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 (Xhour) 
Office Hours: 
Monday,  2:00pm  3:00pm 
Kemeny 320  Tuesday,  12:45pm  1:45pm 
Thursday,  10:00am  11:00am 
Homework:  20% 
Class Participation:  15% 
Exam 1:  20% 
Exam 2:  20% 
Final Exam:  25% 
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 Xhour 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 (Xhour) 
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 1ad, 2ac, 3ab 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 TwentyFold 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 closedform 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 InclusionExclusion Read: 5.1.1 Practice: # 225231 

27  Mar 6 
Lecture: Principle of InclusionExclusion Practice: # 232, 235, 236, 238, 239 

28  Mar 8 
Lecture: Principle of InclusionExclusion Practice: # 232, 235, 236, 238, 239 
Final exam practice problems are posted above. 
Mar 14  Final Exam, Kemeny 007, 8:00am  11:00am 
January 4:  Classes begin 
January 18:  Final day for electing use of the NonRecording 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 