| Date | Topics covered | Reading | Homework Assignments |
| Monday January 12 |
Introduction |
Chapter 1 |
|
| Wednesday January 14 |
Euclid's
Geometry. Origins of geometry, the axiomatic method, undefined terms. |
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| Friday January 16 |
Euclid's first four postulates. |
HW1: Due Friday January 16 .pdf, .tex |
|
| Monday January 19 |
NO CLASS |
NO CLASS | |
| Wednesday
January 21 |
The parallel postulate. |
Chapter 2 | |
| Friday January
23 |
Introduction to LaTex. |
(See the bottom of this webpage) |
HW 2: Due Friday February 6 Chapter 1, Exercises: 1, 2, 3, 6, 9, 10, 12 |
| Monday January 26 |
Misleading diagrams, straight edge and compass constructions. | ||
| Wednesday January 28 |
Logic Introduction to logic. |
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| Friday January 30 |
Theorems and proofs, proof by contradiction. |
HW 3: Due Friday February 6 Chapter 1, Exercises: 14, 15. Chapter 2, Exercises: 1, 2, 3. .pdf, .tex |
|
| Monday
February 2 |
Basic logic, cont. |
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| Wednesday
February 4 |
Incidence geometry. | ||
| Friday
February 6 |
Models. | HW 4: Due Friday February 6 Chapter 2, Exercises: 4, 7, 8, 10 (a)(b), 11. |
|
| Monday February 9 |
Homework review |
||
| Wednesday February 11 |
Review | Sample Midterm I .pdf |
|
| Friday
February 13 |
MIDTERM I |
MIDTERM
I |
|
| Monday
February 16 |
Affine planes |
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| Wednesday
February 18 |
Projective planes |
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| Friday
February 20 |
Hilbert's Axioms Flaws in Euclid. |
Chapter 3 |
HW 5: Due Friday February 20 Chapter 2, Exercise: 14. Chapter 2, ``Major Exercises'': 1-5. |
| Monday February 23 |
Axioms of betweenness. |
||
| Wednesday February 25 |
Axioms of congruence. | ||
| Friday February 27 |
Axioms of continuity. |
HW 6: Due Friday March 6 Chapter 3 Exercises on Betweenness: 1-5 |
|
| Monday
March 2 |
Axiom of parallelism. | ||
| Wednesday
March 4 |
Neutral Geometry Geometry without the parallel axiom. Alternate interior angle theorem. |
Chapter 4 |
|
| Friday
March 6 |
Exterior angle theorem, measure of angles and segments. | HW 7: Due Friday March 13 Chapter 3 Exercises on Congruence: 21-24 |
|
| Monday March 9 |
Sachheri--Legendre theorem. | ||
| Wednesday March 11 |
Equivalence of the parallel postulates. | ||
| Friday March 13 |
Angle sum of a triangle. | HW 8: Due Friday March 13 Begin presentation writing assignment |
|
| Monday
March 16 |
Homework review |
||
| Wednesday
March 18 |
Review | Sample
Midterm II .pdf |
|
| Friday
March 20 |
MIDTERM II |
||
| Week of
March 23-March 27 |
SPRING BREAK | SPRING BREAK | |
| Monday March 30 | Non-Euclidean Hilbert planes, and the defect | Chapter 5, Chapter 6 | |
| Wednesday April 1 |
Similar triangles, parallels admitting a
common perpendicular. |
||
| Friday April 3 |
Limiting parallel rays, hyperbolic planes. |
HW 8: Due Friday April 10 Presentation writing assignment |
|
| Monday
April 6 |
History of the Parallel Postulate (Presentations) Proclus, Equidistance, Wallis, Saccheri. |
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| Wednesday
April 8 |
(Presentations) Clairout's Axiom and Proclus' Theoreom, Legendre, Lambert and Taurinus, F. Bolyai |
||
| Friday
April 10 |
Non-Euclidean Geometry (Presentations) J. Bolyai, Gauss, Lobachevsky |
HW 9: Due Friday April 17 Chapter 4, Exercises 1, 2, 6, 10, 14 |
|
| Monday April 13 |
Classification of parallels. | ||
| Wednesday April 15 |
Independence
of the Parallel Postulate Consistency of hyperbolic geometry. |
||
| Friday April 17 | The Beltrami--Klein model |
HW 10: Due Friday April 24 Chapter 5, Exercises 10, 11, 13 |
|
| Monday
April 20 |
The Poincare models. |
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| Wednesday
April 22 |
Models, cont. |
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| Friday
April 24 |
Further topics |
HW 11: Due Friday May 1 Study for final exam |
|
| Monday April 27 |
Further topics |
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| Wednesday April 29 |
Homework review |
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| Friday May 1 |
Review |
Sample Final .pdf |
|
| Monday May 4 |
FINAL
EXAM 7:30
-10:00 PM ECCR
1B51 (Lecture Room) |
FINAL EXAM | FINAL EXAM |