Honors 213First Hour Exam Review
Disclaimer: I have attempted to be comprehensive in the following, but
important items may have been omitted by mistake. If you see such an omission,
please let me know, but you are responsible for all of the lecture material to
date.
The first hour exam for Honors 213 will be held on Friday, Feb. 16, and will
cover chapters 1, 2 and the course lectures on logic. Please be
sure to bring a compass and straight-edge.
- Definitions:
- Be able to define the terms that appear in chapters 1 and 2
(formal definitions)
- Be able to define terms encountered in a high school
geometry course using the terms we have developed in this class
(eg, problems 1 - 2 at the end of chapter 1)
- Be able to state Euclid's first five postulates
- Truth tables: Be able to say what propositions are and to
construct truth tables for the propositional logic, and to use them to
demonstrate some of the logic rules we have been given (not-not rule, MP,
MT, etc.)
- Be able to describe what predicates and quantifiers are and give
and use rules for their manipulation.
- Basic logic
- Be able to find the converse and contrapositive of statements and
identify sufficient and necessary conditions.
- Be able to construct simple proofs, including proofs involving the
axioms of incidence.
- Be able to discuss what a mathematical proof is, including the RAA
technique.
- Be able to discuss axiomatic systems, interpretations, models, and
isomorphism of models. Be able to discuss what it means for a
statement to be independent of a set of axioms, and say how models can tell
us this.
- Be able to construct, using ruler and straight-edge, the constructions
in the first four parts of major exercise 1 (through the construction of
parallel lines). Be sure to bring a compass and straight-edge.
- Be able to say something about the historical figures that enter into the
textbook material discussed so far.