## 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.

#### 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 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.

#### 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.