Course Syllabus
Math 385 - Topology
Spring 2012

Text: Introduction to Topology by Crump Baker.

The Course: This course will be an introduction to the formal study of point-set topology. Point-set topology is the language of two major branches of mathematics, analysis and topology. We will start with a very general definition of a topological space and define some well-known terms like continuity, compactness, connectedness and will prove theorems in this general setting. The emphasis of this class will be looking at pure mathematics and not focused on applications, but rather the beauty of mathematics. Of primary importance in this class is a focus on learning how to write clear and correct proofs.

Reading: Reading your textbook is essential to success in this class. Reading assignments will be included with homework assignments and must be completed before the lecture on that topic. Read slowly with a pencil and paper in hand. Try to fill in missing steps as you read. Always try to work out examples before you read text solutions. You must be ready to discuss the material you read in class, and this will be part of the participation portion of your grade.

Participation: Each student is expected to be a productive member of the class. This means you should attend each class period and be prepared to discuss the material. Excessive absence or unpreparedness will result in deduction of points in this area. Occasionally students will present homework solutions to the rest of the class and also each student will be responsible for presenting one topic or proof during the course. This presentation will be part of your participation grade. Due to the size of the class this may be done in groups. Participation will be worth 40 points of your final grade.

Homework: You will turn in homework assignment twice a week, on Mondays and Fridays. These homework assignments are where the bulk of your learning will occur and you should set aside a significant amount of time to work on them. There will be three types of assignments you will turn in. Must of the problems will be done in groups of 2-4 students that will be determined early in the semester. These groups are to work together to solve the problems and not simply divide up the problems. You must make sure each student in the group understands the final write-up. The students in each group need to take turns writing up the solutions. In addition, you will be required to work on two problems a week individually. These problems must be solved by yourself (you may ask me for help) and you must write up the solution yourself. Finally, you will be asked to critique other students' proofs. It is very important you learn to be critical (this does not mean negative) about proofs. You will be graded on the quality of your critiques. For all the write-ups your homework must follow the homework guidelines given in class. The homework for the course will be worth 150 points of your total grade.

Quizzes: There will be regular quizzes, covering definitions from the class, group homework assignment questions, and other material from the class. These quizzes combined will be worth 100 points towards your final grade.

Exams: There will be 2 period long exams during the course. The first will be on Friday, March 16 and the second on Wednesday, April 18. The material they will cover will be announced on the website and in class ahead of time. Make-up exams will not be given. If you have a legitimate excuse you may use your final exam score to make up for missing exam scores. Each exam will be worth 100 points.
There will be a comprehensive 2 hour final given on Monday, May 21 at 11 am. The final is worth 150 points.

Learning Outcomes: Upon completion of this class students should be able to:

• understand the definitions of open, closed, compact, connected, limit points, and other major concepts in the context of a general topological space
• know some canonical examples of topological spaces and know how the above definitions apply to these examples
• use theorems of the course to analyze the relationships amongst the above concepts
• be able to write clear, coherent and correct proofs of simple theorems and be able to use counter-examples to verify when the hypotheses of theorems are necessary.

Disability: For accommodations due to a disability please contact me within the first 2 weeks.

Academic Honesty: Cheating and plagiarism are in violation of USD's academic integrity policy and are taken very seriously. Make sure you are aware of this policy.

Have a Good Semester!