Math 327, Introduction to Mathematical Thinking and Discrete Structures, Spring 2009
Week One, January 19 - 23, 2009
Monday: Martin Luther King, Jr. Day, holiday, January 19.
- Wednesday: §Sets. The empty set, "element of," "subset of." §2.1
- Friday: Intersection, union, difference of sets (also complement),
symmetric difference, power set, ordered pairs. §2.2
- Homework 1 due by class time on January 30.
Week Two, January 26 - 30, 2009
- grading percentages MidI 25%; MidII 25%; HW 20%; Final 30%.
- Monday: § 2.2, continued. Demorgan's law. Disjoint sets.
Algebraic properties like two distributive laws. Examples.
- Wednesday: Relations (binary). §2.3
Is a relation more than its graph? Wikipedia thinks it knows.
- Friday: Equivalence relations. §2.4
- Homework 2 due by class time on February 6.
Week Three, February 2 - 6, 2009
- Monday: Equivalence relations and Partitions.
- Wednesday: Examples, problems.
- Friday: Partial orders, Hasse diagrams. §2.5
Week Four, February 9 - 13, 2009
- Monday: least upper bounds, maximum and maximal.
lexicographic orders
§2.5
- Homework 3 due February 18.
- Wednesday: Definition of a function as a
special kind of relation. One to one. Onto. §3.1
- Friday: Cardinality. §3.3
Week Five, February 16 - 20, 2009
- Monday: Composition of Functions. Inverse of a function. §3.2
- Wednesday: The division algorithm. Definition of divisibility.
- Review problems
- Friday: Review
Week Six, February 23 - 27, 2009
- Monday: February 23, Midterm I
- Wednesday: Divisibility on the natural numbers is a partial order
§4.2
- Friday: GCD. Euclidean Algorithm. §4.2
- Homework 4 now due March 9.
Week Seven, March 2 - 6, 2009
- Monday: Prime Factorization. §4.3
- Wednesday: Prime Factorization, continued.
- Friday: Solving linear Congruence equations. §4.4
Week Eight, March 9 - 13, 2009
- Monday: → Solving linear Congruence equations, continued.
- Homework 5 due March 23.
- Wednesday: Chinese Remainder Theorem §4.5
- Friday: Chinese Remainder Theorem, continued. Divisibility tests.
Check digits.
- Reminder: I do not accept late homework. If you can't attend class,
you can scan it and email it in, or slide it under by office door.
Also, I drop the two lowest scores, and will create makeup assignments
for multi-week emergences.
March 16 - 20: Spring Break , 2009
Week Nine, March 23 - 27, 2009
- Monday: Induction. § 5.1
- Homework 6 due March 30.
- Wednesday: Recursively Defined Sequences § 5.2
- Friday: Fibonacci numbers.
- We are skipping § 5.4
Week Ten, March 30 - April 3, 2009
- Monday: homogeneous Linear Recurrence Relations, § 5.3
- Wednesday: Combinatorics using reccurence relations
Problem 22 on page 175. Nonhomogeneous Linear Recurrence Relations
- Homework 7 due April 8.
- Friday: Recurrence Relations, continued.
Week Eleven, April 6 - 10 , 2009
- Monday: Inclusion/Exclusion,
Multipliction for independent choices. §6.1-2
- Wednesday: The pigeonhole principal. §6.3
- Homework 8 due April 13 (short assignment, due in 5 days).
- Monday: Permutations and Combinations. § 7.1.
Week Twelve, April 13 - 17 , 2009
Week Thirteen, April 20 - 24 , 2009
- Monday: The binomial thoerem. § 7.7.
- Wednesday: Semigroups (Not in book.).
- Friday: Semigroup isomorphism. Graphs and the sets that define them. § 9.1-2
- Homework 10 due May 1.
Week Fourteen, April 27 - May 1 , 2009
- Monday: Graph isomorphism § 9.3.
- Wednesday: Graph coloring, § 13.2.
- Friday: The five color theorem.
Week Fifteen, May 4 - 8 , 2009
Finals Week May 11-16, 2009
The registrar counts spring break as a week when it determines that
this is a sixteen week semester. It does not count spring break
as a week when it determines the last day to withdraw without
approval of college dean (end of twelfth week). This is why
our sixteen week semester ends on week fifteen.
Math 327, Spring 2009