MATH 4431
Introduction to Topology
Fall 2014
TThu 9:35-10:55 Skiles 271
INSTRUCTOR
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Stavros Garoufalidis
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Room 105, Skiles
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Telephone: 404-894-6614
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email
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Office hours: Wed 3:30-4:30 or by appointment.
GRADER
TEXTBOOK
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James Munkres, Topology (2nd Edition), Prentice Hall.
COURSE DESCRIPTION
We plan to give a self-contained course in point set topology, after
introducing the relevant concepts of set theory and logic. This is a course
with proofs, and abstract mathematical concepts (such as topological spaces,
compactness, continuity). Despite its abstraction, topological spaces and
continuous maps are very useful in applications, and form the background
of applied mathematics. We promise to give proofs, examples and
counter-examples of many theorems. A goal of the course, aside from topology,
is to learn what is a mathematical proof, and how to present it. This
requires basic mathematical maturity, and familiarity with math 4317.
WHAT IS A PROOF?
See
a note by Chris Heil.
PREREQUISITES
MATH 4317.
HOMEWORK
Homework will be due on Thursdays, collected in the beginning of the class,
and returned back to you the following Tuesday. I will not be assuming that
you know how to think, write and present a mathematical proof, but achieving
this by the end of the semester, will be an important gain for the class.
You are welcomed to work together, but please write down your homework
separately . Please staple your homework, and write clearly, each
problem on a new page. The two lowest homework grades will be dropped. Any
missed homework will be counted as zero.
MIDTERM-EXAMS
There are two in-class midterm exams on Thursday September 25 and Wednesday
November 6. I do not accept make-up exams unless there is a serious
documented reason. The first midterm will cover sections 1.1-2.17. The
second midterm will cover sections 2.18-3.25 (including 3.25).
FINAL EXAM
Conflict in final exams means having 3 final exams in the same day. In that
case, you can reschedule the one in the middle. In case of a final exam
conflict, I need a two week advance notice to accomodate your
request.
ATTENDANCE
Although attendance is not mandatory, you are strongly encouraged to attend.
Students who do not attend
the lectures statistically do below average--and usually end up with a C or
lower grade. Attendance is an important part of learning. During the
lectures, you should turn all powered devices (including phones, laptops,
music players) off.
GRADES
The final course grade will be calculated according to the
following scheme:
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Homework : 15 %
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Midterms : 2 x 20 %
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Final Exam : 45 %
If the average course grade (out of 100) is
- at least 80, then you will get an A,
- at least 70, then you will get an B,
- at least 60, then you will get an C,
- at least 50, then you will get an D,
- less than 50 or your final exam grade is
less than 40, then you will get an F.
ACADEMIC HONOR CODE
All students are required to review and accept the Honor Code
of Georgia Tech, which may be found
here.
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You are not allowed to use calculators, formula sheets, notes or texts
during the midterms and final exams.
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Identification is required in taking tests.
ACADEMIC CALENDAR
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September 1, School Holiday.
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September 25, Midterm I.
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October 10, Last day to withdraw with W.
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October 11-14 Fall recess.
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November 6, Midterm II.
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November 27-28 School Holiday.
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December 5, Last Day of classes.
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December 9, Final Exam. Tuesday 8:00am - 10:50am
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December 15, Grades available.
HOMEWORK ASSIGNEMENTS
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Homework 1 Due Thursday Sep. 4 in the beginning of the class.
Sec. 1.5: 4,5. Sec.1.6: 1b,3,5,6.
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Homework 2 Due Thursday Sep. 11.
Sec.1.7: 6. Sec.1.9: 2,3. Sec.2.13: 7,8.
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Homework 3 Due Thursday Sep. 18.
Sec.2.16:3,8,9,10.
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Homework 4 Due Tuesday Sep. 23.
Sec.2.17:8,9,13,18,20.
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Homework 4 Due Thursday Oct. 2.
Sec.2.18:2,6,8,9,13.
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Homework 5 Due Thursday Oct. 9.
Sec.2.19:8. Sec.2.20:2,4,5.
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Homework 6 Due Thursday Oct. 16.
Sec.2.21:3,4,6. Exrta problem: Let X denote the set of rational numbers.
If r is a rational number, it is a product of powers of primes, with
exponents positive or negative. Let v_2(r) denote the exponent of the prime 2.
Define ||r||_2 = 2^(-v_2(r)), and d_2(r,s)=||r-s||_2. Prove that (X,d_2)
is a metric space. Describe the ball of center 0 and radius 1.
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Homework 7 Due Thursday Oct. 23.
Sec.2.21:7,8,9,11.
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Homework 8 Due Thursday Oct. 30.
Sec.2.22:2,4,5. Sec.3.23:2,3,5,6,7.
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Homework 9 Due Thursday Nov. 13.
Sec.3.24: 2,3,9. Sec.3.25:2. Sec.3.26:1,7,12. Sec.3.27: 4,6. Sec. 3.28: 6,7.
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Homework 10 Due Thursday Nov. 20.
Sec. 4.30: 6,11,12. Sec.4.31: 1,5. Sec.4.32: 1.
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Homework 11 Due Tuesday Dec. 2.
Sec.4.34: 7. Sec.4.35: 2. Sec.4.36:2,3,5.