Math 89 Winter 2012

Set Theory

Set Theory

Syllabus | Homework |
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Rebecca Weber |
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Office: 317 Kemeny Hall |

Office hours: Mon/Fri 45 minutes before and after class and by appointment |

Phone: 646-1720 or email (preferred) |

Note that you do not need an appointment to attend regularly-scheduled office hours. If you have a conflict you may make an appointment to meet outside those times.

**Textbook:** Introduction to Set Theory, Third Edition, by Hrbacek and Jech; available at Wheelock Books.

**Students with disabilities** enrolled in this course and who may need disability-related classroom accommodations are encouraged to see me privately as early as possible in the term. Students requiring disability-related accommodations must register with the Student Accessibility Service office. Once SAS has authorized accommodations, students must show the originally signed SAS Accommodations/Consent Form and/or a letter on SAS letterhead to me. As a first step, if students have questions about whether they qualify to receive accommodations, they should contact the SAS office. All inquiries and discussions about accommodations will remain confidential.

For your convenience, here is the term calendar as set by the registrar, with deadlines for schedule adjustment and other significant dates.

A set is a collection of objects. Set theory is the study of sets: which ones we should claim exist, the consequences of such existence, the sorts of operators and relations we can and should define. One goal for creating a collection of axioms for set existence is to provide a foundational system in which "ordinary mathematics" may be carried out but within which paradoxes are eliminated (for example, the barber paradox: a town has one (male) barber, and he shaves every man who does not shave himself. Who shaves the barber?). The finite world is quite well-understood and corresponds to our intuition; the infinite world gets odd fast. We will study axioms of set theory, what they tell us about sets, and what the world of sets tells us about mathematics.

Math 29, 39/69, and 89 give you a well-rounded experience of modern logic. Math 89 satisfies the culminating experience requirement for math majors, and is appropriate for any graduate student who does not know a lot of set theory. You must be comfortable with working abstractly and the language of first-order logic (writing, reading, and manipulating logical formulas including quantifiers). Speak to me if you are unsure of your preparation.

Lectures will be held Monday, Wednesday, and Friday, 1:45-2:55 in Kemeny **007**.

There will be assigned discussion questions, weekly written homework, two take-home midterms and a final paper and presentation. Homework will typically be due on Mondays; unexcused late homework will be docked 20% per calendar day it is overdue.

Midterm I | Midterm II |
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Distributed: 1 Feb Due: 8 Feb | Distributed: 27 Feb Due: 5 Mar |

**On exams**: Unless otherwise specified, no help may be given or received or external sources consulted. You are free to use your textbook and class notes, and consult your instructor.

**On homework and the paper**: The purpose of the homework is for you to understand and internalize the material, and the purpose of the paper and presentation is for you to stretch into a new topic of set theory and present a coherent introduction to it; the origin of that understanding is less important. Collaboration and discussion is encouraged, and you may discuss problems and paper material with instructors, tutors, and fellow students, and use notes and books. However, you must acknowledge all your sources and collaborators, and each student is to write up his or her assignments individually and independently. This means you cannot copy down a joint solution arrived at by a group, say, working at a chalkboard together; you must put it in your own words.

Discussion questions will be incorporated in the form of a participation grade. That and the written components will be weighted as follows.

Component | Points |
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Written homework | 100 |

Midterm I | 100 |

Midterm II | 100 |

Paper and presentation | 100 |

Participation | 50 |

Total | 450 |

Last modified 17 Jan 2012.