INSTRUCTOR: Dr. Botsko

TEXT: Introduction to Topology and Modern Analysis by Simmons

PREREQUISITE: MA 113

COURSE CONTENT:

We will cover chapters 1, 2, 3, 4, 6, and 7 of the above text. A list of topics that we will study includes the following:

1. The algebra of sets
2. Functions
3. Countable and uncountable sets
4. The Schroeder-Bernstein theorem
5. Metric spaces
6. Open and closed sets
7. Convergence, completeness, and Baire's theorem
8. Continuous mappings
9. Topological spaces
10. Elementary concepts
11. Open bases and subbases
12. Compact spaces
13. Products of spaces
14. Tychonoff's theorem and locally compact spaces
15. Compactness for metric spaces
16. Ascoli's theorem
17. Connected spaces
18. The components of a space
19. Totally disconnected spaces
20. Locally connected spaces
21. The Weierstrass approximation theorem
22. Fixed-point theorems
23. Picard's theorem on first order differential equations

OBJECTIVES:

Students are expected to know the basic definitions and fundamental theorems of Topology, to be able to prove simple propositions and to learn the power of abstraction, and to be able to connect Topology with other branches of mathematics. Class discussions and exams will be used to assess the level to which these objectives are being attained.

EXAMS:

There will be two exams and a final and you will be given a week's notice for each exam.

GRADING POLICY:

The final will count as 1/3 of your grade as will each of the two in class exams. The grading system will be according to the current SVC Bulletin.

CLASS ATTENDANCE:

Please make an effort to attend every class. A significant number of class cuts in an upper division mathematics course almost always leads to disastrous results. If for some reason class is cancelled, an announcement will be posted on the Blackboard site for this course.

“Saint Vincent College assumes that all students come for a serious purpose and expects them to be responsible individuals who demand of themselves high standards of honesty and personal conduct. Therefore, it is college policy to have as few rules and regulations as are consistent with efficient administration and general welfare.

Fundamental to the principle of independent learning and professional growth is the requirement of honesty and integrity in the performance of academic assignments, both in the classroom and outside, and in the conduct of personal life. Accordingly, Saint Vincent College holds its students to the highest standards of intellectual integrity and thus the attempt of any student to present as his or her own any work which he or she has not performed or to pass any examinations by improper means is regarded by the faculty as a most serious offense.”
Saint Vincent College 2003-2005 Bulletin, page 32.

OFFICE HOURS:

I will be in my office (4th floor of Alfred Hall) at the following times during the week. Do feel free to stop in when you are having any difficulty with the material.

Friday: 9:30 to 10:30

If you would like some online help in Topology on the real line, simply click on the following link. To see a nice web site on the various fields of mathematics, click on Math archives. Finally if you would like to see an application of the Cantor Set, click on The Cantor Function.

Topology on the real line

Math archives

The Cantor Function

Assignments and Other Information If this link doesn't work, click here