Abstract Algebra
課程：MATH3121 [原課號：MATH311]
作者：ckhungab [15级 MATH - MP]
創建於：2017-08-05 14:39:20
課程：MATH3121 [原課號：MATH311]
作者：ckhungab [15级 MATH - MP]
創建於：2017-08-05 14:39:20
課程時間：2017年 Summer
授課教授：MOY Allen
TA： LI xilin
這門課的Grade：較好（虽然Allen MOY不给A+）
课程内容：（太长不看的请跳到后面）
Lectures:
M Tu Th F 10:30 - 11:20 and 13:00 - 13:50
Tutorial:
Tu Th F 14:30 - 15:20
Grading:
66% from exams = 26% Midterm (2 hours) + 40% Final Exam (3 hours)
34% from quizzes and homework (2 quizzes and 4 homework)
Textbook:
John Fraleigh, A First Course in Abstract Algebra Prentice
Tentative syllabus and schedule： (http://www.math.ust.hk/~amoy/math3121/2017sum-daily.html)
Week one M/Tu: Monday (June 19):
Basic set theory, mappings, equivalence relations (section 0)
Complex numbers and binary operations (sections 1 and 2)
Integers mod n
Groups and subgroups (section 4)
Week one Th/F: Thursday (June 22):
Subgroups (section 5)
Classification of subgroups of the integers
Cyclic groups (sections 6 and 7)
Permutations groups, cycles (sections 8 and 9)
Week two M/Tu: Monday (June 26):
Cosets, Lagrange's Theorem and order of elements (section 10)
Direct products (section 11)
Homomorphisms, kernel, normal subgroup (section 13)
Quotient groups (section 14 and section 15)
Week two Th/F: Thursday (June 29):
Rings, ring homomorphism, kernel, fields (section 18)
Quotient rings (section 26)
Classification of ideals of the integers
Integers mod n as a quotient ring
Greatest common divisor of two integers and the Euclidean algorithm
Week three M/Tu: Monday (July 03):
Units in a ring
Prime integers and finite fields
Euler phi-function
Fermat and Euler Theorems (section 20)
Week three Th/F: Thursday (July 06):
Chinese Remainder Theorem
RSA encryption
Midterm
Week four M/Tu: Monday (July 10):
1st isomorphism theorems for groups, and rings (section 34)
Unique factorization in the integers Z
The polynomial ring F[x] (section 22)
Ideals in the polynomial ring F[x]
Week four Th/F: Thursday (July 13)
The analogy of the polynomials F[x] with the integers Z
More on finite fields
Symmetries (section 12)
Week five M/Tu: Monday (July 17):
Group actions, orbits, and isotropy/stabilizer subgroup (section 16)
Examples
Orbit stabilizer theorem and Counting (section 17)
Week five Th/F: Thursday (June 20):
Counting (section 17)
Examples
Review
正文部分：
五周结课的抽象代数，workload方面还是比较少的，一共四份HW，不要像我一样最后一晚上才开始写的话会轻松许多。作业难度不算高，唯一比较麻烦的是最后一次HW需要修改Allen MOY上课演示RSA算法的excel档，不过只要认真看一看就能完成。 题目写完建议和同学互相检查一下，避免犯一些低级错误。
课程内容方面主要集中在群上，环次之，域的话更少。不过上课只是提供了各种证明的polynomial ring这部分，反而在final考的比较多，而平常作业也没有相关题目，建议刷点题。
Midterm和quiz的难度比较低，复习一下的话接近满分没有问题。不过final难度要相对的提高了不少，更多地考核了同学们对课程内容的理解和运用，请谨慎备考。（基本每次都有背诵定义，定理，证明的题目，是Allen MOY给大家送分的。定理可以写任意等价的形式、证明大致思路对了，没有明显错误也基本都有满分，考试前请好好的把这些都背一遍 ）
这个summer好像是Allen MOY第一次教3121，由于不是Honor课，所以内容其实并不多，难度也较低，midterm和quiz的题目还没有HW和tuto的难，作为入门课来说还是十分有趣的，加上Allen MOY的板书清晰，
给龟方面相当不错，虽然全堂似乎没有A+，不过A-range应该有20+ %，想刷龟的同学可以考虑上完线代之后的summer来玩一下。
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