| Date | Topics covered | Reading | Homework Assignments |
| Monday January 13 |
Introduction |
Chapter 1 |
|
| Wednesday January 15 |
Euclid's
Geometry. Origins of geometry, the axiomatic method, undefined terms. |
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| Friday January 17 |
Euclid's first four postulates. |
HW1: Due Friday January 24 .pdf, .tex |
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| Monday January 20 |
NO CLASS |
NO CLASS | |
| Wednesday
January 22 |
The parallel postulate. |
Chapter 2 | |
| Friday January
24 |
Introduction to LaTex. |
(See the bottom of this webpage) |
HW 2: Due Friday January 24 Chapter 1, Exercises: 1, 2, 3, 6, 9, 10, 12 |
| Monday January 27 |
Misleading diagrams, straight edge and compass constructions. | ||
| Wednesday January 29 |
Logic Introduction to logic. |
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| Friday January 31 |
Theorems and proofs, proof by contradiction. |
HW 3: Due Wednesday February 5 Chapter 1, Exercises: 14, 15. Chapter 2, Exercises: 1, 2, 3. .pdf, .tex |
|
| Monday
February 3 |
Basic logic, cont. |
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| Wednesday
February 5 |
Incidence geometry. | ||
| Friday
February 7 |
Models. | HW 4: Due Monday February 10 Chapter 2, Exercises: 4, 7, 8, 10 (a)(b), 11. |
|
| Monday February 10 |
Homework review |
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| Wednesday February 12 |
Review | Sample Midterm I .pdf |
|
| Friday
February 14 |
MIDTERM I |
MIDTERM
I |
|
| Monday
February 17 |
Affine planes |
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| Wednesday
February 19 |
Projective planes |
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| Friday
February 21 |
Hilbert's Axioms Flaws in Euclid. |
Chapter 3 |
HW 5: Due Monday February 24 Chapter 2, Exercise: 14. Chapter 2, ``Major Exercises'': 1-5. |
| Monday February 24 |
Axioms of betweenness. |
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| Wednesday February 26 |
Axioms of congruence. | ||
| Friday February 28 |
Axioms of continuity. |
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| Monday
March 3 |
Axiom of parallelism. | HW 6: Due Monday March 3 Chapter 3 Exercises on Betweenness: 1-5 |
|
| Wednesday
March 5 |
Neutral Geometry Geometry without the parallel axiom. Alternate interior angle theorem. |
Chapter 4 |
|
| Friday
March 7 |
Exterior angle theorem, measure of angles and segments. | ||
| Monday March 10 |
Sachheri-Legendre theorem. | ||
| Wednesday March 12 |
Equivalence of the parallel postulates. | ||
| Friday March 14 |
Angle sum of a triangle. | HW 7: Due Friday March 14 Chapter 3 Exercises on Congruence: 21-24 |
|
| Monday
March 17 |
Homework review |
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| Wednesday
March 19 |
Review | Sample
Midterm II .pdf |
|
| Friday
March 21 |
MIDTERM II |
||
| Week of
March 24-March 28 |
SPRING BREAK | SPRING BREAK | |
| Monday March 31 |
History of the Parallel
Postulate (Presentations) Proclus, Equidistance, Wallis, Saccheri. |
Chapter 5 |
|
| Wednesday April 2 |
(Presentations) Clairout's Axiom and Proclus' Theoreom, Legendre, Lambert and Taurinus, F. Bolyai |
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| Friday April 4 |
Non-Euclidean
Geometry (Presentations) J. Bolyai, Gauss, Lobachevsky |
Chapter 6 |
HW 8: Due Friday April 4 Presentation writing assignment |
| Monday
April 7 |
Non-Euclidean Hilbert
planes, and the defect. |
||
| Wednesday
April 9 |
Similar triangles, parallels
admitting a common perpendicular. |
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| Friday
April 11 |
Limiting parallel rays,
hyperbolic planes. |
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| Monday April 14 |
Classification of parallels. | HW 9: Due Monday April 14 Chapter 4, Exercises 1, 2, 6, 10, 14 |
|
| Wednesday April 16 |
Independence
of the Parallel Postulate Consistency of hyperbolic geometry. |
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| Friday April 18 | The Beltrami--Klein model |
|
|
| Monday
April 21 |
The Poincare models. |
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| Wednesday
April 23 |
Models, cont. |
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| Friday
April 25 |
Further topics |
HW 10: Due Monday April 28 Chapter 5, Exercises 10, 11, 13 |
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| Monday April 28 |
Further topics |
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| Wednesday April 30 |
Homework review |
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| Friday May 2 |
Review |
Sample Final .pdf |
|
| Monday May 5 |
FINAL
EXAM 8:00-10:00
AM ECCR
151 (Lecture Room) |
FINAL EXAM | FINAL EXAM |