Math 327, Discrete Mathematics, Fall 2007

Professor Terry Loring, Department of Mathematics and Statistics,

Jump to current week.

• There are many deadlines regarding grading and registration which are listed on the home page of the Office of the Registrar
• List of topics.
• Text: Goodaire and Parmenter, Discrete Mathematics with Graph Theory, third edition, ISBN 0131679953.
• I'll send eMail via your UNM accounts. Check this several times per week, or turn on forwarding to an account you frequent: How To #504 - Forward Your UNM Electronic Mail.
• MidI 25%; MidII 25%; HW 20%; Final 30%.

Week One, August 20-24, 2007

• Monday: Sets. §2.1.
• Wednesday: Intersection, union, symmetric difference, power set, ordered pairs. §2.2.
• Homework 1, due in class wednesday August 29. Please staple together and use a cover page.
• Friday: §2.2, continued.

Week Two, August 27-31, 2007

• Monday: Relations (binary). §2.3.
• Wednesday: Equivalence relations. §2.4.
• Homework 2, due in class Friday September 7.
• Friday: § 2.4, continued.

Week Three, September 3-7, 2007

• Monday: Labor Day Holiday.
• Wednesday: Partial orders and Hasse Diagrams § 2.5
• Friday: § 2.5, continued.

Week Four, September 10-14, 2007

• Homework 3, Problem 5 corrected,Sept 13 due in class Monday September 17.
• Monday: Functions, one-to-one, onto, inverse. § 3.1.
• Wednesday: Composition, inverse, cardinality. § 3.2.
• Friday: Cardinality. § 3.3.

Week Five, September 17-21, 2007

• Monday: The division algorithm. § 4.1.
• Wednesday: GCD and the Euclidean Algorithm.§ 4.2
• Review I. At least start these problems before Friday. Look over all the answer keys.
• Friday: Review

Week Six, September 24-28, 2007

• Monday, September 24: Midterm I
• Wednesday: Prime Factorization, existence and uniqueness. § 4.3
• Homework 4, due in class Wednesday October 3.
• Friday: § 4.3, continued.
• Friday: last day to drop a course without a grade (UNM calander)

Week Seven, October 1-5, 2007

• Monday: Congruence. § 4.4.
• Wednesday: § 4.4, continued.
• Friday: § 4.4, continued.
• Homework 5, due in class Monday October 15.

Week Eight, October 8-12, 2007

• Monday: Applications of Congruence. § 4.5.
• Wednesday: Induction. § 5.1.
• Break, October 11-12. (UNM calander)

Week Nine, October 15-19, 2007

• Monday: § 5.1, continued.
• Homework 6, due in class Monday October 22.
• Wednesday: Recursively Defined Sequences § 5.2
• Friday: homogeneous Linear Recurrence Relations § 5.3
• We are skipping § 5.4

Week Ten, October 22-26, 2007

• Monday: Combinatorics using reccurence relations: Problem 22 on page 175. Nonhomogeneous Linear Recurrence Relations
• Wednesday: Inclusion/Exclusion, §6.1,
• Homework 7 revised Friday AM due in class Wednesday October 31.
• Friday: Multipliction for independent choices. § 6.2

Week Eleven, October 29 - November 2, 2007

• Monday: Combinatorics examples.
• Wednesday: Combinatorics examples.
• Review II.
• Friday: Review

Week Twelve, November 5-9, 2007

• Monday November 5: Midterm II
• Wednesday: The pigeonhole principal. §6.3
• Friday: Permutations and Combinations. § 7.1, 7.2.
• Friday: Last day to withdraw without approval of college dean (UNM calander)
• Homework 8 due Friday November 16.

Week Thirteen, November 12-16, 2007

• Monday: § Probability. § 7.3,7.4.
• Wednesday: Semigroups. See especially the next link.
• semi.pdf
• SemiGroupListJava.html
• SemiGroupListJava.txt
• allOrder2.txt
• Friday: Semigroup isomorphism.

Week Fourteen, November 19-23, 2007

• Monday: § Examples.
• Wednesday: § 9.2-3. Graph definition and isomorphism
• Homework 9 (prob 4 revised, 11/27) due Wednesday November 28.
• Thanksgiving Break, November 22-25 (UNM calander)

suggested problems

Week Fifteen, November 26-30, 2007

• Monday: § 9.2-3. bipartite, degree sequence, connected, complete graphs.
• Wednesday: § 10.1. Euler Circuits.
• How to find Euler Cirtuits.
• Friday: Error detection in Decimal numbers, esp. Verhoeff's Decimal Error Detection
• The Laws of Cryptography with Java Code See pages 48-57 (Acrobat may list these as pages 62-71).
• Homework 10 due Friday December 7. This one I will not accept at all late. It is due at the start of class. We will go over it in class.
• Graph isomorphism examples.

Week Sixteen, December 3-7 , 2007

• Review.
• Review III.
• Friday: Last day to withdraw with approval of college dean (UNM registrar)
• Mathematical Behavior of Pascal's Triangle This might make a fun break from reviewing. Explains why a mod-2 Pascal's triangle can be built by copying sub triangles and padding with zeros.

Finals Week, December 10-15

• Fall 2007 exam shedule
• Friday, December 14, 3:00-5:00 p.m. Final exam.