Holy Cross Mathematics and Computer Science
MATH 243, Algebraic Structures, Section 3, Fall 2012
Syllabus and Schedule
Examples, Class Notes, Solutions, etc.
Assignments
- Guidelines for problem sets
- Problem Set 1:
Section 1.1/1,5bdfhjln,13,15,17,21,22,30;
Section 1.2/4acegi,5ace,8,9ac,14,22. Due: Friday, September 8.
- Problem Set 2:
Section 1.3/1ac, 2, 7, 10, 11, 13;
Section 1.4/1acf, 2ace, 4, 7, 8. Due: Friday, September 15.
- Discussion 1. Group writeups due Monday, September 18.
- Problem Set 3:
Section 1.5/1dln,2dln,6,7,10;
Section 1.6/1ace,2,3acegi,4,6,8,13,16,23. Due: Friday, September 22.
- Problem Set 4:
Section 1.7/2bdf,5,6,10,11b,d.
Section 2.2/3,8,10,29. Due: Friday, October 6.
- Problem Set 5:
Section 2.2/21,23.
Section 2.3/2bdf,19,20,22,23,24,33.
Due: Friday, October 13.
- Problem Set 6:
Section 2.4/2b,3dhl,4b,7,8,9,10,12,18,19.
Due: Friday, October 20.
- Discussion 2
- Problem Set 7:
Section 2.5/10,16,32,35,36,42,49,50;
Section 2.6/3bd,4bd,5f,6bd.
Due: Friday, October 27.
- Problem Set 8:
Section 2.8/6,8,10,17,22;
Section 3.1/1,4,5,14,19,22,24,26,33.
Due: Friday, November 10.
- Problem Set 9:
Section 3.2/4,6a,11,12,14bd,17,18c,22,23;
Section 3.3/8f,9d,13,14,16a.
Due: Friday, November 17.
Information and Announcements
- Happy Holidays!
- Final Exam review sheet and solutions
for final review problems.
- Review session: Friday, December 8, 10:30 -- ??, in Swords 328.
- Definitions to know:
- Union, intersection, difference of two sets, and complement of a set
- f: A -> B is injective (one-to-one)
- f: A -> B is surjective (onto).
- For f : A -> B, the direct image f(S)
of a subset S of A, and the inverse image
f -1(T) for a subset T of B.
- The composite function f circle g
of g : A -> B and f : B -> C.
- A binary operation on a set A, and the
properties of associativity, commutativity,
what it means for e to be an identity element
and what it means for a to have an inverse.
- What it means for f : A -> A to be a
permutation and what the inverse mapping is.
- An equivalence relation on a set.
- Divisibility in Z (the ``divides'' relation:
a | b).
- The greatest common divisor of two integers
((a,b) = gcd(a,b))
- The congruence mod n relation in the integers and
its properties.
- A group.
- A subgroup H of a group G.
- The cyclic subgroup < a > generated by an element
a in a group G.
- A mapping f : G -> H is a group isomorphism;
G and H are isomorphic groups.
A mapping f : G -> H is a group homomorphism.
- The kernel of a group homomorphism.
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Last modified: December 15, 2006