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 Math 300 will be held on Friday, Feb. 17, and will cover chapters 1 and 2, 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 .
• 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.  In particular, we have discussed
• Euclid of Alexandria
• Gottlob Frege
• David Hilbert
• Adrien Marie Legendre
• Moritz Pasch
• Pythagoras of Samos
• Thales of Miletus