Professor: Jeff Johannes
Section 1 MWF
11:30a-12:20p South 328
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 3:30 - 4:30p South 328,
Tuesday 8:00 - 9:00p South 336, Wednesday 10:30 - 11:20a South 328,
Thursday 4:00 - 5:00p Welles 121, Friday 1:00 - 2:00p South 338, and
by appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Textbooks
Introduction to Topology, Bert Mendelson
Additional notes provided on-line and in
handouts.
Course Goals
- Discuss the fundamentals of general topology (topological
spaces, separability, continuous functions, connectedness, and
compactness)
- Apply them to the fascinating topics of geometric topology
(classification of surfaces and manifolds, knots and links)
- Hint toward more advanced topics in fundamental groups
Learning Outcomes: Upon successful completion of Math 338 -
Topology, a student will be able to:
- Define and illustrate the concept of topological spaces and
continuous functions,
- Define and illustrate the concept of product topology and
quotient topology,
- Prove a selection of theorems concerning topological spaces,
continuous functions, product topologies, and quotient
topologies,
- Define and illustrate the concepts of the separation axioms,
- Define connectedness and compactness, and prove a selection of
related theorems, and
- Describe different examples distinguishing general, geometric,
and algebraic topology.
Grading
Your grade in this course will be based on
presenting problems in class, problem sets and one research project.
Problem sets will be worth 13/20, the project 1/5, and presentations
worth 3/20.
Student Presentations
Every two weeks ending on Wednesdays, each
student must present at least one problem. Problems are to be
selected from the material for that day's section(s).
Discussing problems with classmates or me is highly endorsed.
Presentations will be scored out of at most 4 points. The
class presentations will be graded roughly as follows:
4 excellent
3.5 very good - at most minor errors
3 some problems, but the main idea of the solution
is clear
2 some correct things
1 attempted
0 no presentation
I will determine priority for presenting
problems. Each student who has not yet presented will have
priority over students who have presented. A second (or more)
problem may be presented in order to replace a prior presentation.
Problem Sets
Problem sets will consist of 5-10 questions
related to material presented in the previous two weeks. They
will be due two weeks after assigned. They will consist of
assigned problems not presented by students in the prior two
weeks. Before these papers are handed in, I
strongly suggest discussing them with me and others outside of
class. Each problem will be graded on a ten point decile
scale based on completeness, accuracy, and writing.
These problems will be evaluated as follows.
0 missing
3 question copied, nothing written
6 something written that appears that it was only
written to take up space
7 substantially incomplete. Something
written, but does not really answer the main questions.
Major errors. Very poor writing
8 mostly complete. maybe a few minor errors
9 complete, no errors, some personal insight,
well-written
10 wonderful
No late problem sets will be accepted.
Solutions and Plagiarism
There are plenty of places that one can find all
kinds of solutions to problems in this class. Reading them and
not referencing them in your work is plagiarism, and will be
reported as an academic integrity violation. Reading them and
referencing them is not quite plagiarism, but does undermine the
intent of the problems. Therefore, if you reference solutions
you will receive 0 points, but you will *not* be reported for an
academic integrity. Simply - please do not read any solutions
for problems in this class.
Final Project
You will write a 1200-2000 word research paper on
a topology topic not covered in class. Selecting the
topic by the deadline will be worth 5%, annotated bibliography will be
worth 15%, the draft will be worth 20%, the 10-12 minute
presentation will be worth 20%, and the final paper will be worth
40%.
Feedback
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for
how the course is running. Remember, the sooner you tell me
your concerns, the more I can do about them. I have also
created a web-site
which
accepts anonymous comments. If we have not yet discussed
this in class, please encourage me to create a class code.
This site may also be accessed via our
course page on a link entitled anonymous
feedback. Of course, you are always welcome to approach
me outside of class to discuss these issues as well.
Accommodations
SUNY Geneseo is dedicated to providing an
equitable and inclusive educational experience for all students. The
Office of Accessibility will coordinate accommodations, auxiliary
aids, and/or services designed to ensure full participation and
equal access to all academic programs, activities, and services at
SUNY Geneseo. Students with letters of accommodation should submit a
letter and discuss needs at the beginning of the semester. Please
contact the Office of Accessibility Services for questions related
to access and accommodations. Erwin Hall 22 (585) 245-5112 access@geneseo.edu
www.geneseo.edu/accessibility-office.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the opportunity to make
up missed work. You are responsible for notifying me no later
than September 12 of plans to observe the holiday.
Military Obligations
Federal and New York State law requires
institutions of higher education to provide an excused leave of
absence from classes without penalty to students enrolled in the
National Guard or armed forces reserves who are called to active
duty. If you are called to active military duty and need to miss
classes, please let me know and consult as soon as possible with the
Dean of Students.
Tentative Schedule subject to change (details will be added as the
semester unfolds - check back)
Date
Topic
Assigned
Due
August 29 Induction, Day 0
31
Day 1, Review M.Chapter
1
PS1
September 2 M3.1-2 (finish the half-paragraph
on p. 73, then skip to Def. 2.4 on p. 74)
7 some M3.3 (just p. 76 starting
with "Given two distinct points ending with the paragraph on the
top of p. 77, then do read questions 3-4, replacing
"neighbourhood" with "open set" )
9 discuss
PS1
PS2
PS1
12 M3.4
(skip p. 81 and Lemma 4.1 on p. 82)
14 M3.5
(skip the top of page 88, before Theorem 5.3, which we will use as
a definition; therefore skip its proof)
16 M3.6
19 M3.7
Project Topic
21 M3.8
23
discuss PS2
PS3
PS2
26 C1.1,4
28 C2.1,2
30 discuss
PS3, C3.1,2
PS4
PS3
October 3
C3.2,3
5 C3.4
7 C4.1
12 M4.2
14 M4.3,
4.4
Annotated
Bibliography
17 discuss
PS4
PS5
PS4
19 M4.5,
4.6
21 replanning
24 discuss
PS5
PS6
PS5
26 M5.2
28 M5.3,
5.4
31 discuss PS6 - choice
November 2 Manifolds
4 M4.7
7 discuss PS7 M4.7/8?
PS7
PS6
9 M4.8
11
Project Draft
14
16
18
21 discuss
PS7
PS8
PS7
28
30
December 2
5
7
9 discus PS8
PS8
12
Project
Paper due
Thursday, December 15 8:30 - 11a Project
presentations