Instructor: Terence Tao, MS 5622, ph. 206-4844 (tao@math.ucla.edu)

Lectures: MWF 11-12, at MS 5138

Sections: Th 11-12, at MS 5138

Office hours: Monday 2-3, Tu 10-12, or by appointment.

TA: Vrej Zarikian, MS 6617F (zarikian@math.ucla.edu)

TA Office hours: Tu 12-1,Th 12-1

Textbook: Introduction to Topology, T.W. Gamelin and R.E. Greene, Second Edition, Dover.  We will follow the textbook closely; it is strongly recommended that you read the textbook concurrently with the lectures.

Homework: Homework will be due Friday afternoons (in Vrej Zarikian's mailbox) and returned in section meetings. There will be nine assignments. Each homework will consist of about ten problems, most of which will be from the textbook. Only three of the questions will actually be graded; two of which will be of average difficulty, and one of which will be of high difficulty (these questions will be indicated in the homework assignments by an asterisk).

The assignments will be quite challenging, and will require a fair amount of thought.  Being able to get six or more of the questions on your own is already a very substantial achievement.  Doing the homework is very important to the understanding of the course, so don't skimp on it!

Many of the questions will require you to prove an abstract result. It is expected that you provide a reasonably rigorous mathematical proof, or at least an outline of such a proof. Most proofs should consist of a number of mathematical statements interspersed with logical connectives, definitions, verbal arguments, and citations of standard theorems. Presentation and logical structure will be important; you must convince the grader that you know what you are talking about, and that your statements are arranged in an intelligent and logical order, and come with an adequate explanation of the critical steps. Steps which are tedious but straightforward can be skipped or merely sketched, and this is acceptable (and even encouraged) so long as it is clear that you could in principle work out the step in detail. A verbal explanation relying on intuitive concepts or on a sketched picture is worth partial credit, but be warned that intuition is often wrong in topology, and that pictures are sometimes misleading; even experienced mathematicians fall into these traps occasionally. Finally, you should be aware that some responses fall short of a proof; for example, to prove a universal statement (e.g. all compact sets are closed) it is not sufficient to provide a single example of a compact closed set.

Late homework will not be accepted, however it is possible to miss one assignment without affecting one's grade (see below).

Examinations: There will be one mid-term during the course, on Friday, April 28, 11am-11:50 am, as well as a final examination on Tuesday June 13, 11:30am - 2:30am.

The examinations will be open-book, open-notes; all written materials are allowed. Calculators are permitted, but are unlikely to be useful.    No consultation with third parties is allowed.

Grading: The final grade is based on the homework (15%), mid-term (40%), and the final examination (45%). Only the best eight homework assignments will be counted (i.e. the lowest score will be dropped).

If you cannot make one of the examinations, contact me on or before the day of the exam to arrange a meeting. If you have a very good excuse for missing the exam, and your progress in the rest of the course is good, it should be possible to find a satisfactory solution.

World-Wide Web: You are encouraged to visit the web-page for this section at

http://www.math.ucla.edu/~tao/resource/general/121.1.00s