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Math 123: General Course Outline |
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Catalog Description
123. Foundations of Geometry.
(4) Lecture, three hours; discussion, one hour. Requisite: course 115A.
Axioms and models, Euclidean geometry, Hilbert axioms, neutral (absolute) geometry,
hyperbolic geometry, Poincaré model, independence of parallel postulate.
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Textbook
Henderson, Experiencing Geometry, 3rd Ed., Prentice Hall.
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Reviews & Exams
The following schedule, with textbook
sections and topics, is based on 24 lectures. The remaining classroom meetings
are for leeway, reviews and midterm exams. These are scheduled by the individual
instructor.
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Schedule of Lectures
Lecture |
Section |
Topics |
| 1-2 |
Chapt. 1 |
Euclid's geometry;
Euclid's Elements, common notions, Euclid's five axioms, Propositions 1,
2 and 4 from Book 1. Instructor should consult Book 1 of Euclid's Elements.* |
| 3-6 |
Chapt.
2 |
Logic;
incidence geometry, affine and projective planes, finite geometries. |
| 7-11 |
Chapt.
3 |
Hilbert's
axioms. |
| 12-16 |
Chapt.
4 |
Neutral
geometry. |
| 17-19 |
Chapt. 5 |
History of the parallel
postulate; Wallis' postulate, Clairaut's axiom. |
| 20-21 |
Chapt. 6 |
(pp. 177-191) "Discovery"
of non-Euclidean geometry, AAA criterion in hyperbolic geometry. |
| 22-24 |
Chapt. 7 |
(pp. 223-241) Beltrami-Klein
and Poincaré models, isomorphism of the models. |
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Comments
*The standard source for Euclid's
Elements is the Heath translation published in three volumes by Dover Press.
It is important to cover at least the items from Book 1 listed above.
Outline update: T. Gamelin, 4/00 |
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