Math 361: Set Theory
Rutgers University
Instructor: Tom Benhamou
My Office: Hill 205
Office hours: Wed 11:00 am to 12:00 pm
E-Mail tom.benhamou at rutgers .edu
Wed 12:00pm to 1:20pm and Fri 2:00pm to 3:20pm at ARC 107
Textbook: Herbert B. Enderton, Elements of Set Theory, Academic Press
Description
Set theory plays several important roles in the mathematical landscape. First, it lays the formal foundations for most mathematical theories. Secondly, set theory is an attempt to quantify the infinite and to rigorously treat infinite objects. In this course, we will develop the formal axiomatic set theory ZFC and present the formal construction of all regular mathematics from the point of view of modern Set theory. Then we will continue with the investigation of mre subtle axioms such as he axiom of choice and Cantor's theory of inifine and transfinite.
The students are assumed to be familiar with naive set theoretic concept such as: basic sets definition, sets operations, functions. Also familiarity with proof writing is assumed
Syllabus
- The Zermelo Fraenkel Axioms of Set Theory.
- The construction of the real numbers.
- Countable and uncountable sets.
- Cardinals arithmetic.
- The Axiom of Choice.
- Well-orderings and ordinal numbers.
Final Grade
The final grade will be based on the results of the examinations and the solutions of the homework problems. Here are the weights of the different components of the course:
- Homework 20%
- Midterm I 20%
- Midterm II 20%
- Final exam 40%
Home Work:
Home Work Solutions:
Midterms and exams:
MidTermI-Solutions
MidTermII-Solutions
Other material:
Class Notes
Logic Identities
Set Operations Identities