Tuesdays and Thursdays 2:55–4:10, Malott Hall 406 Synopsis. Topology could be described as qualitative geometry. It concerns essential features that are unchanged on stretching or bending a space. The course will begin with what is known as point–set topology. We will introduce the abstract notion of a topological space, give an assortment of examples, are discuss properties a space may enjoy such as connectedness and compactness. We will then venture into basic algebraic topology, where topics may include the classification of surfaces (such as the Klein bottle and Möbius band), elementary knot theory, the fundamental group, covering spaces, and fixed–point theorems. Some of the theory will be developed via the homework and students will be asked to present some of their answers in class. As explained in more detail here, towards the end of the course students will be asked to write short papers on supplementary topics in topology. |  |
Homeworks
| 1. Due 1st September | Solutions | |
| 2. Due 8th September | Solutions | |
| 3. Due 15th September | Solutions | |
| 4. Due 22nd September | Solutions | |
| 5. Due 29th September | Solutions | |
| 6. Due 15th October | The final problem is based on these notes by Ken Brown on Tychonoff's Problem. | |
| 7. Due 20th October | Solutions | |
| 8. Due 27th October | Solutions | |
| 9. Due 3rd November | Solutions | |
| 10. Due 10th November | Solutions | |
| 11. Due 17th November | ||
| 12. Due 1st December |
The lowest homework score will not count. (After all, everyone has a bad week.) Extensions and other allowances are likely to be available in the event of illness or other serious circumstances — please contact your instructor.
Office Hours
| Tim Riley | Mondays 1pm–3pm | Malott 401 | |
| Andrew Marshall | Mondays 12pm–1pm | Malott 218 | |
| Tuesdays 1pm–2pm | Malott 218 |
Exams
| Midterm | 1st October | in class | The exam | The solutions | |
| Final exam | Wednesday 16th December, 7pm | location t.b.a. |
Make–up exams or other accommodations may be made in the event of illness or other serious circumstances — please contact your instructor as early as possible.
Practice Exams — Warning: past exams are likely to differ both in style and subject matter to this year's exams.
| Midterms | 2006, 2007 | |
| Final | 2006, 2007 |
Grading. Homework will count 22%, the midterm 14%, the essay 18%, and the final 46%.
Prerequisites. A linear algebra course (MATH 2210, 2230, 2310 or 2940) and at least one MATH course numbered 3000 or above, or permission of the lecturer.
Principal text. Students are not required to purchase a textbook: the course is not based on any one source and all course material will be presented in class or via problem sets, and there are many good free resources on the subject on the web (some listed below). However, a recommended text is —
- J. R. Munkres, Topology, 2nd Edition
Further reading
- G. K. Francis and J. R. Weeks, Conway's ZIP Proof (of the classification of surfaces)
- A. Hatcher, Notes on Introductory Point-Set Topology
- W. A. Sutherland, Introduction to Metric and Topological Spaces
- O.Viro, O.Ivanov, V.Kharlamov, N.Netsvetaev, Elementary Topology