CSCI 1323 (Discrete Structures), Spring 2004:
Review for Midterm Exam
The exam will be in class March 8. You will have 50 minutes.
You may use your textbook and any notes or papers you care to bring,
but you may not use other books, a calculator or computer,
or (of course!) each other's papers.
Most questions will be similar in form to those in the quizzes
and homework assignments.
You are responsible for all material covered in class or in the
assigned reading.
(See Lecture Topics and Assignments
for a list of assigned reading.)
You should review in particular the following
topics. This list is not necessarily exhaustive, but should
give you an idea of what topics I think are most significant.
- Propositional logic:
- Translating English into propositional-logic wffs
(emphasizing understanding of propositional logic
connectives over ability to untangle complicated
English).
- Proving that a propositional-logic
wff is a tautology using truth tables.
- Proving that a propositional-logic
wff is a tautology using proof rules.
- Predicate logic (propositional logic plus quantifiers):
- Translating English into predicate-logic wffs
(emphasizing understanding of quantifiers
over ability to untangle complicated
English).
- Determining whether a predicate-logic wff is true
in a given interpretation.
- Proving that a predicate-logic wff is valid using
proof rules.
- Proofs of program correctness:
- Rules for assignment, conditional statements,
loops.
- Combining these rules to verify correctness of
simple programs.
- Meaning of Hoare triples.
- Proof techniques:
- Direct proofs, proof by cases, proof by contraposition,
proof by contradiction.
- Proofs by induction.
- Recursion and recurrence relations:
- Recursive definitions of sequences, sets, operations,
and algorithms.
- Defining and solving recurrence relations.
- Analysis of algorithms:
- Defining and solving recurrence relations to
estimate the number of basic operations performed
by a recursive algorithm.
Berna Massingill
2004-04-28