set to give its points a sense of 'distance.'
What is a metric?
This is a morphism between categories.
What is a functor?
This function calculates the number of integers coprime and less than or equal to the input.
What is the (Euler) phi function?
What is a normal group?
A graph that is connected but without cycles.
What is a tree?
This theorem states that every bounded sequence has a convergent subsequence.
What is Bolzano-Weiresstrass theorem?
This morphism has a two sided inverse.
What is an isomorphism?
6/pi^2
The theorem that says: given G,H groups and f:G->H a homomorphism, then ker f(G) is normal in G.
What is the first isomorphism theorem?
Every vertex in this type of graph is of the same degree.
What is a regular graph?
In this space, every subset is open.
What is a discrete space/topology?
For every object, there is a unique map to this object in a given category.
What is a terminal object?
This technique counts the number of solutions to Diophantine equations?
What is the circle method?
This group has approximately 8.0802 × 10^53 many elements.
What is the monster group?
The number of edges in the complete graph on 4 vertices (give exact number).
What is 6?
This group contains formal sequences of reduced words.
What is a free group?
Given a functor F:A->B and a functor G: A-> C, this is a functor from B->C, extending the functors naturally.
What is a Kan extension?
The parity problem arises in this technique of analytic number theory.
What is sieve theory?
This is the smallest non-solvable group.
What is A_5?
This is a bijection between matrices A with non-negative integer entries and pairs (P,Q) of semistandard Young tableaux of equal shape, whose size equals the sum of the entries of A.
What is the Robinson-Schensted-Knuth correspondence?
This is the most extensive enlargement/compactification of a space.
What is Stone-Cech compactification?