Spring 2008

MATH 415:  TOPOLOGY

(1:00 – 1:50 MWF     McInnis 121)

 

Dr. Nicola McLallen

Email:  nmclalle@eastern.edu

Office: McInnis 216

Office Phone:  5079  (610-225-5079)

 

Office Hours: Mon, Wed, Fri 11 – 11:30 am; 2 – 2:30 pm

 

 

 

Course Prerequisites: Math 240 (Discrete Mathematics).

 

Course Description: This course is an introduction to topology.   It will provide a basic introduction to the definitions and concepts of point set topology, and a brief introduction to algebraic topology (homotopy and the fundamental group).

The course will cover

  • definitions of topological spaces and metrics
  • examples of topologies on a given space – order topology, product topology, subspace topology, metric topology, quotient topology
  • open and closed sets, limit points and continuity in a topological space
  • connectedness and compactness
  • homotopy and the fundamental group.

 

Course Objectives: Upon completion of this course, students should be able to:

1.      Demonstrate an understanding of the fundamental definitions and theorems of point set topology.

2.      Define, construct examples of, and explore properties of topological spaces and metric spaces.

3.      Write mathematical proofs and reason abstractly in exploring properties of topological spaces.

4.      Define and compute the fundamental group of a given topological space.

 

Text: Topology, point set and geometric by Paul L. Shick.

 

Attendance Policy: Attendance is absolutely essential to success in this class. You are expected to attend every class; please notify the professor if you know you are going to be absent.  All exams must be taken at the scheduled time. 

 

Student Disability Policy: If you have any documented special educational needs, you are encouraged to work with the Cushing Center for Counseling and Academic Support to prepare a written request for the accommodations you need in this course.  To receive accommodations in this course, the professor must receive a written request from CCAS at the beginning of the course, or as soon as the disability is diagnosed.

 

College Policies: Please note that all college policies pertaining to academic dishonesty, drop/add procedures, and grade appeal should be followed by students enrolled in this class.  Consult the undergraduate college catalog or ask the professor if you have questions about these policies.

 

Teaching Methods: In order to succeed in this course, you need to be an active participant in learning – both in class and out of class.  Class time will be spent on lecture as well as discussion of homework problems and some group work.  To actively participate in class, you need to prepare by reading the textbook and doing all assigned homework before class (homework will be assigned each class period, to be discussed the following period). You should be prepared to discuss your homework (including presenting your solutions to the class) at each class meeting.

You are encouraged to work together with other students and to ask questions and seek help from the professor, both in and out of class.

 

Grading and Testing Procedures: Grades will be calculated from grades on weekly assignments, three exams and a final exam, using the scheme

Weekly Assignments     35 %

            Exams 1 - 3                  45 %

            Final                             20 %.

 

Weekly assignments will be due at the beginning of class on Fridays, according to the attached schedule.  Instructions for each assignment will be given in advance.  These assignments will consist of a selection of problems, some from homework.  These assignments must be neat, clear and well-written.  You may work together with others on these assignments, but your written solutions must be your own.  No late assignments will be accepted.

 

There will be three in-class exams, to be given on February 8, February 29 and April 11. 

The final exam is cumulative, and is scheduled for 12:30 PM on Friday, May 2.  All exams must be taken at the scheduled time. 

 

Letter grades will be assigned using the scale

            93-100 A

            90-92    A-

            87-90    B+

            83-86    B

            80-82    B-

            77-79    C+

            73-76    C

            70-72    C-

            67-69    D+

            63-66    D

            60-62    D-

            0-59      F

 

MONDAY

WEDNESDAY

FRIDAY

January 14

 

January 16

 

18

 

21

MARTIN LUTHER KING DAY

23

 

25

 

Assignment #1

28

 

30

 

 

February 1

 

Assignment #2

4

6

 

8

EXAM 1

 

11

 

13

 

15

 

 

18

20

 

 

22

 

Assignment #3

25

 

27

 

 

29

EXAM 2

March 3

MID-

5

SEMESTER

7

VACATION

10

 

12

14

 

17

 

19

 

21

GOOD FRIDAY

 

24

EASTER MONDAY

26

 

 

28

 

Assignment #4

31

 

April 2

 

 

4

 

Assignment #5

7

 

9

 

 

11

EXAM 3

14

 

16

 

 

18

 

 

21

 

23

 

 

25

 

Assignment #6

28

Last Class

30

 

May 2

FINAL EXAM

12:30 – 2:30

May 5