Here you can find an UNOFFICIAL list of what we have more or less covered in the lectures
and what will be coming up soon. I will try to update this once a week.
It is NOT guaranteed to be 100 % accurate but I would think it would be more or less.
Probably about 90 % of what is presented will be in the book but NOT everything.
First, I consider Chapters 1-9 more or less background material (although I will very briefly
discuss relations (pg 57) and elementary arithmetic section 8.4). (Note that there is much more
background material in this edition of the book than the earlier one).

.........................................................................................
sept 2: My substitute covered a quick review of some elementary combinatorics such as
the "sum rule", the "product rule", permutations, combinations, binomial coefficients and
multinomial coefficients.
This would be more or less covered in Sections 10.1, 10.4, 10.5, 11.1 and a part of 12.3.

sept 9: Review of some of the things done the first day plus
further things concerning binomial coefficients. Also, the general
discussion concerning the number of ways to give n candies to k
children and how there are 4 formulations of this question.
See Sections 11.2 and 11.3.
It takes a little thought to see that the combinatorial problem
discussed in Theorem 11.2 is equivalent to the problem of
the number of ways to give n indistinguishable candies to
k distinguishable children where there is NO requirement of given
each child one candy. This was used to solve the 3rd formulation of the
above question.

Sept 10: We continued the discussion concerning
the number of ways to give n candies to k
children and the 4 formulations of this question.
See Sections 12.1, 12.3 and 12.4.
Next we computed the number of binary sequences of length n which contain
no adjacent 1's. This was done by deriving a recurrence relation
for these and then applying a general theorem concerning the solution
of a two step recurrence relation. We then proved this theorem.
See Section 19.2 for this theorem.

Sept 11: We will go through the first homework assignment.

Sept 12: We finished the first homework. For one of the problems
we went through "double counting", see Section 10.2. Then we moved into
graph theory. Sections 15.1 and 15.4. We proved the theorem
characterizing which graphs have Eulerian paths as those for which
the number of vertices with odd degree is 0 or 2. (See end of Section 15.4).

Sept 16: Sections 15.3,15.4, 15.5, started 16.3.

Sept 17: Finished Section 16.3. Then Section 15.6 and then theorem
15.7.2 in Section 15.7.

Sept 18 and 19. Went through homework 2.

Sept 23. Finished Section 15.7. (Decided not to do 17.4).
We then started doing the max flow-min cut theorem.
(Sections 18.3 and 18.4)

Sept 24. We finished up Sections 18.3 and 18.4 and had an exercise session.

sept. 25. We will go through parts of Homework number 3 and be done
with graph theory.

On Sept 26, sept 30 and October 1, we did the following topics.
(Modular arithmetic) 13.1-13.5 (not 13.4). (13.5 was Latin Squares)
(Equivalence relations) 12.2.
(Euler's phi-function) 10.3 (but not Theorem 10.3).
Sieve principle (Section 11.4).
Statement of Theorem 11.5.1 in Section 11.5.


Thursday, October 2, we had an exercise session
where people will work on their own (homework 4).

Friday, October 3, we completed the proof of Theorem 11.5.1 (but not
do other parts of Section 11.5) and did RSA cryptography.

October 7, we went through parts of Homework 4.

October 8. we did more on permutations (10.6 and 12.6 except the proof
of Theorem 12.6.1) with the example on page 139 as a motivating problem.

October 9. We proved Theorem 12.6.1 (which was the key theory for solving
the problem in the example on page 139). We then started on group theory.
We did sections 20.1-20.5.

The rest of the course will be contained in Sections 20.6-20.8
(more group theory) and 21.1-21.4 (groups of permutations and
applications to counting). So if you read these, you will be fine.
And I recommend that you do read this before I present it if possible
so that the lectures are more understandable and so that you can work on
homework 5. We won't necessarily do all of this; for example, we won't
do all of 20.8.

The plan is as follows: I will be lecturing October 10 and 14 on this
last material. On Oct 15th, we have an exercise session where people work
on problems from homework 5 and I go around answering questions or
helping out. Then on Thursday and Friday, I will go through homework 5
and also finish up or review parts from this last section of the course
since it is probably more difficult than the other sections.

[THIS IS THE LAST TIME I UPDATE THIS HOMEPAGE]