Summary | Topics | Prerequisites | Grading | Problem Sets & Collaboration Policy | Sections | Readings | Related Courses
Lecturer: Prof. Madhu Sudan
Teaching Fellow: Richard Wang
Course website: http://madhu.seas.harvard.edu/courses/Fall2017
Time & place: MW 2:30-4, Pierce 209
Algebra is the study of operations (such as addition, multiplication, composition) on sets of objects (such as numbers, polynomials, matrices, permutations). In addition to studying specific operations on specific sets, we also abstract properties that such operations commonly satisfy and the implications of these properties, thereby unifying the study of a wide variety of mathematical objects. In addition to being a beautiful subfield of mathematics, algebra has numerous applications in science and engineering. It is extremely useful for studying symmetries of physical objects, and for encoding data and computations to provide properties such as error-correction and privacy.
In this course, we will cover:
topics above might be too much to cover in the course, but we will
try to get at least a sample of all the above.
The formal prerequisite for the course is (Applied) Math 21ab or equivalent, but general "mathematical maturity" is more important than the specific material in these courses. At times, we will assume familiarity with basic linear algebra as covered in Math 21b, but students who have instead taken a prior proof-based course on a different topic (such as AM 107, Math 101, CS 121, or CS 124) should also be adequately prepared.
Your class participation grade is based on participation in
lecture, but can also be boosted by participation in section
and/or coming to office hours or section with questions or
comments that show genuine interest in the material (i.e. is not
just aimed to help you answer questions on the problem set or
exam). Do not be afraid of asking "stupid" questions!
The course will have weekly problem sets, due by 11:59PM sharp electronically via Canvas. You are allowed 6 late days for the semester, of which at most 2 can be used on any individual problem set. (1 late day = 24 hours exactly). For any exceptions to these rules, I require a note from your senior tutor.
Students are encouraged to discuss the course material and the homework problems with each other in small groups (2-3 people). Discussion of homework problems may include brainstorming and verbally walking through possible solutions, but should not include one person telling the others how to solve the problem. In addition, each person must write up their solutions independently, and these write-ups should not be checked against each other or passed around.
While working on your problem sets, you may not refer to existing solutions, whether from other students, past offerings of this course, materials available on the internet, or elsewhere. All sources of ideas, including the names of any collaborators, must be listed on your homework paper.
There will be weekly sections, which will be used to clarify difficult points from lecture, review background material, go over previous homework solutions, and sometimes provide interesting supplementary material.
The handouts for the course will be made
available at the
Joseph A. Gallian. Contemporary Abstract Algebra, 9th edition.It has been ordered at the Coop, and placed on reserve in the libraries. This book will include most of the topics covered in the course, and a lot more too, but it will not cover all the topics in the course. In particular it does not cover some of the applications and the algorithmic discussions. So it is important that you also attend lecture.