Geometry, Math 461

Fall 2008, 12:05 MWF, B135 Van Vleck Hall

Prof. Robert Wilson

I want to thank all of my students over the years for making teaching so wonderful. Thanks to you for putting up with me this semester!
Bob W.

Final Exam: Take home, due Sunday 12/14 at 8 AM.

Here is the exam as handed out

Here is the exam with answers

Midterm Exam: Wednesday, October 29, in class

Here is the exam as given (Except that I have corrected a typo.)

Here is the exam with answers (There can be other correct answers! Please tell me if you find errors in these.)

The exam will go through chapter 3, and the problems will mostly be similar to the ones in the homework assignment on chapter 3 given below.

The textbook is Euclidean and Non-Euclidean Geometries, 4th edition, by Marvin Greenberg. Note the plural "geometries" in the title: we will be studying both Euclidean geometry, which is what you probably perceive as the geometry of the world around you, and other geometries. But "other" does not mean unreal: Some of what we will look at is exactly what is needed to make things like general relativity and modern cosmology work.

Student background: The official prerequisite is Math 234. In practice little specific information from calculus courses will be required, but the "mathematical maturity", the ability to think creatively about things you may not be able to see or measure, will be useful. Most students will have had a course, probably in high school, labelled geometry, but this course should be accessible without it.

Reading assignments:

	For Friday, September 5: Pages xxv through 20
	For Monday, September 8: continue through page 40, i.e. finish Chapter 1
	For Monday, September 15: Pages 53-68 on logic and proof
	For Wednesday, September 17: Pages 69-76 on incidence geometry and models
	For Monday, September 29: Finish Chapter 2
	For Wednesday, October 8: Read Chapter 3
	For Monday, November 10: Read Chapter 4 through "Equivalence of Euclidean Parallel Postulates", ending on page 176
	For Friday, November 14: Finish Chapter 4.

Homework assignments

	For Monday, September 15: Do all of the "Review Exercises" on Chapter 1, starting on 41. These are true/false statements for you to think about, not to be handed in. Also try all of Exercises 1-13, but only write up to turn in exercises 1, 3, 4, 5, 8, 9, and 12.
	For Monday, September 29: End of chapter two, exercises 1,4,6,7,9,13 (starting on page 91) to be handed in.
	For Wednesday, October 8: Write up in detail proofs of Propositions 3.3 and 3.4, found on pages 112-114 in our textbook. The text gives proofs for these. You may take those proofs and "fill in the gaps"; Where the book tersely says something like "(Proposition 2.1)" or "(steps 3 and 8 and the corollary to Betweenness Axiom 4)", spell out how the things this proof is talking about match up with the things named in the proposition, etc. If there is any question as to how the logic works, e.g. if it depends on careful use of one of our logical reasoning rules, explain that. Or, you are welcome to come up with an independent proof for one or both instead of using the book's proof. But your proof also should explain things in detail. There is a judgement call here: "in detail" could run to virtually all of the book so far, and you certainly are not asked for that. What I have in mind could certainly fit on three pages, maybe a little less, for the two propositions together. If possible, please don't go beyond six! (that is not a factorial...)
	For Wednesday, October 22: (postponed to 10/24!) Exercises 1, 6, 15, 17, 20, 24, 32 at the end of chapter 3, i.e. starting on page 146
	For Monday, November 24: (assigned 11/5/08) Problems 1, 2, 3, 5, 6, 7 from the end of chapter four, starting on page 192. Note that this is not due for quite a while: I wanted (a) to get you started so you can use material we cover in class as we cover it, some of the terms used in the problems we have not yet got to, and (b) to give you time to work on it and have a chance to work for a while and ask questions where you can't find your way through.

My office is 411 Van Vleck Hall. My schedule including office hours is available at my website, http://www.math.wisc.edu/~wilson. You can email me at wilson@math.wisc.edu.