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.
Changes discussed in class on 2/21/08 are in italic boldface in
the following
The first hour exam for Honors 213 will be held on Friday, Feb. 22, and will
cover chapters 1, 2, the course lectures on logic and the first three betweeness
axioms. Please be
sure to bring a compass and straight-edge.
- Definitions:
- Be able to define the terms that appear in chapters 1. 2, and chapter
3 through the first three betweeness axioms. (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, the three incidence
axioms, and the first three axioms of betweeness.
- Be able to describe the logic rules given in class
- 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 give definitions of affine and projective planes.
- Be able to construct, using ruler and straight-edge, the constructions
in problem 14 on page 46. . 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.
- Unlike last year's exam, there will not be a page of definitions
and axioms for this exam.