Sets, Groups, and Topology Syllabus

Fall 2000

Sets, Groups, and Topology

Syllabus

Sets, Maps and Topology

Math 101 / TuTh 10-11:30 / Science Center 216
Harvard University - Fall 2000

Instructor: Ilia A Binder (ilia@math.harvard.edu)

Course Assistants: David Dumas(ddumas@math.harvard.edu)

Required Texts:

Fraleigh, A First Course in Abstract Algebra. Addison-Wesley, 1994.
Halmos, Naive Set Theory. Springer-Verlag, 1987.

Prerequisites. An interest in mathematical reasoning. Acquaintance with algebra, geometry and/or calculus is desirable. Students who have already taken Math 25a,b or 55a,b should not take this course for credit.

Topics. We will discuss mathematical proofs, sets and mappings, group theory and topology. Some possible topics include:

Proofs and Set Theory
- Methods of proof: induction, contradiction.
- Sets, maps, functions and relations
- Cardinality; different sizes of infinity
- Ordinals
- The axiom of choice
Group Theory
- Groups, subgroups and quotient groups
- Symmetries of Platonic solids
- The symmetric group
- The Cayley graph; group presentations
- Groups actions; counting orbits
- Linear groups
Topology
- Basic point set topology
- Manifolds
- Covering spaces
- Fundamental group

Reading. Students must read the assigned material before coming to class.

Sections. Attending sections is an essential part of the course, especially for learning to write proofs.

Homework. Weekly homework assignments will be due on Thursdays. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators.

Late and Early Homework. Late homework will not be accepted. If you need to hand your homework in early , bring it to class and give it to a course assistant.

Midterm. There will be one in-class midterm, on Thursday, 26 October.

Final. Pending the registrar's approval, there will be a take-home final, available at 12 pm on Monday, 8 January, and due by 4:00 pm on Friday, 12 January. The final should be picked up and returned to the Math Department Office, 325 Science Center. Collaboration on the final is not permitted, but you may refer to your course notes and the texts for the course.

Grading. Grades will be based on regular weekly homework (30%), the midterm (20%) and the final (50%). The two lowest homework grades will be dropped.

URL: http://www.courses.fas.harvard.edu
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