Official Course Description

Euclidean and non-Euclidean geometries. Affine geometry, projective geometry. Transformations and transformation groups.

Prerequisites

MAT1302/1702 or MAT1341/1741.

Course Text

The course lectures are based on various textbooks. It is important to follow the course notes which will be uploaded on Virtual Campus. The following textbook will be used as the main reference:

• Jennings, G. A., Modern Geometry with Applications, Springer, 1997.

Another auxiliary reference is Geomety by David A. Brannan, Matthew F. Esplen and Jeremy J. Gray.

How to Succeed in MAT2355

You will likely find MAT2355 to be different from first year math courses. The biggest difference is that in this course we will emphasize conceptual understanding over computation. The course material includes many mathematical proofs. If you are not comfortable with mathematical proofs, this course is not for you.

Homework assignments and tests will also require students to do proofs. The best way to learn the course material and get used to mathematical proofs is to do as many exercises as possible. It will be very hard to learn the material passively – you must take an active role in your learning. Students who wish to succeed are advised to do the following, starting from the beginning of the course:

• Read the section/notes for each lecture before the following class. Each lecture is based on the material that has already been taught in previous lectures. Make sure you do not fall behind!
• Do the recommended exercises for each lecture after each class and before the next class. Try not to fall behind. If you find some of the exercises difficult, come to office hours. Since homework problems will often be closely related to the recommended exercises, you will also have a head start on the homework.
• When your homework is returned to you, study it again to learn from your mistakes. Look at the posted solutions and see where you went wrong. Even for the questions you got right, you should look at the posted solutions. There is often more than one way to solve a problem. Learning the ideas of a different approach can be helpful in solving another problem.