第一次作业：[Problem Set 1](Problem Set 1.pdf) ，9月30日上课时交。请写在A4纸上。建议大家合理安排作业时间，一定不要等到最后再开始。
关于数学题目的解答，可以参考 Evan Chen的 [proof writing](proof writing.pdf) 。这篇主要是为高中生参加IMO准备的，但是证明写法的规范性适用于从数学学习到科研的各种情况。
Xiaoyi Cui
海滨红楼8号楼105
本课程的教学内容是抽象代数(通常又称为“近世代数”)，是现代数学的重要基础之一，并且各个科技领域有广泛的应用。本学期内容包括：群论（含群映射，群在集合上的作用，西罗定理，有限群的分类等），环论（含理想，素理想，极大理想，欧几里得整环，主理想整环，唯一因子分解整环等）和域论（含域扩张，域扩张的性质，域扩张的自同构群，Galois理论等）的基本知识。通过本课程的学习，学生应该牢固掌握群论、环论、域论的基本理论与主要结果，一般掌握这些代数对象的基本研究方法以及各个定理的灵活运用，从而提高抽象思维和推理的能力，为后续的学习和研究打下坚实基础。
数学分析，高等代数。
The official textbook is Algebra (Second Edition), Michael Artin, 机械工业出版社，2017年。
10% 平时考核 + 25% 作业 + 15% 期中考查 + 50% 期末考试
Homeworks will be posted on this webpage. Students must make arrangements in advance if they will not be handing in homework on time. Please don't wait until the last hour to do the homework.
You are encouraged to discuss about homeowork problems with others, but each one of you must write your own answers (using your own words). Copy and plagiarism will not be tolerated (see Academic Honesty policy).
Your homework will be graded out of four scales:
- A: If you solved 100% of the problems, or at least tried with good efforts; the homewokr is well-written; you showed your descent understanding on the subject.
- B: If you solved 75% or more of the problems, or at least tried with reasonable efforts; the writing is easily recognisable; you showed basic understanding on the subject.
- C: If you solved 50% of the problems, or at least tried with reasonable efforts; or the writing is very hard to recognise, or the understanding is doubtful, with some very visible mistakes.
- D: If you solved less than 50% of the problems, or with not enough efforts; or the homework has lots of mistakes; which basically means the assignment is not acceptable.
With the exception of exams, we encourage you to discuss all of the course activities with your classmates as you are working on them. You will definitely learn more in this class if you work with others. Please ask questions, answer questions, and share ideas liberally.
Collaborating on homework is fine but copying is NOT. At the same time, you should not share your homework answers directly with others. Please feel free to discuss the problems with others, but not the solutions. If you suspect other people may be plagiarizing you, let me know as soon as possible.
Cheating in any form will be strictly prohibited. Anyone found cheating will get an 0 for the corresponding score, and will be reported to the students conduct center. If you are having trouble with assignments or studying for an exam, or if you are uncertain about permissible and impermissible conduct or collaboration, please come to me with your questions.
I encourage you to ask questions about the syllabus, covered material, and homeworks during and after lectures. However, if those conflict with your schedule, please use email to set up a one-on-one meeting with me. Use the subject line "Meeting Request" for your message, and please include a brief description of the reason for the meeting.