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.