Text: Massey, A Basic Course in Algebraic Topology (Ch. I and V-IX) and Hatcher, Algebraic Topology (Ch. 0, I, Appendix).

This course introduces the basic ideas of "algebraic topology" – using algebra to answer topological questions such as:  Are these two spaces homeomorphic? Are these two mappings homotopic? Does a mapping  f:X®X  have a fixed point?  To answer such questions, we will develop ways of associating various algebraic things (e.g. numbers, groups, rings, vector spaces, homomorphisms) to topological things (spaces and maps) in such a way that similar spaces and maps have similar algebraic things associated.  .

Please see my web page for last fall’s course for a more detailed introduction to the mathematics, grading policies, etc.

http://www.math.uiowa.edu/~jsimon/COURSES/M201Fall05/

In addition to the “official” Course Description, you also can see various handouts on mathematical topics, and even the sample final exam problems from which most of the 7-problem final was taken.

Prerequisites:  22M:132 or equivalent (but please see comments below about your background) or consent of instructor.  This course is not a "continuation" of 22M:132: it is not a course in general topology.  But some of the material from a 132-type course is important background (e.g. “pasting lemma”, “quotient topology”).  You may have learned enough topology ideas from another prior course (like our Topology 22M:130 or old 22M:115) to be well prepared.  The course 22M:133 is not a prerequisite for M201.  However, most of the students in M201 are likely to have just finished M133, so some material from 133 may be assumed in introducing or motivating some topics.  Also, people who have taken M133 bring additional mathematical maturity that I may assume everyone has.  We do also assume some algebra, at least at the level of a one-semester abstract algebra course such as 22M:120.  If you have any questions about the course, especially any doubts about your background, I will be very happy to meet with you to discuss your concerns.

Special note for students thinking of taking their Ph.D. Comprehensive Exam in Topology:  Department rules allow students to take either a written exam based on 22M:201-200 type material, or exams (oral or written) designed individually for students with more clear research plans.

22M:203  

Instructor: Maggy Tomova
Time: 10:30-11:20 MWF 
Place: 110 MLH

Text: 1. Notes on Basic 3-Manifold Topology, Hatcher (on-line)
2. Heegaard Splittings of Compact 3-Manifolds, Scharlemann (on-line)
3. Lectures on 3-Manifold Topology, Jaco (you don’t need to buy this book)
4. Thin Position in the Theory of Classical Knots, Scharlemann (on-line)
 

This course will cover basic 3-manifold Topology with a focus on Heegaard splittings. The following topics will be addressed: Compressing disks, Essential surfaces, Prime decomposition of 3-manifolds, Loop Theorem, Handlebodies, compression bodies and the surfaces in them, Heegaard splittings for manifolds with and without boundary, Haken’s lemma, Seifert manifolds and the essential surfaces in them.

Depending on time and student interest some of the following topics might also be covered: Thin position for 3-manifolds, Thin position for knots, Basic normal surface theory, Heegaard splittings of Seifert manifolds, The curve complex and distance of Heegaard splittings, Uniqueness of Heegaard splittings and the stabilization problem.
 

Prerequisite: 22M:200 & 201 or consent of instructor. 3 s.h.

22M:205  

Instructor: Dan Anderson
Time: 11:30-12:20 MWF 
Place: 114 MLH 

Abstract algebra: semigroups, groups, rings, integral domains, polynomial rings, division rings, fields, vector spaces, matrices, modules over rings, lattices, categories.

Prerequisite: 22M:120 or consent of instructor. 3 s.h.

22M:210  

Instructor: Colleen Mitchell
Time: 9:30-10:20 MWF
Place: 22 SH

Prerequisite: 22M:116 or equivalent. 3 s.h.

Partial  Differential Equations

22M:216

Instructor: Gerhard Strohmer
Time: 2:30-3:20 MWF
Place: 210 MLH

First Year Seminar

22M:224

Instructor: Dan Anderson
Time: 3:30-4:20 F
Place: 218 MLH

Differential Geometry I

22M:260

Instructor: Oguz Durumeric
Time: 1:30-2:20 MWF
Place: 214 MLH