HONORS 213
QUANTIFICATION: Foundations of Geometry
I. Introduction
B. Objectives
II. Required Topics
2. Logic: truth tables, negation, quantifiers, proofs.
3. Hilbert's Axioms: incidence, betweenness, congruence, continuity, parallelism
4. Models
5. Neutral Geometry: geometry without parallel axiom, exterior,angle theorems, angle sum of a triangle
6. History of the Parallel Postulate
7. Discovery of Non-Euclidean Geometry
III. Bibliography
Hilbert Foundations of Geometry
Moise Geometry
Poincaré Science and Method
Reid Hilbert
Lakatos Proofs and Refutations, The Logic of Mathematical Discovery