Math 300First 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 Math 300 will be held on
Friday, Feb. 22, and will cover chapters 1, 2, and the first few axioms of betweeness from chapter 3 together with 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
- Be able to state 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.
- 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 describe affine and projective planes, and discuss the
projective completion of an affine plane.
- 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.