Math
4160  Combinatorial Mathematics

Professor: Mike Zabrocki email: Meetings: TuesThurs 2:304pm TEL 0005 Office hours: Ross N518  TBA Textbook: (optional) How to count by Allenby and Slomson, class notes, 

assignments  55% 
midterm  20% 
final  25% 
Lecture 
dates 
Topic/sections in text 
notes/relevant handouts 
1 
Tues, Sept 9 
sums, Stirling numbers, addition/multiplication principle 

2 
Thurs, Sept 11 
sums of rising factorials,
Stirling numbers of the first kind $s'(n,k)$ 

3 
Tues, Sept 16 
a proof that $x^n = \sum_{k=1}^n (1)^{nk} S(n,k) (x)^{(k)}$
 $n!$, ${n \choose k}$, $S(n,k)$, $s'(n,k)$, $B(n)$, $n^k$, $(n)_k$, $(n)^{(k)}$ 

4 
Thurs, Sept 18 
basic counting, cards and combinatorial identities 
HW1 available as of Sept 20 
5 
Tues, Sept 23 
rising factorial, summation solution, distributions 

6 
Thurs, Sept 25 
choose and multichoose, proving combinatorial identities, sequences and generating functions 

7 
Tues, Sept 30 
intro to generating functions (video + ex 18 on worksheet), paths and combinatorial identities 

8 
Thurs, Oct 2 
proving combinatorial identities w/paths, coefficients in gfs 
HW #1 due 
9 
Tues, Oct 7 
more coefficients in gfs, combinatorial interpretations 

10 
Thurs, Oct 9 
more g.fs, combinatorics with gfs 
HW2 assigned 
11 
Tues, Oct 14 
Fibonacci and Lucas identities with g.fs 

12 
Thurs, Oct 16 
complex numbers, partition generating functions 

13 
Tues, Oct 21 
exponential generating functions 
HW2 due, 
14 
Thurs, Oct 23 
exponential generating functions 
take home midterm 
15 
Tues, Oct 28 
solving problems 
midterm due 
Thurs, Oct 30 
reading half of a "week" 
hw 3 assigned 

16 
Tues, Nov 4 
groups and symmetries of the square and triangle 

17 
Thurs, Nov 6 
groups, homomorphisms, group actions, symmetries of 3d shapes 

18 
Tues, Nov 11 
groups, actions, orbit stablizer theorem 
hw 3 due 
19 
Thurs, Nov 13 
relations, equvialence classes 

20 
Tues, Nov 18 
Burnsides Lemma and Polya's theorem 

21 
Thurs, Nov 20 
Burnsides Lemma and Polya's theorem 

22 
Tues, Nov 25 
Polya's theorem and necklaces 

23 
Thurs, Nov 27 
partial orders and Möbius inversion 
hw 4 due 
24 
Thurs, Dec 4 
final exam, necklaces, a research problem 