MATH GU4051: TOPOLOGY
Fall 2016
The most up-to-date information on this course will eventually be found on the Courseworks page for this course.
Time and place: MW 1:10-2:25, Final exam
Mon 12/19 1:10pm-4:00pm. Locations: Math 520
Lecturer: Walter Neumann (x45074, 616 Mathematics,
Office hours: MW 10-11 and by appointment
Email: neumann@math.columbia.edu,
Home page: www.math.columbia.edu/~neumann).
Prerequisites: You should already have familiarity with writing proofs. A course in Analysis such as Honors Math B of Intro Modern Analysis is strongly recommended. One semester of "Intro Modern Algebra" or equivalent is required, since the second half of the class will use some group theory.
Brief description Topology, the study of topological spaces
and continuous maps, is roughly the qualitative as opposed to
quantitative study of
shape.
The first half of the semester will be mostly
point-set topology and the second half will be an introduction
to algebraic topology using the fundamental group and covering
space theory.
Text: James R Munkres, TOPOLOGY, 2nd edition, Pearson 2000.
Available at the University bookstore; see
also AddALL.
Also recommended are:
Klaus Jänich. Topology. Springer, 1984,1995 Addall
M A Armstrong. Basic Topology. Springer, 1983,1997
Addall
Homework: There will be weekly problem sets, due in the homework box on the 4th floor Mathematics by 1pm on Wednesdays.
Although only a portion of the homework may be graded, you should attempt every homework problem and eventually understand how to do every problem correctly.
You may use any resources you like to solve problems, but any resource other than the textbook must be cited in your homework. This includes other texts, electronic resources such as Google and Wikipedia, help from classmates or helproom staff. In particular, collaboration and discussion with classmates is encouraged, but you must write up assignments individually. Failure to follow these rules appropriately constitutes academic misconduct.
Grading:
Homework 40%Final Exam is centrally scheduled by the University and must be taken at the scheduled time (see above). If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam.
Midterm 25%
Final 35%
Help: My office hours are MW 10-11 or by appointment. Help will also be available without appointment in the Mathematics help room (406 Mathematics).