Math 403, Spring 2007 - Euclidean Geometry


Office hours: Thurs. May 3, 1:00-5:00.

The final exam is Tuesday, May 8, 7:00-10:00pm

The final exam covers the entire course. The format will be similar to the other three exams. It will be about a two hour test, but you can use the entire three hours if you wish. For the final, you should be able to prove the following:
*Ceva’s Theorem (either the “if” direction or the “only if” direction – your choice)
*Cauchy-Schwarz inequality
*An isometry with three noncollinear fixed points must be the identity.
*Any isometry can be written as the composition of one, two or three reflections (see pages 2-3 of lecture notes).
This is in addition to other, shorter proofs which are not listed, for example any homework problem, or any theorem which follows fairly quickly from the definitions.

Course evaluations will be filled out in the first 10 minutes of the final exam period.

Note there were two corrections on page 10 of the lecture notes.  The links below are to the corrected versions.

 

Assignments...HandoutsProject...Calendar...Score Reports

Test #1 from 2002Test #2 from 2002..Test #3 Review Questions

Final Exam from 2002….Test #3 SolutionsLecture Notes pages 1-5Lecture Notes pages 6-8Lecture Notes pages 9-12


MWF 12:00-12:50, 345 Altgeld Hall

Instructor: Dr. Karen Mortensen
247 Illini Hall, phone 244-4128, email  kmortens@math.uiuc.edu
Office hours: Wednesdays 2:00-3:00 and Thursdays 1:00-2:00,  and by appointment.

Course webpage: http://www.math.uiuc.edu/~jms/m303

Textbook:  Philippe Tondeur,  Vectors and Transformations in Plane Geometry, Publish or Perish, Inc. 1993.

Prerequisites:  Official prerequisite is Math 241 or Math 242 or Math 243.  In fact the course will use little calculus, but you need about this level of mathematical experience.   Since the course will emphasize definitions, theorems and proofs, Math 247 or similar experience is advised.

Goals:  The course will cover the entire textbook, plus some additional material.  Euclidean geometry is treated using vector methods, rather than purely axiomatically.  Groups of transformations will play a major role in the course.  Students will find significant links with abstract algebra (groups) and with linear algebra.  It is hoped that students will gain an historical perspective and also glimpse some of the modern applications of Euclidean geometry.

Some relevant websites:
http://mathworld.wolfram.com/
http://www.cut-the-knot.com/

Exam dates:

Test #1 - Wednesday, Feb. 14
Test #2 - Monday, March 12
Test #3 - Friday, April 13

Final exam  7:00-10:00 pm Tuesday May 8, location to be announced.  The final exam will cover the entire course. Note:   Please arrange any travel, etc., so that you can take the final on this date.   Math 402 has a "non-combined" final exam.  There will be no conflict exam given except for those few individuals who meet the official university criteria given here in the student code.

Missed exams:  If you miss an exam, you will receive a 0 for your grade.  The only exception is if you have a valid excuse for missing, such as a major illness or a serious emergency - if so, you must inform me before the exam or, if this is physically impossible, then as soon as possible afterwards.  In this case, you will be given a make-up exam as soon as possible.

Problem sets:
Problem sets will be due approximately once a week.  You may work with others on the problem sets if you wish.  However, you should each write up the solutions on your own; to do otherwise will be considered plagiarism.

Problem sets will be graded and returned to you and will count as part of your course grade.

I normally do not accept late problem sets.  If you cannot turn in a problem set on time due to some very unusual circumstances. please contact me as soon as possible.

Individual Projects:  Each student will do an individual project on a topic chosen in consultation with the instructor.  The project will include a written report and also either a class presentation of about 15 minutes or a  poster for an in-class poster session.  Students may work alone or with one other person.  In the case of two people working together, they will collaborate on a single written report and class presentation and both will receive the same grade for the project.

Office hours:  I am happy to meet with you in my office to discuss course material.  During my regular office hours, you can just drop in without an appointment.  I can also meet you at other times - please make an appointment to do so.  I will usually be able to see you within a day or two.  I also answer questions by email.

I am glad to discuss homework problems with you during office hours.  However, I will expect you to have made a good effort to do the problem ahead of time and to bring your scratch work with you.

Calculators: Calculators may be used on problem sets and exams.  No special calculator is need.

Course grade:  Your course grade will be determined as follows:
Test #1 -  15%
Test #2 -  15%
Test #3 -  15%
Final Exam - 25%
Problem sets -15%
Individual Project - 15%

The follow scale describes approximately how the course grades will be assigned.  The instructor reserves the right to adjust this scale slightly (for the whole class, not for individual students):

90%  or above = A+, A or A-
80%-89% = B+, B or B-
70%-79% = C+, C or C-
60%-69% = D
below 60% = F

You will be able to check your homework and exam grades at Score Reports, which is the Math Department's gradebook program.  This will be available beginning approximately two weeks into the semester.  Please check score reports regularly to make sure your grades have been correctly reported and tell me promptly about any errors.  You are responsible for keeping all of your graded work so that any discrepancies in recorded grades can be settled.