Math 211

Exam #3 review

(material in boldface was added or modified after Wednesday's review)

Cavaet:  Although I try to be comprehensive in these exam reviews, please understand that you are responsible for the material covered since the last exam.  If you notice something that I have missed, please do let me know.

The second hour exam will be Friday, Nov. 14, and will cover sections 2.7 (matrices) through section 4.4 (skipping 3.5 and 3.6).  (note - I think that should have read "through section 4.5").  In your review look over assigned problems, definitions, and biographical essays.  In particular, be able to

• Be able to calculate with matrices, including 0-1 matrices.  Be able to construct an incidence matrix of a graph.
• Be able to describe in detail what a proof using mathematical induction looks like, and be able to prove basic theorems (on the order of the homework exercises) using mathematical induction.
• Be able to construct and use recursive definitions.
• Be able to use the pigeonhole principle(s).
• Be able to work with summations and sequences
• Be able to count using permutations and combinations.  One important feature of this section is knowing which to use.. In particular, be able to work with
• The multiplication rule
• The sum rule
• Counting power sets
• The inclusion-exclusion principle
• Permutations
• Combinations
• Permutations and combinations with repetition.
• Know and be able to use the Binomial Theorem, including the recursive definition of the binomial coefficients.
• Know (as always) the brief biographies in the reading (same sort of question as before).
• We didn't talk very much about proof methods (except for mathematical induction).  Mathematical induction will be on this test, but the other material (including descriptions of famous problems) will not - but will likely appear on the final.

Any questions?  Please ask!  - Bob