# Introduction

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## For Freshmen and New-comers

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.

NOTICE

- The seminars are mostly offered to students who want to study pure mathematics in the future.
- Some certain seminars contains topics which serve as the mathematical background of other subjects such as physics and theoretic computer science. Students from different majors are welcomed.
- Be sure to contact the coordinator beforehand to make sure what is the content and objectivity of the seminar.
- On average, one should spend more than 5 hours a week (besides the seminar) to study the content of the seminar.

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.

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