# Autumn Term 2015 : Topics in Modern Geometry

M.C. Escher, "Circle Limit III", 1959 Woodcut
## Lecturer (Weeks 1-3): Thomas Oliver

Topology

Notes

Some highly recommended supplemental material

Homework, Exercises, and Problems

Fourth Year Potential Projects List

## Lecturer (Weeks 4-6): Jim Stankewicz

Hyperbolic geometry

Notes

Homework 1

Homework 1 Sample Latex File ( edit your answers in as you go along!)

Homework 1 Rubric

Homework 1 Rubric Latex File

Homework 2

Homework 2 Sample Latex File

Homework 2 Rubric

Homework 2 Rubric Latex File

Homework 3

Homework 3 Sample Latex File

Homework 3 Rubric

Please have a look at the book "Fuchsian groups" by Svetlana Katok for supplemental material on Hyperbolic geometry. (The course is essentially based on the first two chapters)

See also:

Notes on the special linear group over the reals and the Iwasawa decomposition

Notes on generating the special linear group over the integers

Fourth Year Potential Projects List

Linear Fractional Transformations revealed

## Practical details

The course will meet at the following times in SM4 of the Main Mathematics Building

Monday at 15:00

Tuesday at 9:00

Thursday at 10:00

There will also be an office hour in 6B of Howard House on Thursdays at 15:00.

If you do a final project, it is expected to be submitted in LaTeX (pronounced Lah-Tech). You might also consider submitting your homework in LaTeX! If you do not have LaTeX installed, you can use your Bristol Google account to use the following service with minimal fuss. It is strongly recommended that you remember when turning in your homework that good mathematical writing is good writing first and foremost. For tips on this, please see the notes of Donald Knuth. Especially recall point number 13: [Y]our sentences should flow smoothly when all but the simplest formulas are
replaced by `blah' or some other grunting noise.