Jay Pantone

John Wesley Young Research Instructor
Dartmouth College

jaypantone@dartmouth.edu


Math 28

Combinatorics is the study of structures in mathematics. This course will start by developing basic set theory and counting principles, and proceed to the study of graphs, permutations, lattice walks, and more. Other topics that will be covered include proof techniques (induction, etc.), probability, and generating functions.

  • Lectures:
    M, W, F, 10:10am - 11:15am
    Kemeny 007 Th, 12:15pm - 1:05pm (X-hour)
  • Office Hours:
    Monday, 2:00pm - 3:00pm
    Kemeny 320 Tuesday, 12:45pm - 1:45pm
    Thursday, 10:00am - 11:00am

Course Information

The official syllabus is here.
Textbooks

Combinatorics Through Guided Discovery,
   by K. Bogart

Generatingfunctionology,
   by H. Wilf

Extra Practice Problems

Grading Scheme
Homework: 20%
Class Participation: 15%
Exam 1: 20%
Exam 2: 20%
Final Exam: 25%


 
Homework Assignments
Problems from the textbook will be assigned each day. Each Wednesday, all problems from the previous Monday-Friday are due. See my homework policy in the syllabus.
Exams
Each midterms will be two hours long and will be held in the evening. The final exam will be three hours long and will be held at the time scheduled by registrar (likely March 14).
Extra Notes
Tips
Daily Calendar
Read = Read the exposition in this section of the text before coming to class.
Lecture = A short topic I will discuss before group work.
Practice = We will work on these problems in class.
Homework = These problems are due in the next homework assignment.
# Date Topics Announcements
1 Jan 4 Class Information
Lecture: Sets
Practice: # 1, 2, 3, 5
Homework: # 4, 6
Welcome to Math 28!
2 Jan 6 Lecture: Sum and Product Principles
Read: 1.0, 1.1, 1.2.1
Practice: # 8, 12, 13
Homework: # 7, 12, 17, 18
If you are auditing the class, please email me so I can add you to our email list.
3 Jan 9 Lecture: Digraphs, Bijection Principle, Counting Subsets
Read: 1.2.2, 1.2.3, 1.2.4
Practice:
Homework: # 26
We will use the X-hour this week.
4 Jan 11 Lecture: Pascal's Triangle
Read: 1.2.5
Practice: # 23, 24, 25, 29
Homework: # 30, 31
Homework 1 due today
Office hours today end at 1:45pm.
5 Jan 12
(X-hour)
Lecture: The Quotient Principle
Read: 1.2.6
Practice: # 35, 36, 37
Homework: # 38, 40
No class or office hours on Monday (MLK Jr. day)
6 Jan 13 Lecture: Stars and Bars, Lattice Paths
Read: none
Practice: # 37, 43, 45, 47, 48
Homework: # 49, 50
Wednesday office hours have been permanently moved to Tuesday, 12:45pm - 1:45pm.
7 Jan 18 Lecture: The Binomial Theorem
Read: 1.3.2
Practice: # 53, 54, 55, 56
Homework 2 due today
The time and date of Exam 1 are posted above.
Homework 3 is posted above as a pdf.
8 Jan 19 Lecture: The Pigeonhole Principle
Read: 1.3.3
Practice: # 61, 62, E1, E2, E4
9 Jan 20 Lecture: Ramsey Theory
Read: 1.3.4
Practice: # 67, 65, 66, 68
10 Jan 23 Lecture: Proofs and Induction
Read: 2.1.0 - 2.1.3
Practice: # 72, 73, 74, 76
worksheet 1a-d, 2a-c, 3a-b
grade faulty proofs
11 Jan 25 Lecture: Recurrence Relations
Read: 2.2
Practice: # 87, 88, 89, 94, 95
Homework 3 due today
12 Jan 27 Lecture: Graphs
Read: 2.3.1, 2.3.2, 2.3.3
Practice: # 100, 102, 103, 104, 105, 106, 107
13 Jan 30 Lecture: The Twenty-Fold Way, Ordered Functions
Read: 3.1.1
Practice: # 122, 123
14 Feb 1 Lecture: Exam Review Exam 1, 5pm - 7pm, Wilder 111
Homework 4 due today
15 Feb 3 Lecture: Distribution Problems
Read: 3.1.4, 3.1.5, 3.1.6
Practice: # 128, 129, 133
Homework 2 resubmissions due
16 Feb 6 Lecture: Distribution Problems, Stirling Numbers
Read: 3.2
Practice: # 134, 135, 136, 137, 138
17 Feb 8 Lecture: Distribution Problems, Stirling Numbers
Read: 3.2
Practice: # 134 - 138, 143 - 145
Homework 5 due today
18 Feb 10 Lecture: Integer Partitions
Read: 3.3
Practice: # 157, 158, 161, 162, 163, 164
Homework 3 resubmissions due
19 Feb 13 Lecture: Generating Functions
Read: Bogart: 4.1.1, Wilf: 1.0, 1.1
Homework 4 resubmissions due
20 Feb 15 Lecture: Generating Functions
Read: Wilf: 1.1, 1.2, 1.3
Practice: Extra Practice, # E5
Homework 6 due
21 Feb 17 Lecture: Generating Functions
Read: Wilf: 1.1, 1.2, 1.3
Practice: Extra Practice, # E5, E6
Homework 5 resubmissions due
22 Feb 20 Lecture: Converting a GF to a closed-form formula
Read: Wilf: 1.1, 1.2, 1.3
Practice: Extra Practice, # E7
The final exam date and time are posted above.
23 Feb 22 Lecture: Exam Review Exam 2 today
Homework 7 due
Feb 24 No class today.
24 Feb 27 Lecture: Newton's Generalized Binomial Theorem
Practice: Extra Practice, # E8 - E16
Homework 7 resubmissions due
25 Mar 1 Lecture: Newton's Generalized Binomial Theorem, exam 2 review
Practice: Extra Practice, # E8 - E16
Homework 8 due
26 Mar 3 Lecture: Principle of Inclusion-Exclusion
Read: 5.1.1
Practice: # 225-231
27 Mar 6 Lecture: Principle of Inclusion-Exclusion
Practice: # 232, 235, 236, 238, 239
28 Mar 8 Lecture: Principle of Inclusion-Exclusion
Practice: # 232, 235, 236, 238, 239
Final exam practice problems are posted above.
Mar 14 Final Exam, Kemeny 007, 8:00am - 11:00am

Important Dates
January 4: Classes begin
January 18: Final day for electing use of the Non-Recording Option (NRO)
February 14: Final day for dropping a fourth course without a grade notation of "W"
February 20: Final day to withdraw from a course
March 8: Last day of classes
March 14: Math 28 final exam