Math 5251: Error-correcting codes, finite fields, algebraic curves

  • Spring 2020: Professor Andrew Odlyzko

  • Classes: MW 4:00 - 5:15, Vincent 113

  • Office Vincent Hall 511

  • Office hours (starting Mon Jan 27): Mon 5:30 - 7:00, Tue 2:00 - 5:30, and by appointment. However, always check this web page before coming over, as on some days the hours may be restricted.

  • Textbook: "The Mathematics of Coding: Information, Compression, Error Correction, and Finite Fields" by Paul Garrett. An electronic copy can be downloaded freely and legally from the author's web page textbook, PDF. If you would like a hard copy, please print this one out, or else buy a used copy. (This book has not been revised recently, so recent used copies will be fine. The book is out of print, so there are no brand new copies to purchase.)

  • Additional material: You might find useful two books that are available freely (and legally) online, Victor Shoup's A Computational Introduction to Number Theory and Algebra, and Jonathan Hall's Notes on Coding Theory.

  • Computer algebra systems (very helpful, but not essential and not required): Maple, Mathematica, available in Math computer labs, and also (for CSE undergrads) for free downloads at CSE Labs. One can also do well with the freely available Web-based Wolfram Alpha, or other systems. A calculator is advisable, even if you use a computer algebra system, to reduce the tedium of computations. (Calculators are allowed on midterms, whereas computer algebra systems are not.)

  • Tests: No final, but a term paper (described below) and three 75-minute in-class mid-terms on Wed Feb 19, Wed Apr 1, and Mon May 4 (last class day).

  • Weekly homework assignments (usually, excluding mid-term weeks), due (usually) on Wednesdays, first one (a small one) due Jan 29. Will be posted by the preceding Friday, and will (usually) cover material through the preceding Wednesday. Always due at the beginning of a class, late homeworks will not be accepted. If you can't make it to class, you can leave your homework in my mailbox in Vincent 107, or email it to me (in either typeset or scanned form, in either case PDF is preferred).

  • Special challenge problems: There will be occasional challenge problems for extra credit. No collaborations are permitted on those.

  • Solutions to homework problems will be available through this site, usually posted the evening of the day they are due. However, they will not be live links, but URLs that you will have to paste into your browser to download (to keep crawlers from downloading and archiving them). These are for your use only, do not put them up on any web sites, Facebook pages, etc.

  • Tests will be open book: you may bring books, notes, and calculators, but no smart phones, iPads, or other communication devices can be used, and you have to do all the work yourself.

  • Term paper: due Fri May 8 by 11:00 am via email (PDF format strongly preferred).

  • Grades: homework will count for 30%, term project for 15%, the three tests for 15%, 20%, and 20%, respectively.

  • Expected effort: This is a 4-credit course, so you are expected to devote 12 hours per week, on average (including lectures).

  • Solution files for homeworks and midterms are provided for your personal use only. Do not distribute them via email or posting anyplace.

  • Scholastic Conduct: Cheating or other misconduct will not be tolerated. The standard University policies will be followed.

  • General remarks: How can music CDs that have been scratched still produce perfect music? How does your smart phone get the texts and videos? How do spacecraft out past Saturn communicate with Earth? And how do high quality movies fit on DCDs? All these depend on some pretty mathematics that is not too complicated and can be learned with minimal prerequisites, given the willingness to pick up some abstract algebraic, combinatorial, and probabilistic concepts.

    This course develops basic ideas of information theory, compression, and error-correction. It does not present a comprehensive coverage of these topics. Instead, the stress is on basic concepts that have cohesive mathematical foundations.

  • Homework assignments and other notes:

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