Instructor: | Harm Derksen 3066 East Hall (734) 763 2309 hderksen@umich.edu |
Office hours: | Monday 2pm(changed), Wednesday 11am, Friday 1pm. |
Time: |
Monday, Wednesday, Friday, noon-1:00pm 1084 East Hall |
Grade: | Midterm Exam 1 (20%), Midterm Exam 2 (25%), Final Exam (40%), Homework (15%). Calculators will not be allowed in the exams (nor would they be useful). 90% overall score is an A- or higher, 80% overall score is an B- or higher, 65% overall score is an C- or higher. You may work together on homework assignments, as long as you write up your own solutions. |
Book: | Marvin Jay Greenberg Euclidean and non-Euclidean geometries 4th edition We will try to cover Chapters 1-4, and parts of Chapter 5 and Chapter 9. |
Exams: | Midterm 1: October 10, in class. Midterm 2: November 12, in class final: December 16, 1:30-3:30pm (may be shorter), place TBA |
Homework: |
homework 1, due September 22. homework 2, due October 1 (deadline extended), homework 3, due October 8. Midterm 1 solutions homework 4, due October 24. homework 5, due November 7. homework 6, due November 26. Midterm 2 solutions Final exam solutions |
September 19: | affine and projective geometries, examples, real projective geometry. |
September 22: | homework 1 due, we discussed real projective geometry, the construction of other projective geometries and duality in projective geometry. We also discussed Pappus' theorem and Desargue's theorem. |
September 24: | Review of Chapter 1, Chapter 2, logic and proofs. |
September 26: | Review of projective and affine geometry. |
September 29: | We'll start with Chapter 3. Hilbert's axiomatic approach, in betweenness. |
October 1: | We'll continue with Chapter 3, ``in betweenness''. Homework 2 due. |
October 3: | In betweenness, Pasch's theorem. |
October 6: | The crossbar theorem. Start reading ``congruence'' |
October 8: | We will discuss exercises in preparation of the midterm. |
October 10: | Midterm 1, in class. Topics: Chapter 2, and Chapter 3, ``in betweenness''. You don't need to learn all the axiom's by heart. I will give them to you. But you do need to know how to use them! |
October 27: | We finish Chapter 3, and start with Chapter 4. |
October 29: | read Chapter 4, up to page 168. |
November 7: | Euclidean parallel postulates. From now on, homework solutions will be distributed by email and/or in class, and will no longer be posted on this website. |
November 10: | Review |
November 12: | Midterm 2, Chapter 3, Chapter 4, up to (and including) "measures of angles and line segments". You should also know that in a Hilbert plane, the sum of the angles in a triangle is at most 180^{o}. |
December 9: | Last class (taught by Ryan Kinser). |
December 7-December 14: |
I will be away, but I should be able to answer emails with questions.
You can also contact Loren Spice, who is also teaching this course (lspice AT umich DOT edu, 1851 EH, 763 2423). His course page is: http://www.math.lsa.umich.edu/~lspice/class/431/F2008/ |
December 15: | Question and Answer session, time and place to be announced. |
December 16: | Final Exam, 1:30-3:30, 1084 East Hall. Chapters 2,3,4. You also need to know and understand the definition of Poincare's half-plane model(see page 307). |