This is the page for the past set theory seminar in 2011. For the upcoming set theory seminar, please see Set Theory 2012.

Coordinator: Wu Wei (吴为)

Email: wwu AT zju DOT edu DOT cn

Mobile: 150 8868 1309 (659309)

Textbook: Elements of Set Theory, by Herbert Enderton

and Zermelo-Fraenkel Set Theory, by S. Hayden and J.F. Kennison

03.06. Introductions to logic and set theory, speaker: Wu Wei (吴为)

03.13. Russell's Paradox and the Axiomatic Method (Chapter 1 and 2), speaker: Lv Renjie (吕人杰)

03.20. Relations and Functions，Partial Orders (Chapter 3), speaker: Wang Changhan (王昌翰), Zhouyou (周游)

03.27. Natural Numbers (Chapter 4), speaker: Lei Qi (雷琦), Guo Zhengyang (郭政扬)

04.03. Cardinal Numbers (Chapter 6), speaker: Xue Yeguang (薛烨光)

04.10. Axiom of Choice and Cardinal Arithemetics (Chapter 6) speaker: Lv Renjie (吕人杰)

04.17. Construction of the Reals (Chapter 5), speaker: Lei Qi (雷琦)

04.24. BREAK: Exam Week

05.01. BREAK: Holiday

05.08. Ordinals, Replacement (Chapter 7), speaker: Wu Wei (吴为)

05.15. Transfinite Induction (Chapter 7) speaker: Lv Renjie (吕人杰), Zhang Xiping (张希平)

05.22. Ordinal Arithmetic (Chapter 8) speaker: Lv Renjie (吕人杰)

05.29. Special Topics speaker: Zhou Yang (周杨), Lv Renjie (吕人杰)

For those who want to major in mathematics, set theory is a good place to start. This gives you more insight into what mathematics is all about. It gives you a good training in logical and abstract thinking. It also provides you the precise definitions of some of the most often used concepts in mathematics, such as function, equivalence relation, binary operation, and ordinal and cardinal numbers.

Set theory is a relatively new field in modern mathematics. It serves as a foundation of mathematics. In this seminar, we will study the ZFC axioms of set theory, and learn how to formalize objects in mathematics(such as the naturals and the reals) in this axiomatic system. Some fundamentals of algebra and topology will also be covered.

This is an introductory seminar to set theory. Advanced topics in set theory, such as Goedel's Completeness and Incompleteness Theorem, the independence proofs and large cardinals, will not be mentioned, because they are irrelevant to everything you will learn in undergraduate level Unfortunately, no one in China is studying set theory, although it is very interesting and worth studying.

- To get acquainted with abstract ideas and the abstract ways of thinking in mathematics.
- To learn how to express mathematical ideas precisely and lucidly
- To learn how to self-study.
- To learn how to communicate mathematically and exchange ideas with others.

1. Each presentation should be meticulously prepared, not only by the speaker, but also by the audience (in order to understand the talk).

2. Because of the time limit, you have to tailor the contents. Focus on the most central and essential ideas and leave out the secondary stuffs.

3. Definitions and theorems should always be stated clearly, precisely, and concisely.

4. Do not try to give all the details of a proof unless it involves useful techniques or it is very interesting. Just sketch the main line of thought.

5. Be prepared to answer and discuss any question posed by the audience.

6. For effective learning, English should be used as much as possible, at least for the blackboard writing.