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

  • Spring 2012: Professor Andrew Odlyzko

  • Classes: MW 4:00 - 5:15, in MechE 102 and on UNITE

  • Office Vincent Hall 511

  • Office hours: M 3:00 - 4:00, W 5:30 - 7:00, and by appointment. However, always check this web page before coming over, as on some days the hours may be changed.

  • Office hours of the grader, Kyle Johnson, john7608@umn.edu: Tuesday 1:10 - 2:10, in the grad student lounge in Vincent 502.

  • Textbook: "The Mathematics of Coding: Information, Compression, Error Correction, and Finite Fields" by Paul Garrett, available in the Campus Bookstore. (This book has not been revised recently, so used copies will do just fine.) Please note that some corrections are available at textbook errata.

  • Additional material: Web page from 2003 version of the course, with lecture overheads, etc. at Paul Garrett's home page. You might also 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.

  • Exams: No final, three 75-minute in-class exams on Wed Feb 15, Wed Mar 28, and Wed May 2. These will all be held in MechE 212, upstairs from the regular classroom.

  • Weekly homework assignments (usually), due (usually) on Wednesdays, first one due Jan 26. 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. These you can only work on by yourself.

  • Exams 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 project: due Mon May 7, by 11:00 am either via email (PDF format strongly preferred) or in my mail box in Vincent 107.

  • Grades: homework will count for 35%, term project for 15%, the three exams for 15%, 15%, and 20%, respectively.

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

  • 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.

  • General remarks: How can music CDs that have been scratched still produce perfect music? 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:

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