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Jargon
Modular Arithmetic
Group Theory
Ring Theory
Polynomials
100
A true statement.
What is a theorem?
100
Number of equivalence classes modulo n.
What is n?
100
A group in which a*b = b*a for all elements a and b.
What is an abelian (or commuatative) group?
100
A commutative ring without proper divisors of zero.
What is an integral domain?
100
This 16th century Italian mathematician published a solution of the cubic equation.
Who is Girolamo Cardano?
200
An example showing a conjecture not to be true.
What is a counter-example
200
The ring of integers modulo a prime.
What is a field?
200
A group generated by the powers of a single element.
What is a cyclic group?
200
A ring in which X*X = X.
What is a Boolean ring?
200
A polynomial ring with coefficients from an integral domain.
What is an integral domain?
300
A result that f.ollows easily from a theorem
What is a corollary?
300
2 X 3 + 7 = [x] (modulo 5).
What is 3?
300
A group of bijective functions.
What is a permutation group?
300
A ring without proper 2-sided ideals.
What is a simple ring?
300
A polynomial that has only constants as favtors.
What is an irreducible polynomial?
400
A relation that is reflexive, symmetric and transitive.
What is an eqivalence relation>
400
Non-zero elements that multiply to give zero.
What are divisors of zero?
400
The kernel of a group homomorphism.
What is a normal subgroup?
400
An ordered complete field.
What are the real numbers?
400
A criterion for the irreducibility of polynomials in Z[x}.
What is the Eisenstein Irreducibility Criterion?
500
Reasoning from the specific to the general.
What is inductive reasoning>
500
The units digit of 1947 raised to the 2009 power.
What is 7?
500
The order of a group with fewer that 100 elements that has subgroups of orders 15 and 30.
What is 60 or 90?
500
The number of factors of a Gaussian prime.
What is 8?
500
The number of factorization of x^100 - 10x +25 in Z[x].
What is more than one.