Show:
Jargon
Modular Arithmetic
Groups
Rings
Polynomials
100
A statement that may or may not be true.
What is a conjecture?
100
152 (mod 3).
What is 2?
100
Equivalence class under the relation a ~ b iff a(b**-1) is in the subgroup H.
What is a coset?
100
The n by n matrix rings.
What are noncommutative rings?
100
The remainder when the polynomial x**10 +2 is divided by x - 2.
What is 1026?
200
The symbol for a set that is countably infinite.
What is aleph naught?
200
The solutions of X*X + 6X + 102 = 0 (mod 3).
What are 1 and 2.
200
The oder of the symetric group on 5 elements.
What is 120?
200
A ring without infinitely increasing sequences of ideals.
What is Noetherian.
200
The number of factorizations in Z[x] of x**50 - 6x**2 + 48x - 15.
What is 1.
300
A small theorem that is used in the proof of other theorems.
What is a lemma?
300
The relation between modular addition and modular multiplication.
What is distributive?
300
The theorem that states a relation between a finite group and its subgroups.
What is LaGrange's Theorem?
300
The ring of integres modulo n is a _______ ring.
What is a quotient ring.
300
This Noregian mathematician showed that an equation of degree 5 or higher cannot be solved by attaching roots.
Who is Niels Henrik Abel?
400
Can be used to prove the principle of mathematical induction.
What is the well ordering principle?
400
The moduli n for which 18 = 0 (mod n).
What are 2, 3, 6, 9
400
A surjection between groups G and H that has a trivial kernel.
What is an isomorphism?
400
The ring Z[i].
What are the Gaussian integers?
400
John Nash won the Nobel Prize in mathematics.
What is no? There is no Nobel prize in mathematics.
500
Reasoning from the general to the specific.
What is deductive reasoning?
500
Congruence modulo n.
What is an equivalence relation?
500
Isomorphism classes of abelian groups of order 8.
What is 3?
500
This theorem explians the relations between a ring, its homomorphic images and kernels.
What is the Fundamental Homomorphism Theorem for Rings.
500
Another term expressing that a ring is an integral domain.
What is zero product rule?