Concrete Mathematics

Instructor:	Dr. André Kündgen	akundgen@csusm.edu
Lecture :	TR 17:30-18:45	308 Science Hall 2
Office hours:	TR 15:00-16:30	339 Science Hall 2

Presentations

• 11/11, Gina Sanders: Perfect codes
• 11/16, Hector Contreras: Finite fields
• 11/18, Joshua Lovelace: Hadamard matrices
• 11/23, Azrrik Hahn: Dinitz's conjecture
• 11/25, everybody: Thanksgiving.
• 11/30, Class cancelled due to Illness.
• 12/2, Carl Bobkoski: Latin squares
• 12/7, Mary Zangari: Baranyai's theorem
• 12/9, Eduardo Mariscal: Difference systems
• 12/14, Serena Mercado: Lattices

• 12/15: Final exam solutions.
• 12/09: Final exam instructions. Updated 12/10-13
  • Here is the Final exam.
  • The final exam is due Tuesday, 12/14, 4PM in our regular lecture room.
  • Treat this like an open book, open notes, open anything in-class exam.
  • If you find a proof in a book, paper, ... then write up the proof in your own words (including proofs of all Lemmas that we didn't prove in course so far) and precisely state the source of the information (including author, page number s, ...).
  • You may talk/email to me about any questions -- if I tell you anything I wi ll also post it on the web, so check the web periodically.
  • You may not talk to any of your class mates about any aspect of thi s final. This includes "Have you started/finished yet?". In short: if it's not a llowed in a regular exam, it isn't allowed here either.
  • #2: A chain cover is a collection of chains in a poset such that each element is in AT LEAST one of the chains. A chain partition (lecture 2) is a special case of a chain cover in which each element is in EXACTLY one of the chains.
  • #2: (c) implies (a) is the hardest implication of (a) implies (b) implies ( c) implies (a). A collection of "perfect matchings" between consecutive levels in P' yields a chain partition in P' and thus a chain cover in P.
  • #2(c): Of course this statement can only be true for 1 <= k < h.
  • #3: Each subset of {1,2,...,n} gets a color (not each element). Hint: think what you can say about all the sets of the same color.
  • #3b): incomparable means incomporable under the "is a subset of" relation.
  • #5b): one case is fairly tedious. Substantial partial credit given, if all the other cases are done correctly.
  • #6: you may not assume that this is a Hamming code, or anything else we didn't prove.
  • #6: For definition of Ai see lecture 16, pg 1.
  • #6: throughout you may assume that n>1 to avoid trivialities.
• 12/07: the solutions to assignment 5 are on Eres.
• 11/25: Hints to HW5
  • 5: Prove a Lemma first that says that each (v,v-1,v-2)-design is unique.
  • 5: you may assume that projective and affine planes of order at most 4 are unique up to isomorphism.
  • 6a): you may assume that p=2 is a multiplier, even though this does not follow from the multiplier theorem.
  • 6c): this part has been dropped and need not be attempted.
  • 6d): 57 is not prime.
• 11/22: the solutions to assignment 4 are on Eres.
• 11/17: Homework 5 has been posted and is due 12/2.
• #2c): the code derived from Hadamard matrices need not be linear (so this does not need to be verified.)
• 11/1: Homework 4 has been posted and is due 11/16.
• 10/29: Exam 1 solutions are now on electronic reserve.
• 10/28: Exam 1 scores.
• 10/26: On Assignment 1#5d solution: in P= each n_i should have a 1 added to it, and the same for each m_i in the k-tuple in P. (Thanks, Mary)
• 10/26: Your homeworks have been graded and can be picked up in my office hours.
• 10/19: since nobody expressed concerns, and several of you expressed support, the midterm exam has been moved to 10/26.
• 10/19, Hint on #2b: for the odd case your graph should be connected, but have at least one edge whose removal disconnects the graph.
• 10/17: the midterm exam is currently scheduled for 10/21. I am thinking of postponing it to 10/26, since we have a homework assignment due 10/21. Please email me to let me know your preference, since I will only reschedule the exam if everybody is OK with moving it.
• 10/17: Exam 1 guide.
• 10/17; a few possible presentation topics:
  • Lattices and combinatorial geometries
  • Baranyai's theorem
  • Projective Planes
  • Orthogonal Latin squares and Orthogonal arrays
• 10/14: The dates for presentations are 11/11,11/16,11/18,11/23,11/30,12/2,12/7,12/9 or any date before that. If you want to speak on a particular date, then now is the time to let me know.
• 10/12: Solutions to Assignment 2 now on eres.
• 10/12: everybody got 2 bonus points on Assignment 2, since the hint on problem 6a) was wrong.
• 10/10: Assignment 3 has been slightly changed.
• 10/8: Assignment 3 has now been posted.
• 10/8: Two remarks on lecture 12:
  • Paley's theorem: the n should be a q.
  • Top of pg 7: we can assume that a_i is odd, since the only remaining cases for which we need constructions is when n is odd.
• 9/21: Today's lecture: The 4CT, Planar thickness, List coloring, Precolorings and coloring extensions, Hadwiger's conjecture.
• 9/10: We will have two guest speakers from Macalester College:
  • On 9/22 Stan Wagon will deliver a Colloquium talk directed at a general mathematical audience.
  • On 9/23 Joan Hutchinson will speak in our class on open problems in graph coloring.
• 9/9: I will be answering homework questions in class today, so make sure to look at the questions before coming to class, so that you can at least understand what we are talking about.
• 9/5: I am looking for a grader for GEM 100. If you or somebody you know is interested, then let me know.
• 8/31: Welcome to Math 540!
• 8/14: MathSciNet: On campus or remotely.
• 8/14: Universal grade change form.
• 8/14: All course announcements will remain here, except for homework assignments and comments (archived on homework page) and lectures and homework solutions (archived on electronic reserve).
• 8/14: This is where all course announcements will be posted.