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PMATH 360
Introduction to Geometry
Spring term, 2013

Course Description

Introduction to Geometry, PMath 360, covers elementary properties of two non-Euclidean geometries, the real projective plane and the real hyperbolic plane.

The real projective plane with homogeneous coordinates is introduced as as an extension of the real Euclidean plane with with Cartesian coordinates. Topics include duality, cross ratio, harmonic conjugates, conics and their poles and polars; also included are the theorems of Pappus, Desargues, and Pascal. Other models of the real projective plane are given and finite projective planes are introduced, including the smallest finite projective plane, called the Fano plane.

The construction of the real hyperbolic plane is based on results that arise from the study of inversion with respect to a circle in the plane.

Stereographic projection gives us insights into inversion in the plane, as well as a deeper understanding of imaginary circles in the real plane. and is applied to give a simple proof of the bundle theorem. Inversion in three space also helps to better understand stereographic projection and poles and polars in three space.

Instructor

Professor Dickey often keeps hours in DC 2126 on Wednesday and Friday at 12:30 and on Monday, Wednesday, and some Fridays at 14:30.  He is also available many other times during the week.  Ask for an appointment or drop in.  To find a time convenient for both of you, it may be helpful to look at his schedule which suggests some other possible times.

Email

Professor Dickey may be reached by e-mail at LJDickey@Math.UWaterloo.CA, Mention of the secret password (the course number) in the the subject line of your e-mail to get it through the spam filters. He may also be reached during office hours in DC 2126, or, (whenever he is around), by phone at 888-4567, extension 35557. Voicemail is not recommended.

Course Notes

A set of notes called Non-Euclidean Geometry: Course Notes for PMath 360 by Leroy J. Dickey is available for purchase from Graphic Services. This is the third edition.   The price is well under $20. There are some older editions floating around, but this edition has improvments and additions suggested by last year's users.

Lab

There is a optional one hour Lab held every Wednesday. The assignments for which these labs provide assistence are not optional. Some students are scheduled for 15:30 and other for 16:30.  The recommended software is GoeGebra which is available at no cost from GeoGebra.org.   It is the only geometry package presently known that allows the export of PDF (portable document files) or SVG (scalable vector graphics) images.  This may decrease the pain of pixelation in publications.  Assignments may be done before, during or after lab.  There are some other courses that may be scheduled in the lab from time to time, but there are many open times when you are also permitted to use the lab.  The professor often attends the Lab, but the presence of a lab assistant is not guaranteed.  

Assignments

The assignments are available on-line.

Assignment Due Dates

The assignments are due before the lecture on the Friday following the Lab. 

There will be a drop boxes for this course near room MC 4066 (the Tutorial Centre) on the fourth floor of the Math and Computer building. In recent years we have had boxes 7 or 8, and slots 11 or 11 or 12. Please put your paper in the box and slot that is marked for the course. You might have to get down on your hands and knees to read the labels. Put your paper in the appropriately labelled slot! 

One year papers that were in the wrong slot made their way to our hands us months later.

The plan is that the marked papers will be returned to you the following Wednesday, during the optional Lab or later, in class.

Evaluation

Weekly assignments will count for 10% of your mark. There will be n+1 assignments (n yet to be determined). The best n-1 of the first n, together with the last, will determine the homework component of your mark.

Two midterm tests will each count for 15% of your mark. The dates will be announced in advance.

The final exam will count for 60% of your mark. This will be at a date and time scheduled and annnounced by the registrar.

Normally, a passing mark for the homework and for the final exam are required to earn a passing mark in the course.

There may be an optional final bonus assignment that you may use to boost the homework component of your mark. More about this will appear in the announcements

Announcements

Watch for announcements that will be made from time to time.

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Last update: 2012-06-13