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

All. Construct an 1-1 correspondence between R and R - Q.

22

3, 5, 6, 8, 9, 12, 20, 21, 24, 26, 31, 39

5, 7, 8, 10, 14, 15, 16, 21, 26, 28, 40, 41, 57, 58, 59, 60

5, 6, 7, 10, 19, 24, 25, 34 - 38

02.26. Introduction: Axiomatic Set Theory (Chapter 1, 2), speaker: Wu Wei (吴为)

03.4. Chapter 3: Relations and Functions , speaker: 肖羚晏 郭赫

03.11. Chapter 4: Natural Numbers, speaker: 陈俊杰 雷宇环

03.18. Chapter 5: Real Numbers, speaker: 罗之麟

03.25. Chapter 6.1 – 6.4 : Cardinal Numbers, speaker: 李聪 吴梦颖

04.8. Chapter 6.5 – 6.8 : Axiom of Choice, speaker: 雷宇环

04.15. Chapter 7.1 – 7.4: Ordering and Axiom of Replacement, speaker: 张曜勃 雷宇环

04.22. Chapter 7.5 – 7.8: Ordinal Numbers, speaker: 肖羚晏

04.29. Chapter 8: More on Ordinals (I): Transfinite Recursion, speaker: 罗之麟 张一鸣

05.06. Chapter 8: More on Ordinals (II): Ordinal Arithmetic, speaker: 罗之麟 张一鸣

05.13. Special Topics

05.20. Exercises

05.27. TBA

If you want to participate in the seminar, please contact the coordinator.

- 郭赫
- 陈俊杰
- 雷宇环
- 李聪
- 吴梦颖
- 周武洁
- 张曜勃
- 罗之麟
- 张一鸣
- 肖羚晏
- 张启迪
- 刘远通
- 罗逸芝
- 应雨平
- 马超
- 陈子隽
- 李宇琼

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. (These parts may be eliminated since in past set theory seminars, we usually did not have enough time for the last chapter on transfinite induction)

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.

Objectives of the seminar

- 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.

On the presentations

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.