Math 5335: Geometry I

Fall 2001

Prerequisites: Linear algebra (e.g. Math 2243, 2373, or 4242)
and multivariable calculus (e.g. Math 2263, 2374, or 2574).
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Classes: Tues-Thurs 1:25-3:20 pm in Amundson Hall 116.  
Office hours: Mon-Wed 10:10-11:00 AM,
Tues 3:35-4:25 PM, and also by appointment.  
Course content: This is an advanced undergrad course on Euclidean geometry of the plane, and an introduction to 2-dimensional hyperbolic geometry. Aside from learning all sorts of things about the usual planar geometry, we'll find out what it's like living in the brave new world of hyperbolic geometry in the plane. In this world, given any line and a point not on it, there are exactly two lines passing through this point parallel to the first line! Bring along your intellectual curiosity.

(The second semester continuation, Math 5336, deals with Euclidean geometry in 3-dimensional space, and projective geometry).
Required text: There is no published text, but a required set of course notes:
Geometry I, by Prof. B. Fristedt
These notes are available for $26.50 from bin number 1 at Alpha Print in Dinkytown
(1407 4th St. SE, (612) 379-8535).
Our plan is to follow these notes, mostly sequentially, covering much (but not all) of it.
Other useful texts:
(On reserve in Math Library,
3rd floor of Vincent Hall)
The Poincare half-plane : a gateway to modern geometry, by Saul Stahl.
Jones and Bartlett, 1993.
A course in modern geometries, by Judith N. Cederberg.
Springer-Verlag 1989.
Euclidean and non-Euclidean geometries : development and history , by Marvin Jay Greenberg.
W. H. Freeman 1980.
Homework: There will be homework assignments due every week (except weeks with exams) at the beginning of the Thursday class, starting with Thurs Sept. 13. The assignments will be problems from the course notes, and I will try to write up solutions for the ones whose solution is not in the back. Late homework will not be accepted. I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.  
Exams and grading:  There will be three 50-minute in-class midterm exams on the Thursdays listed below, each worth 15% of the course grade. There will be a two-hour final exam 4-6 PM on Thursday Dec. 20 (in a room to be announced) worth 25% of the course grade. The remaining 30% of the course grade will be based on the quality and quantity of homework turned in.  
Policy on incompletes:  Incompletes will be given only in exceptional circumstances, where the student has completed almost the entire course with a passing grade, but something unexpected happens to prevent completion of the course. Incompletes will never be made up by taking the course again later. You must talk to me before the final exam if you think an incomplete may be warranted.  
Other expectations  This is a 4-credit course, so I would guess that the average student should spend about 8 hours per week outside of class to get a decent grade. Part of this time each week would be well-spent making a first pass through the material in the course notes that we anticipate to cover in class that week, so that you can bring your questions/confusions to class and ask about them.
Homework assignments
Assignment Due date Problems
1 Tues 9/18 (due date moved) Section 1.6 # 4, 19, 24, 27, 28, 61, 63, 68
2 Thur 9/27 Section 1.6 # 36, 35, 56, 72, 73, 76
Section 2.12 # 1,6,7
Midterm I Thur 10/4 in-class
3 Thur 10/11 Section 2.12 # 13, 19, 26, 52, 60, 92, 94
4 Thur 10/18 Section 3.4 # 1, 8, 14, 16, 17, 43, 45
Midterm II Thur 10/25 in-class
5 Thur 11/1 Section 3.4 # 13, 27, 30, 32, 34, 35, 48
- Thur 11/8 No assignment
6 Thur 11/15 Section 4.11 #1,6,12,29,36,(#40 removed),42,62,65
(Note: in #12, use any method, not necessarily (4.9)
as asked for in the notes)
Thanksgiving Thur 11/22
Midterm III Thur 11/29 in-class
7 Thur 12/6 Section 5.9 # 3,9,11,17,22,24,37,44,45
8 Thur 12/13 Section 6.6 # 5,6,8,12,23,27,31,46
Section 7.3 # 8,14
Final Exam Thur 12/20, 4-6 PM In Ford Hall B10 (not in our lecture room!)

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