Syllabus for Math 4452.

Syllabus for Math 4452 (Algebraic Coding Theory) Spring 2020

MW 2-3:15 pm, New Cabell 058.

Instructor: Mikhail Ershov
Office: Kerchof 302
e-mail: ershov at virginia dot edu
Office hours: 2 hrs 30 min TBA and by APPOINTMENT
Course webpage: https://m-ershov.github.io/4452_Spring2020/

Main text (required): Coding Theory: A First Course by San Ling and Chaoping Xing, first edition, ISBN 9780521529235.

Other recommended sources:

Lecture notes by Prof. Jonathan Hall, based on an advanced undergraduate/graduate course at Michigan State University
Lecture notes by Prof. Yehuda Lindell, based on a graduate course for computer science students at Bar-Ilan University
A First Course in Coding Theory by Raymond Hill, ISBN 9780198538035
Coding Theory and Cryptography: The Essentials by D.C. Hankerson, Gary Hoffman, D.A. Leonard, Charles C. Lindner, K.T. Phelps, C.A. Rodger and J.R. Wall, ISBN 9780824704650
Introduction to Coding Theory by Ron Roth, ISBN 9780521845045

Course outline and prerequisites

This course is an introduction to the theory of error-correcting codes, that is, codes designed to provide reliable transmission of information in the presence of noise. The topics will include a general theory of linear codes, a detailed discussion of some particular classes of codes (e.g. Hamming codes, BCH codes), and the associated encoding and decoding algorithms. Specific (real life) applications of codes will also be briefly discussed. A few lectures will be devoted to developing necessary algebraic background for the course, mainly basic theory of finite fields. The precise selection of topics will depend on the interests of the students taking the course and may not be determined until a few weeks after the start of the semester.

The official prerequisites for Math 4452 are Math 3351 Elementary Linear Algebra and Math 3354 Survey of Algebra. The linear algebra prerequisite is essential and will be assumed. If you have not taken a prior course in abstract algebra, it is possible to take 4452 if you are willing to learn basic number theory and modular arithmetic (roughly first 4 weeks of 3354) on your own (see, e.g. Lectures 1-9 of my 3354 notes). In addition, a substantial prior exposure to proof-based mathematics will be expected.

Evaluation

The course grade will be based on homework, two midterms and the final, with weights distributed as follows:

homework: 30%
midterms: 20% each
final: 30%

Exams

The format of the exams has not been finalized at this point, but most likely the final and one of the midterms will be in-class while the other midterm will be take-home. The midterm dates given below are tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed (in case the exam is held in class).

First midterm exam: Wed, Feb 26th
Second midterm exam: Wed, Apr 10th
Final exam: Thu, May 7th, 9am-12pm

Make-up policy for exams

Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as serious illness). Except for emergencies, you must obtain my permission for a make-up (resp. extension) before the exam (resp. due date).
If you miss an in-class exam or fail to submit a take-home exam by the due date without a compelling reason, you will be assigned the score of 0 on that exam.
University regulations specifically prohibit early make-ups.

Homework

Homework will be assigned weekly and will usually be due on Wednesdays, in class.
Please STAPLE your homework.
No late homework will be accepted. However, two lowest homework scores will be dropped.
GRADING: it will not be possible to grade all homework problems. In each assignment 3-4 selected (but not announced in advance) problems will be graded for credit.

Collaboration policy on homework.

On homework: you are welcome (and even encouraged) to work on homework together, but you must write up solutions independently, in your own words. In particular, you should not be consulting others during the process of writing down your solution.
On take-home exams: you MAY NOT discuss problems with other people or use any resources (including web) except for the class textbook and your class notes. You may ask me questions about the exam problems, but normally I will only provide very brief hints.

Announcements

Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Monday, January 27 -- Last day to drop a class, add a class, select the AU (audit) option or change to or from "Credit/No Credit" Option
Monday, March 16 -- Last day to withdraw from a course

SDAC

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.