Math 432: Set theory and topology, Spring 2009

Section F1 meeting MWF 2:00-2:50 in 148 Henry Admin. Building

Introduction

• Instructor: John Mackay

  Office: 337 Illini Hall,
  Phone: (217)244-4697,
  Email: jmmackay at illinois dot edu

• Course website: http://www.math.uiuc.edu/~jmmackay/09s-432.html
• Prerequisites: Math 347 or 348, or equivalent.
• Office hours: Monday 3-4pm, Wednesday 3-4pm, or by arrangement.
• Textbook: Kaplansky: Set Theory and Metric Spaces, AMS
• Homework assignments and week-to-week schedule.

We'll be exploring some of the foundational concepts of modern mathematics: (informal) set theory, cardinal and ordinal numbers, and the axiom of choice; the topology of metric spaces and an introduction to general topological spaces. Here are a couple of questions to think about:

1. Are there more rational numbers than integers?
2. Are there more points on the plane than points on the line?

Homework

There will be weekly homework assignments, collected at the start of class on Fridays. The first homework assignment will be due the end of the second week of class.

You are free (and encouraged) to work with fellow students on the homework problems. However, you must write up your final solutions by yourself.
On each assignment write one of the following statements:

• "I did not work with anyone else."
• "I worked with [...]."

Your lowest homework score will be dropped.

Exams

There will be two hour long exams in class, and a final. The class exams are set to be on March 4 and April 22.

The first class exam will cover material through Chapter 2. The second class exam will cover material through to the end of Chapter 4.

(Note that this is provisional and may be adjusted as the semester progresses.)

The final will be at 1:30–4:30 PM, Friday, May 8, and will cover all the material we have seen on the course.

Grades

Your grade will be determined as follows:

20% homework, 2 * 20% hour exams, 40% final.

Letter grades will be assigned according to: A 90%, B 80%, C 70%, D 60%, F for less than 60%. This may be adjusted downwards if necessary.

I reserve the right to give a lower grade in exceptional circumstances, such as failing to complete multiple homework assignments, or missing exams without reason. Cheating may result in a substantially lower grade, or even an F.

Other policies

If you are ill or otherwise unable to complete an assignment on time, or take an exam, please get a letter from the dean's office (http://www.odos.uiuc.edu/).

To insure that disability-related concerns are properly addressed from the beginning, students with disabilities who require assistance to participate in this class, or alternative exam arrangements, are asked to contact me as soon as possible.

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