We’ll use this page to keep track of what has happened each day in class. It won’t contain any of the nitty-gritty details, but will instead serve to summarize what has transpired each day.

Week 1

  • Monday, January 14: First day! The first few minutes of class were devoted to me attempting to learn names. I think I got them all! Next, we did a very quick tour of BbLearn and the course website. The remainder of the class meeting was devoted to discussing isomorphisms as they occur in multiple mathematical contexts and we started to explore an example of a bijection between collections of "combinatorial objects" where some aspect of the structure is preserved.
  • Wednesday, January 16: After answering a few quick questions about the syllabus, I wrapped up the "prologue". Next, we had VM/DW and AM/JG2 present the recursive formula and closed form, respectively, for the minimum number of moves required to solve the $n$-disk Towers of Hanoi. Great first day of student presentations!
  • Friday, January 18: Busy day! We didn't discuss anything too ground breaking, but we covered a lot of territory. After a quick discussion of LaTeX and the first Weekly Homework assignment, we jumped into student presentations. We had JC, MG, MF, ND, and MS present Problems 3, 4, 5, 6, and 7, respectively. This left of us with plenty of time to get started on the next couple problems. After students worked in groups of 2-3, MR and VM presented two different approaches to Problem 8. I spent the remaining few minutes tying some ideas together.

Week 2

  • Monday, January 21: MLK Day, no class.
  • Wednesday, January 23: We had JG1, PG/AM/JW, JL, and JG3 present Problems 9, 10, 11, and 13, respectively. We had a nice discussion about the connection between Problem 8 (edges in complete graph) and Problem 9 (dominoes). Seeing multiple approaches to Problem 10 was cool.
  • Friday, January 25: We had FA, DW, RW, JG1, RW, and MS present Problems 14(2), 14(3), 14(4), 16, 18(via product principle), and 18(via induction), respectively.

Week 3

  • Monday, January 28: We kicked off with me summarizing Problems 19 and 20. Then we had JC, MF, and MG present Problems 22, 24, and 25, respectively. With the time we had left, we discussed permutations in their various guises.
  • Wednesday, January 30: We spent the first few minutes setting the stage and then jumped into student presentations. We had PG, JL, MR, AM and MG present Problems 27/29/30, 31(algebraic), 31(bijection), 32(algebraic), and 32(bijection), respectively.
  • Friday, February 1: JG3, RW, AM, and JG1 presented Problems 34, 36, 37, and 38, respectively. We very quickly summarized Problems 39 and 30 in the last couple minutes of class.

Week 4

  • Monday, February 4: I had my doubts about getting through everything today, but somehow we pulled it off. We had MS/AM, FA, JL, and PG present Problems 41, 42, 43/44, and 46, respectively. Along the way, I summarized Problem 45.
  • Wednesday, February 6: We had DW, ND, VM, and AM present Problems 47, 48/49/50, 51, and 52, respectively. We'll tackle Problem 53 on Friday.
  • Friday, February 8: After discussing the upcoming exam, we had MR present Problem 53. This was followed by a class discussion of all six parts of Problem 54. Next, we had LD and RW present parts 1/2 and 3 of Problem 55, respectively. We should have time to get caught up on Problem 56 on Monday.

Week 5

  • Monday, February 11: After discussing the upcoming exam, we cranked through all of the problems. We had JG1, FA, JG2/MS, and MF present Problems 56, 57, 58, and 60, respectively.
  • Wednesday, February 13: The students took the in-class portion of Exam 1.
  • Friday, February 15: I lectured today. We discussed Problems 61 and 62 and introduced generating functions.

Week 6

  • Monday, February 18: After handing back the in-class portion of Exam 1, we spent the entire class period discussing problems from both the in-class exam and the take-home exam.
  • Wednesday, February 20: Today we continued our discussion of generating functions. Along the way, we covered Problems 63-66.
  • Friday, February 22: Snow day!

Week 7

  • Monday, February 25: After discussing the plan for the upcoming week, we had FA and RW present both parts of Problem 67. Next, we discussed Problem 68.
  • Wednesday, February 27: Dr. Sieben covered for me while I was out of town. JC, JG3, MF, RW, ND/VM, and AM presented Problems 69(1,2), 69(3), 69(4), 69(4,5), 70, and 71, respectively.
  • Friday, March 1: After diving the class up into small groups, we had JL, MG, JG1 presented Problems 72, 73, and 74, respectively.

Week 8

  • Monday, March 4: We had JC, PG, MR, and AM present Problems 75(1), 75(2), 75(3), and 76, respectively.
  • Wednesday, March 6: We covered a lot of ground today! We had JG2, MS, JG3, AM, and MG present Problems 77, 78, 79, 80, and 81, respectively. With the few minutes we had left at the end of class, we briefly discussed Bell numbers.
  • Friday, March 8: After splitting the class up into several small groups, we had RW and MR present Problems 82 and 83, respectively. With the time we had left, we summarized Problem 84.

Week 9

  • Monday, March 11: We had JG1 and ND present Problems 85 and 86, respectively. This left us with plenty of time to get a jump on Problem 87.
  • Wednesday, March 13: Coming soon.
  • Friday, March 15: Coming soon.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 441: Topology
  MAT 526: Combinatorics

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