Course: MAT 365
Instructor: Szabo
F 2017

Description of Course Goals and Curriculum

The course begins with a thorough introduction to point-set topology before speeding towards its ultimate goal of introducing some algebraic topology via the fundamental group. In doing so, the course covers Munkres's Topology in its near entirety, which is the best way of describing exactly what the course covers.

Learning From Classroom Instruction

The class consists of two 1.33 hour lectures per week. Often, the lectures present the information found in Munkres in a new light, offering additional examples of the numerous examples and counterexamples that dominate the field of point-set topology. Despite the fact that the course follows Munkres, I would recommend against skipping class to simply read the book. Szabo does a wonderful job of addressing questions on the spot and presenting the material in a lucid way.

Learning For and From Assignments

The homework assignments are weekly, drawn from the exercises in Munkres, and usually consist of 6-8 problems. The majority of them are not particularly time-consuming and are a useful test of your ability to the apply the numerous definitions you will learn. The minority of them are more challenging and require some creative thinking and an application of techniques found in the book and/or lecture. There is one take-home midterm examination. It tends to be around 9 questions in length, the problems often being of a difficulty equal to the more difficult problems from the weekly assignments, if not harder. To adequately prepare for the midterm, you should make every effort to tackle the difficult weekly homework problems before seeking help from classmates. Although you will have plenty of time to do the midterm, it requires a significant amount of time to complete, so you should be careful to plan accordingly. There is a take-home final examination. It tends to be around 9 questions in length as well, but some of the problems will be drawn from algebraic topology. As a result, the final exam is even harder than the midterm, which is difficult as it is. All of the problems may be solved using techniques found in Munkres and lecture, but the more difficult problems in algebraic topology will inevitably require some clever analysis. To help yourself, make every effort to work on the old exams that will be distributed before the release of your current year's exams and discuss them with Szabo in office hours. The problems will of course be new, but you may pick up an idea or too that will help you.  

External Resources

Professor Szabo is very accessible outside of class, and he is your best resource for help. Additional help and discussion may also be provided by the class TA(s).

What Students Should Know About This Course For Purposes Of Course Selection

It satisfies the Math Department requirement for a course in the field of geometry. Additionally, it serves as a math course above the 300 level that can count towards the Physics requirements. The class is a QR. An alternative course in the field of geometry is MAT 355, Differential Geometry. Topology is offered in the fall while differential geometry is offered in the spring. However, for those persons pursuing a concentration in mathematics, I strongly recommend that they take this class.

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