Math 348 - Topics in Geometry
May 2012
This is a cross section of the Hopf Fibration. Click here for a great video of the entire thing!
May 2012
This is a cross section of the Hopf Fibration. Click here for a great video of the entire thing!
- Course Outline
- Further Reading
- Assignments:
- Assignment 1
- Assignment 2
- Assignment 3
- Bonus Assignment
- If ever you are stuck on your assignment and don't know what to do, this link should help
- Midterm:
Sample midterm
- Final Exam: This has been schedualed and will take place on Friday, June 1 at 2 pm.
Sample Final
- TA information: Juan Ignacio Restrepo - can be emailed at jignacio1985 at gmail dot com.
- Course Notes:
Week 1 - Euclidean Geometry
- Lecture 1 - Euclid's Elements
- Lecture 2 - Triangles and Cricles
- Lecture 3 - Triangle Centers
- Lecture 4 - Geometric Gems
Week 2 - Symmetry in Geometry
- Lecture 5 - Isometries
- Lecture 6 - Symmetry and Group Theory
- Lecture 7 - Symmetry in the Plane
- Lecture 8 - Crystals, Friezes and Wallpapers
Week 3 - Polyhedra, Graphs and Surfaces
- Lecture 9 - From Polyhedra to Graphs
- Lecture 10 - Platonic Solids and Beyond!
- Lecture 11 - Surfaces and Topology
- Lecture 12 - Classification of Surfaces
Week 4 - Group Theory and Linear Algebra
- Lecture 13 - Triangle groups
- Lecture 14 - Complex numbers and Quaternions
- Lecture 15 - Review and Questions
- Ruler and compass constructions - Here you will find an animated image of the construction of a hexagon, pentagon and square. You may have to watch this several times because its too quick!
- Pythagorean triples and rational points on a circle
- Ptolemy's Theorem - This result was used by our special guest Fermat in the construction of the Fermat point of a triangle.
- Hyperbolic geometry and Einstein's rotating disk thought experiment - This is a very easy to watch short lecture given by Dr. Richard Epp at the Permiter Institute in Waterloo, Ontario. This guy is awesome and is largely the reason I study geometry today. Check out more of Richard Epp here.
- The Hopf Fibration