COURSE OUTLINE

MATH 426 Section 201, Term 2 of 2007-2008

MWF at 10 am in Math Annex 1102

Instructor: Dale Rolfsen

Textbook: M. A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer Verlag. (any edition)

Course description:

Outline of Topics:

• (1) Introduction: Euler's theorem, topological equivalence, surfaces and spaces. (Chapter 1)
• (2) Continuity: topology of the line, plane and 3-space, topological spaces, continuity, Tietze extension theorem. (Chapter 2)
• (3) Compactness, connectedness, identification spaces: Heine-Borel Theorem, product spaces, connectedness, paths, quotient spaces, topological groups and orbit spaces. (Chapters 3 and 4)
• (4) Fundamental group: homotopy, calculations, applications: Brouwer fixed point theorem and Jordan curve theorem. (Chapter 5)
• (5) Covering spaces: knots, surfaces, manifolds, connection with fundamental group. (Chapter 10)
• (6) Other topics, as time permits.

Homework, exams, grading policy:

Regular homework will be assigned, and some of the homework will be discussed in class during regular weekly discussion sessions. The course will be given partially in seminar style. Students will be expected to present their homework solutions and related ideas in class, with active discussion and critique by fellow students. One objective of the course is to encourage mathematical thinking and creativity, through dialogue and theoretical practice.

Appropriate examination and grading policies will be decided in consultation with the students in the course.