Text: Derek Goldrei, Classic Set Theory for guided independent study,. Chapman & Hall/CRC, 1996.
Objective: This course is designed to introduce the student to the ideas of classical set theory and the mathematics which depends particularly on it, namely, Transfinite Arithmetic. A short time will be spent discussing the progression from the Natural Numbers to the Integers to the Rationals to the Reals. We will then focus on the Zermelo-Fraaenkel Axioms for set theory, proceeding to the Axiom of Choice. We will look at Cardinal Numbers without the Axiom of Choice, then at ordered sets and Ordinal Number arithmetic. We will end with Cardinial Number arithmetic with the Axiom of Choice, the Well Ordering Principle, the Continuum Hypothesis, and finally, the Well-Ordering of the Reals.
Method: As a small enrollment class, this course will be conducted as a seminar. Homework will be assigned and students will be expected to share their work in the following days. The instructor will provide explanation and guidance.
Grading: Grading will be based on class participation and an oral final. If at any time you are concerned about your grade please come to me to talk about it.
This course will probably be the most abstract mathematics course you will take, and you should expect to struggle with it. It is the struggle itself, and engaging the material that is important rather than any method of counting successses and failures. There will probably be more failures than successes; don't expect to be penalized for this. It's part of the normal process.
Special Question: What is yellow and depends on the axiom of choice?
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www.otterbein.edu --> Academics --> Academic Departments --> Mathematics and Computer Science --> Full Time and Emeritus Faculty --> Deever, David L. (Dr.) --> Mathematics 420, Transfinite Arithmetic |