About The Course

In Winter 2010, Mathematics 89 will be on the topic of set theory.

We consider set theory to be a branch of logic and foundations for two reasons. First, the development of a formalized theory of sets was at least partially motivated by the desire to create a logically consistent foundation for mathematics. Indeed, as a foundation for mathematics, set theory is remarkably successful. Second, set theorists are constantly and explicitly aware of the impact of mathematical logic on their work. While Godel's Incompleteness Theorem, for example, affects virtually all areas of mathematics, only a set theorist is likely to begin the statement of a theorem with, If set theory is consistent, then...

In Math 89, we will never lose sight of the considerations of formal logic, but our main interest will be in set theory itself as a branch of mathematics. We will study the axioms of set theory, what they tell us about the universe of sets, and how we can use the universe of sets to study the universe of mathematics.

Prerequisite for this course: Math 39 or Math 69 OR familiarity with the language of first-order logic and readiness for an upper level math course. If you are unsure about your preparation, please talk to Professor Groszek.

Math 89 satisfies the culminating experience requirement for mathematics majors.

Math 89 is appropriate for any graduate student who wants to take a course in logic and doesn't yet know a lot of set theory.

Textbook

Introduction to Set Theory by Karel Hrbacek and Thomas Jech, 3rd edition

Scheduled Lectures

Groszek

MWF 1:45 - 2:50 (x-hour) Th 1:00 - 1:50

28 Haldeman Center.

Instructor

Professor Marcia Groszek

Office: 330 Kemeny Hall

Office Hours: M 3:00-4:30, Th 2:00-3:30, and by appointment.

Phone: 646 - 2313 or BlitzMail (preferred)

Exams

There will be two midterm exams, both take-home. Most likely one will be during the fourth week of class and one during the seventh. There will be more information later about the final exam or paper.

Here are some resources that may be helpful for writing mathematics papers (and, in some cases, for writing proofs for homework): The booklet Sources sets out guildelines for citing and acknowledging sources. The Student Center for Research, Writing and Information Technology in Baker Library provides a number of resources, including peer tutors. Here is a guide to writing in mathematics courses; the intended audience is first term calculus students who are writing rather short papers describing the solutions to calculus problems. Here is a paper about writing mathematics; the intended audience is undergraduate mathematics majors writing serious mathematics papers.

Homework Policy

Homework will be assigned each class day, and wil include both discussion questions and a written homework assignment.

Be prepared at each class to discuss the discussion questions assigned from the previous class and/or to present their solutions.

Written homework will generally be due on Mondays. Late (written) homework will receive partial credit; missing homework will count as zero.

Grades

Your course grade will be based on class participation, written homework, exams and final project. Written homework and exams will be graded both on content and on clarity of writing. Writing clear and understandable proofs is critical in all areas of mathematics, but particularly called for in the study of mathematical logic.

Homework, midterm exams (counted as a single unit), and the final will be weighted approximately equally. Class participation will be decisive in borderline cases, and may raise or lower your grade by a single step (B to B+, not B to A).

The Honor Principle

Academic integrity and intellectual honesty are an integral part of academic practice. This does not mean that you can't work on homework together or get ideas and help from other people. It does mean that you can't present somebody else's work or ideas without giving them due credit.

Feel free to discuss homework problems with other people and to work together to answer them. You must write up the answers yourself without copying from anybody. (This means you cannot copy down a joint solution arrived at by a group working together, even if you were part of the group. You must write up the solution in your own words.) You must also acknowledge any sources your consulted or people you worked with; working with other people or consulting other sources will not lower your grade.

Of course, no help may be given or received on exams. For take-home exams, unless otherwise specified, the only sources you may consult are your textbook, your class notes and the instructor.

Disabilities

Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see the instructor as soon as possible. Also, they should stop by the Academic Skills Center in Collis Center to register for support services.

Marcia J. Groszek
Last updated June 27, 2012 12:26:15 EDT