Instructor. Dr. Marta Lewicka (office hours in Thackeray
408, Tuesday 4:00 - 5:00pm, or by appointment)
Textbook.
James Munkres: Topology (2nd Edition)
Prerequisites. The course covers the rudiments of
point-set topology as well as a variety of techniques and
applications from geometric and algebraic topology.
Prerequisite is: MATH 0420 or MATH 0450.
If you do not feel comfortable with the prerequisite material,
please contact the instructor
in the beginning of the course.
Grades. Exam grading is curved.
Grades will be based on two midterms (25% + 25%) and the final exam (50%).
There will be no make up midterm exams. If you miss the midterm exam
for a *documented* medical reason, your grade on it will be the prorated grade of your final exam.
Incompletes will almost never be given,
and only for cases of extreme personal tragedy.
Homework. Homework will be assigned each Thursday
(starting in the first week of the semester) and it will consist of
suggested problems from the textbook. Homework will not be collected
or graded. You are advised to collaborate and discuss the problems
with each other and with the instructor during office hours.
Core topics.
The course covers the rudiments of point-set topology as well as a
variety of techniques and applications from geometric and algebraic
topology. Highlights of the course will include: Urysohn's lemma,
Tietze’s extension theorem, Thychonoff’s theorem, the Heine-Borel
theorem, Brower’s fixed point theorem, the Jordan curve theorem, the
classification of compact surfaces, the Euler characteristic, the
Borsuk-Ulam theorem, the Lusternik-Schnirelmann theorem.
Calendar.
7 Jan (Tue): First Class
11 Feb (Tue): Midterm 1.
11, 13 March (Tue, Th): Spring Break -- no class
25 March (Tue): Midterm 2.
17 Apr (Tue): Last Class Final Exam: 26 Apr (Sat), 10:00am-11:50am, 525 Thack