Department of Computer Science

Discrete Structures

Spring Semester 2008

Dr. Maury Eggen

Examination Two Review

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

• 1. Functions, domain, codomain, range, injections, surjections bijections, proofs.
• 2. Relations, reflexive, symmetric, transitive, antisymmetric, asymmetric, irreflexive, proofs.
• 3. Equivalence relations, partitions, theorem on partitions and equivalence relations. Modular arithmetic.
• 4. Partially ordered sets.
• 5. Permutations and combinations. Counting problems. Duplicates.
• 6. The principle of exclusion and inclusion.
• 7. Counting principles--addition principle, multiplication principle.
• 8. Sets and set theory. 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. Anything from "day one" may be included 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.

The examination covers everything we have learned this semester up to and including injections, surjections and bijections, composition of functions and inverse functions. This will be our stopping point.

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.)