Jen Paulhus, Ph.D.

Combinatorics

email: paulhus@math.grinnell.edu     pgp key
Jen Office Hours:
Office Hours: Mondays 10 - 11 AM, Tuesdays 1:30 - 2:30 PM,
          Wednesdays 11 AM -12 PM, Thursdays 2:30 -3:30 PM,
          or by appointment (all on Zoom for now)

Text: Combinatorics by Joy Morris (M below)
      Combinatorics Through Guided Discovery by Kenneth P. Bogart (B below)

Syllabus
Homework

Daily Topics

Class Date Pages and Section(s) Topics
Aug. 27 M Ch. 1 pp. 1-5, B Preface pp ix-xv Introduction
Aug. 30 M Ch. 2 pp. 9-18, B Ch. 1.2 #1-5,9 Basic Counting
Sep. 1 M Ch. 3.1 pp. 19-22, B Ch. 1.2 #6,7,13,19-22,38 Permutations/How to Read Math
Sep. 3 M Ch. 3.1 pp. 22-26, B Ch. 1.2 #8,37,40 Combinations
Sep. 6 M Ch. 3.3 pp. 26-28 , B Ch. 1.3 # 53, 54 Binomial Theorem
Sep. 8 M Ch. 4.1 pp. 29-32 , B Ch. 1.4 #55, 56 Bijections
Sep. 10 M Ch. 4.2, 4.3 pp. 31-38, B Ch. 1.2, 1.3 #29, 57, 59 Combinatorial Proofs
Sep. 13 M Ch. 5.1-5.1 pp. 39-42, B Ch. 3.1 #124, 125, 126, 127 Unlimited Repetition
Sep. 15 M Ch. 5.2 pp. 42-44, B Ch. 3.1 #124, 125, 126, 127 Permutations with Repetition
Sep. 17 M Ch. 10.1 pp. 89-91, B Ch. 1.3 #60, 61, 62 Pigeonhole Principle
Sep. 20 M Ch. 10.1/10.2 pp. 91-92 B Ch. 1.3 #64, 65 More Pigeonole Principle
Sep. 22 This article, this article, and this cartoon. What to do when math gets hard?
Sep. 24 M 10.2 pp. 94-98 B Ch. 5.1 #225-229 Inclusion-Exclusion
Sep. 27 M 6.1 pp. 47-49 B Ch. 5.1 #231 Derangements
Sep. 29 M 6.2 pp. 49-52 B Ch. 2.2 #87, 88, Ch. 2.1 #73 Basic Induction
Oct. 1 M 6.3 pp. 52-56 B Ch. 2.1 #76 More Induction
Oct. 4 B Section A.2 (under Back Matter) Equivalence Relations
Oct. 6 Exam 1 M 1-6.2, 10
Oct. 8 B 3.1.1-3.1.3, 3.1.5 Summary of Distribution Problems
Oct. 11 B 3.1.4 Weak Compositions, Set Partitions
Oct. 13 B 3.2.1, 3.2.2 Stirling Numbers of the 2nd Kind
Oct. 15 B 3.2.3 Stirling Numbers of the 1st Kind and Polynomials
Oct. 25 B 3.3.1 and 3.3.2 Permutations, Partitions of Integers
Oct. 27 B 3.3.3 Young Diagrams
Oct. 29 M 7.1 B 4.1.1-4.1.2 Derangements and e, Intro to Generating Functions
Nov. 1 M 7.3 B4.1.3-4.1.4 Examples of Generating Functions, Series
Nov. 3 M 7.3 Math Major, Algebraic Manipuations of Generating Functions
Nov. 5 M 7.2, 7.3 B4.1.5, 4.1.6 Generalized Binomial Theorem, Finding Coefficients
Nov. 8 M 8.1-8.3 B 4.3.1, 4.3.4 Partial Fractions, Solving Recurrence Relations
Nov. 10 M 8.3, 7.2 Tower of Hanoi and Square Roots
Nov. 12 M 9.2 B 4.3.5 Catalan Numbers
Nov. 15 B Appendix C.1-C.2 Exponential Generating Functions, Studying for Exams
Nov. 17 M 11.1-11.3 B 2.3.1 Introduction to Graphs
Nov. 19 M 11.4 Isomorphism of Graphs
Nov. 22 Exam 2 M: 6.2-6.3, 7-9.2, B: 3, 4, A.2, B
Nov. 24 M 12.1-12.3, B 1.2.2, 2.3.2 Walks, Paths, and Cycles
Nov. 29 M 13.1-13.2 Eulerian Tours, Hamiltonian Cycles
Dec. 1 M 12.4 B Ch 2.3 #107-110 Trees
Dec. 3 B 2.3.4-2.3.6 Spanning Trees

Homework Assignments

Make sure you are familiar with the Academic Honesty policies for the class as well as the Grading Rubric and Guidelines. Writing assignments will be submitted on PWeb and returned on OneDrive. You will be encouraged to use LaTeX to write your solutions. Brief solutions to homeworks will also be posted on PWeb.

HW Due Date Problems
# 0 Aug. 30 Email me with answers from class 8/27, and read syllabus
# 1 Sep. 1 Homework 1
# 2 Sep. 6 Homework 2
# 3 Sep. 10 Homework 3
# 4 Sep. 15 Homework 4
# 5 Sep. 20 Homework 5
# 6 Sep. 24 Homework 6
# 7 Sep. 29 Homework 7
# 8 Oct. 4 Homework 8
# 9 Oct. 15 Homework 9
# 10 Oct. 27 Homework 10
# 11 Nov. 1 Homework 11
# 12 Nov. 5 Homework 12
# 13 Nov. 10 Homework 13
# 14 Nov. 15 Homework 14
# 15 Nov. 19 Homework 15
# 16 Dec. 1 Homework 16
# 17 Dec. 6 TBA
# 18 Dec. 10 TBA