AM 106 & 206:
Applied Algebra & Combinatorics
Lecturer: Prof. Salil Vadhan
Teaching Fellow(s): Thiago Costa, Derek Lietz, Yongning Wu
Course website: http://www.courses.fas.harvard.edu/3871
Staff e-mail: email@example.com
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:
The above list is overly ambitious for the time we have. We will certainly not be able to cover all of the algorithmic aspects and applications mentioned, but AM 206 students will have the opportunity to explore some of these as part of their "extra assignments".
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.
AM 106 students:
AM 206 students:
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 comme~nts 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"
AM206 problem sets will have some more advanced problems substituted in..
The course will have weekly problem sets, due Wednesdays by 1:10 PM sharp (electronically or in the box labelled AM 106 in the basement of Maxwell Dworkin.) 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 required text is:
· Joseph A. Gallian. Contemporary Abstract Algebra, 7th edition. It has been ordered at the Coop, and for reserve in the libraries.
However, we will also be covering some material (particularly applications and algorithmic discussions) that is not in Gallian, so it is important that you also attend lecture.