MAT 530: Fall 2010 | ||||||

Home Schedule Syllabus |
## MAT 530
Syllabus: We will cover most of the basic core course syllabus given below. I will also discuss appropriate additional topics, as time permits. Basic point-set topology - Metric Spaces
- Topological spaces and continuous maps
- Comparison of topologies
- Separation axioms and limits
- Countability axioms, the Urysohn metrization theorem
- Compactness and paracompactness, the Tychonoff theorem
- Connectedness
- Product spaces
- Function spaces and their topologies, Ascoli's theorem
- Fundamental group
- Fundamental group of S
^{n}; examples of fundamental groups of surfaces - Seifert-van Kampen theorem
- Classification of covering spaces, universal covering spaces; examples
- Homotopy; essential and inessential maps
Textbook
Your grade will be based upon your performance on the homework and class participation (30%) the mid-term (30%), and the Final Exam 40(%). Incompletes will be granted only if documented circumstances beyond your control prevent you from taking the final exam. Important: Please (pretty please with sugar on top) write up your solutions neatly, be sure to put your name on them and staple all pages. Illegible homework will not be graded. Late homework will not be accepted. You are welcome to discuss the problem with other students and to consult books, but you (and only you and nobody else but you) are responsible for writing the solutions and all your collaborators and sources should be listed. A good guide for writing math is here. I will assume you are familiar with the material in Chapter 1 of Munkress. We will discuss (most of) the material in Chapters 2 through 7 of Munkress, as well as Chapters 9, 11 and 13. Below is a tentative schedule. Homework is due every Tuesday. The list of problems is a lower bound. There is no upper bound. Try to work as many problems as you can. Homework assignments and other useful information regarding the course will be posted regularly on this web-page.
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