SUNY at Stony Brook MAT 530:
Fall 2010

MAT 530

Instructor: Moira Chas
email moira at
Office: 3-119 Math Tower
Office hours:
  • Tuesday 9 to 10am P 143 Math Tower
  • Thursday 10:30 - 12:30 in 3-119 Math Tower.

: Mathew Wrotten
email matthew.wroten at
Office: 2-120 Math Tower.
Office hours:
  • Tuesday and Thursday 5-6 at MLC
  • Monday 4-5 2-120 Math Tower.

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
Introduction to algebraic topology
  • Fundamental group
  • Fundamental group of Sn; examples of fundamental groups of surfaces
  • Seifert-van Kampen theorem
  • Classification of covering spaces, universal covering spaces; examples
  • Homotopy; essential and inessential maps


Textbook: J. Munkres, Topology,
2nd edition, Prentice Hall, 1999.
Algebraic Topology
For the second part of the course, we will also use
A. Hatcher, Algebraic topology,
Cambridge University Press in 2002

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.

The most efficient method to contact me is by email (moira at This is also the best method for making appointments outside normal office hours.

Stony Brook University expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws as well as University regulations; and to respect the rights, privileges, and property of other people. Faculty must notify the Office of Judicial Affairs of any disruptive behavior that interferes with their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information regarding any disability will be treated as strictly confidential.

Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.