Non-Euclidean Geometry, spring 2007


For the oral presentations, the class will take place in Hodson 315 on Monday 4/16 and Tuesday 4/17, and in Hodson 305 on Wednesday 4/18.

Homework assignment for this week: 

Calendar, instructions, references for your junior research project here.

Week 10: Review chapter 7 and read chapter 8.

Quiz #1 with solutions.

A list of possible topics for your junior research project, second draft.

Week 6:-Read sections 7.4-7.6.
-Do exercises 7.10, 7.11, 7.12, 7.18 and 7.29. Hint for 7.18: start by proving the following fact: if two circles don't intersect, there exists an inversion which sends them to two concentric circles (be careful and remember that when an inversion sends a circle to a circle, the center of the image is not the image of the center). This fact can be proven without any calculations.

Week 4:-Finish exercise sheet #1.
-Read sections 6.1 and 7.1-7.4. Do exercises 7.1-7.5.

***THE UNIVERSITY IS CLOSED TODAY 2/14*** I will need your homework in my office (Krieger 222) before tomorrow Thursday 2/15 noon, so that you can get it back on Friday.

Week 3: After reviewing the basic material on groups in your favorite book, do the following exercise sheet #1. You should hand in all but question 2)2)d) (which is for next week) in class on Wednesday.

Week 2: The homework for this week is to review (well) the material we've covered, ie an introduction to groups. Next week we will have covered enough material to have a proper exercise sheet. You will probably need to study the material on groups in another book. Any algebra book for undergraduates will do; I have personally checked the following:
- Abstract algebra, by David Dummit and Richard Foote (3d ed., Wiley)
- Groups and geometry, by Peter Neumann, Gabrielle Stoy and Edward Thompson (Oxford Science Publications)
... and the classic treatises by Nathan Jacobson or Serge Lang (harder to read). I have copies of all these in my office, which you can borrow whenever you want.

Week 1: Read the introduction and sections 1.1-1.7 and 1.9-1.11 of the textbook. You will be expected to know the notions and results from these sections.

Lectures:  Monday, Tuesday, Wednesday at 1 in Shaffer 202, Professor Paupert.

Textbook:  A Survey of Classical and Modern Geometries by Arthur Baragar.
Additional references will be given as we go along, for certain specific topics.

Material:  The material we will cover in this course should roughly correspond to (parts of) chapters 5-11 of the textbook, though not in that order. If time and motivation permit, we will add some topics.

Prerequisites:  You don't need to know much before taking this course (hopefully you will know more after you take it). You should however be familiar with plane Euclidean geometry (sections 1.1-1.11 of the book are a minimum; we will review the laws of sines and cosines), and basic linear algebra (mostly 2 by 2 and 3 by 3 matrices). All new concepts will be introduced from the beginning (please let me know whenever something is entirely new to you...except plane Euclidean geometry and 2 by 2 matrices).

Homework:  Assignments will be given on-line each week, usually by Tuesday. The homework problems need to be done in order to develop command of the material. In writing up any problem, you must show all the steps leading to your solution. A few problems are to be submitted at the beginning of the lecture the following Tuesday. Selected problems will be graded by your TA and returned in Section the following Friday. No late homework will be accepted.
If some of you are interested in giving an oral presentation in class, I will give a list of possible themes (but you can choose your favorite topic...somewhat related to geometry). I would especially recommend this if you intend to teach or go to grad school.

Exams:  There will be one or two (possibly take-home) exams, and the final grade will be some mix of the homework and exam grades. In this kind of course, you shouldn't worry about your grade if you follow the lectures seriously and do the homework.

Office hours:  Tuesday from 3pm to 5pm in my office, Krieger 222. If you can't make it, write me an email at paupert@math.jhu.edu, or call 410-516-5132 to schedule an appointment.
In addition, there are pooled TA office hours in the Math help room, Krieger 213, in which the Math department TAs are on duty in shifts. The hours are Monday-Thursday 9am-9pm and Friday 9am-5pm.

A word from the Ethics Board:  The following text is quoted from the Academic Ethics for Undergraduates guide:
"Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies. Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.(...) On every exam, you will sign the following pledge: I agree to complete this exam without unauthorized assistance form any person, material or device. [Signed and dated] For more information, see the guide on Academic Ethics for Undergraduates and the Ethics Board web site (http://ethics.jhu.edu)."