Department of Computer Science

Discrete Structures

Spring Semester 2010

Dr. Maury Eggen

Examination Two Review

The topics for the second examination include, but are not necessarily limited to, the following:

• 1. Principle of mathematical induction
• 2. The second principle of mathematical induction
• 3. Recurrence relations: expand, guess, verify (pmi)
• 4. Finite probability
• 5. Permutations and combinations. Counting problems.
• 6. The principle of exclusion and inclusion.
• 7. Counting principles--addition principle, multiplication principle.
• 8. Sets and set theory. Element chasing arguments. Intersection, union, difference, subsets, complements, proofs, power set, sets of sets. families of sets, family unions, family intersections, proofs
• 9. Set theory, cartesian products, ordered pairs, proofs.
• 10. Binomial theorem.
• 11. Anything covered in class -- you expect it on the exam.

You will be expected to write reasonable mathematical exposition. Proofs, proof techniques studied in class will be expected on the exam.

You will be exposed to problems you have seen before, problems like you have seen before, and problems unlike anything you have ever seen. You will be expected to assimilate, synthesize, and apply the knowledge you have learned so far.

You may bring one 8 1/2 by 11 sheet of paper to the exam with anything you wish on it. This "cheat sheet" may be utilized during the exam. You may write information on both sides of the sheet. No other assistance will be allowed on the exam. (Closed book, closed notes, closed workstation, etc.)