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MATH 101/E101: SETS, GROUPS AND TOPOLOGY
Math 101/E101: The goal of this course is to introduce you to
abstract mathematical
thought, through a consideration of several topics – sets,
metric spaces, finite groups and
a little bit of topology. I will stress the unity of areas of
mathematics that include
algebra, geometry, analysis and topology. If you are currently
enrolled in Math 21 or
even Math 1b, and are thinking about concentrating in
mathematics, you should consider
taking this course. It will help to prepare you for the language
and rigor of our other math
courses at the 100 level. A rough syllabus is provided
below.
My contact information:
Cliff Taubes
Science Center room 504
617-495-5579 [email protected].
My scheduled office hours during the semester will be posted to
the course website when
the semester starts. In any event, send me an email to schedule
a chat if you can’t make
these office hours. Also, drop in at other times; if my office
door is even slightly open,
then I am in the room so just knock loudly.
The course website: The website for the course is
https://canvas.harvard.edu/courses/9966
All homework assignments, announcements, handouts and
information about the course
writing projects will be posted at this website during the term.
You should check this
website the day before each class meeting.
Those of you enrolled through Math E101: Take note that this is
not the Math
E101 website. You will need your Harvard ID number to access
this site. I won’t be
using the Math E101 website once the term begins.
Required text books: There are two required text books for this
course, these being
a) The real numbers. An introduction to set theory and
analysis by John Stillwell
(Springer undergraduate texts in Mathematics)
b) A book of abstract algebra, by Charles C. Pinter (Dover
2010 edition).
Stillwell’s book can be downloaded for free from the following
website if you have a
Harvard ID number:
http://link.springer.com.ezp-prod1.hul.harvard.edu/book/10.1007/978-3-319-01577-4
(If you don’t yet have a Harvard ID number, contact me to get a
free copy.) Pinter’s
book is available at the Harvard Coop (and directly from Dover
Press at
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http://store.doverpublications.com/0486474178.html .)
Supplemental lecture notes by me to will be supplied if
needed.
Course meeting times: The course will meet twice per week,
Tuesdays and Thursdays
from 11:30-1pm, with another hour to be scheduled to discuss the
homework problemsand other topics of concern. This extra hour’s
meeting will be run by our course
assistant. The course assistant will also schedule a weekly
office hour.
The course meets in Room 507 of the Science Center at
Harvard.
Homework: There will be a homework assignment each week, which
will be due on the
Thursday of the subsequent week. Collaboration on homework is
encouraged, but the
final write up should be your own. Late homework is accepted
only with my approval.
Email me to ask. All homework assignments will be posted to the
course website on
Sundays during the term. The solutions to the homework
assignments will also be posted
to the website.
Grading: The final grade in the course will be based on the
homework grades (30%), a
midterm take-home writing project/exam (30%) and a final
take-home writing project/
exam (40%). The instructions for the midterm take-home will
be posted to the course
website on Sunday, March 6 and due (in electronic form) on
Tuesday, March 22. The
take-home final instructions will be posted to the course
website on Sunday, April 24 and
it will be due on May 4.
Syllabus: I hope to first cover Chapters 1-5 in Stillwell’s
book, and maybe other partsalso. These chapters of Stillwell’s book
constitute a thorough introduction to both
analysis and point set topology; and I will be teaching these
topics intertwined. The
material in Stillwell’s book occupy (roughly) the first six or
seven weeks of the course.
The plan for the second half of the course is to cover Chapters
1-16 in Pinter’s book.
These chapters in Pinter’s book constitute a very nice
introduction to group theory and
some of its applications.
