Exam 2 study guide
- Calculators will not be allowed for this exam.
- For problems that have numerical answers, I expect the answer
in closed form (say, involving a few binomial coefficients ...).
- This exam will not be purely computational. You will have to do
some proofs as well.
- This exam will be covering lectures 8-16 (February 10 to March 16)
and assignments 4-7.
The exact sections in the book this corresponds to
can be found in the Tentative schedule.
- You are NOT allowed to use the content of lecture 17 (7.2:
Solving linear homogeneous recurrence relations).
- You are not allowed, it isn't necessary, and probably not even helpful
to use material from later sections.
- Material from earlier lectures is still background material
even though I will not be "specifically" testing it. This means you can't
just forget what a multiset is, or what the the multiplication principle
does.
- You should be familiar with all the terminology we have defined so far.
- You should know the correct statements of the Major results
we have covered so far. This includes counting techniques (like the principles of Inclusion-Exclusion, Addition, and Multiplication), Binomial identities
(like Pascal's formula and (5.11)-(5.14)), the versions of the Binomial
Theorem (simple, multinomial and Newton's version).
- Since we had many results you will be allowed to use a cheat sheet:
- Your sheet must be handwritten.
- Your sheet should be just the front page of a 8.5 x 11 page.
- Write down all equation/theorem numbers, since you will
need those to justify your reasoning.
- Use the following notations:
(5.11) to denote equation (5.11) in the book,
Thm 5.6.1 to denote
Theorem 5.6.1 in the book (or you can use Newton's Binomial Theorem),
Cor 5.4.2 to denote Corollary 5.4.2 in the book,
and #7.1a) to denote Exercise
1 part a) from assignment 7.
- You may not quote problems from the book (since we didn't solve
all of those), only problems from the Homework.
- You should know how to apply these results to count the number
of various things: integral solutions to simple equations (with constraints),
permutations or rook placements (with forbidden positions), doughnuts in
a box, rabbits in an enclosure, ...
- You should understand the main idea of the proofs of
these results as well. I MAY ask you to reproduce one of
the shorter, straight forward proofs from lecture or homework.
- There will definitely be at least one proof of a result
you have not seen yet, so have your "tool box" ready.
- You should understand the solutions (either mine or yours)
to as many homework problems as possible.
- If you have the time for it, then doing extra problems
from the book can also help. The more you work with the concepts,
the "readier" you are going to be.
- Some problems on the exam may throw you off at first.
Make sure that you get a good nights sleep, so that you are fresh,
rested and ready to go!