MATC 25 (A survey of Modern and classical geometries ) Fall 2006

Course Description

This course is a survery of Euclidean and Hyperbolic geometries, with particular emphasis on hyperbolic geometry

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Course Text

A Survery of Classcial and Modern Geometries

• Instructor: Yi Lin
• Office Location: S642 
• Office Phone:   
• Office Hours: F 10:00-11:00 , 12:00-1:00 
• Email: mailto:yilin@math.toronto.edu

Grader: Matthieu Willems
mailto: mwillems@math.toronto.edu

• Homework

Homework problems will be assigned bi-weekly and will be due each Friday.
They are supposed to be turned in during the class. If you want to turn in your hw outside the classroom, please have your homework dated, put it into an envelope and slide it under the door of my office, H 507 A, by 3:00 PM Friday, Please also attach a short note which briefly states the reason why you can not make it in the class.

The homework assignments are all posted at http://www.math.toronto.edu/~yilin/hwmatc25.html.
The grader will grade a selected number of the submitted homework problems.

• Exams
  Solotion to the mideterm

  Go check your own score for the midterm

  Review of MATC 25

• Grading Policy:

Grades will be computed according to the following percentages:

• Policies regarding late assignments:

  Late homework will be accepted only if arrangements have been made with me before the deadline. However, exceptions can be made in other cases, for example, for documented medical or family emergency. At the end of the semester I will drop the lowest two homework scores.

  No make-up exams will be given. If a midterm exam is missed because of a serious and documented illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.

  If you have a conflict with any of these dates, particularly with the date of the final exam, please contact me to discuss the matter as soon as you are aware of the conflict.

• Resources:

If you have questions regarding the course material at any time during the semester, you are encouraged to send email. It is not always easy to explain mathematical concepts via email, however, so if your question is a mathematical one, you should probably ask me in person during my office hours.

• Student feedback:

I am interested in your opinions on how the course is progressing, aspects which you feel are particularly helpful and those which you feel could be improved. For this purpose I have specifically created a Yahoo group.
You may submit comments and raise mathematical questions regarding the course.

• Schedule of Topics

  (Note: This schedule is tentative and may be revised at a later date.)
  

  Week of	Topics	Remarks
  September 11	1.2:   The axioms of Euclidean Geometry
  September 15	1.3 :   SSS, SAS,and ASA 1.4:  Parallel Lines
  September 18	6.1 :   Models   6.2:  Results from Neutral Geometry
  September 22	6.2:    Results from Neutral geoemtry   6.3:   The Conguence of Similar Triangles   6.4:  Parallel and Ultraparrallel Lines
  September 25	6.5:    Singly Asymptotic Triangles
  September 29		-
  October 2
  October 6	Doubly and Triply Asymptotic Triangles
  October 13	7.1:    The Poincare Upper plane Model 7.2: Vertical ( Euclidean ) Lines 7.3 : Isometries;
  October 16	7.4 : Inversion in the Circle
  October  20	7.6 : Fractional linear transormation
  October 23	7.7: The Cross Ratio
  October 27	Midterm
  October 30	7.8: Translations
  November 3	7.9 : Rotations 7.10 : Reflections
  November 6	7.13 : Lengths
  November 10	7.12 : The Axioms of Hyperbolic Geometry 7.13 : The area of triangles
  November 14	A survey talk of three dimensional Hyperbolic geometry by some expert (tentative)
  November 17	7.14 : The Poincare Disc Model 7.17 : Circles and Horocycles
  November 20	Hyperbolic Trigonometry