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| Coordinates |
RKC 102, MW 1:30-2:50 PM, CRN 99335 |
| Professor |
Greg Landweber |
| Office Hours |
Albee 304, Tuesday 11:30 AM - 12:50 PM, Wednesday 3:00 - 4:20 PM, or by appointment. |
| No Class |
Yom Kippur: Monday, September 28,
Away at Conference: Monday, October 5,
Fall Break: Monday, October 12,
Advising Day: Wednesday, November 18.
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| Content |
The digital transmission of information is considered to be extremely reliable, and yet it suffers from the same sorts of interference, corruption, and data loss that plague analog transmission. The reliability of digital transmission comes from the use of sophisticated techniques that encode the digital data so that errors can be easily detected and corrected. This theory of error correcting codes, while having broad applications ranging from CDs to the internet to high definition television, requires some surprisingly beautiful mathematics. We will interpret strings of bits as vectors in an abstract vector space, which allows us to manipulate binary data using linear algebra over finite fields. This class will introduce students to the basics of error correcting codes, as well as touching on the mathematics of data compression and encryption. If time permits, we will also discuss quantum error correction. Although this course will mention encryption, the emphasis will NOT be on cryptography. This course will not involve any programming. |
| Prerequisite |
Math 242 and either Math 261 and CMSC 242 (Discrete Mathematics).
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| Textbook |
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Fundamentals of Error-Correcting Codes
by Huffman and Pless |
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| Homework |
Homework must be stapled and is due at the start of class each Wednesday, starting Wednesday, September 2. Late or unstapled homework will not be accepted. You are encouraged to work together on the homework, although you must write up your solutions on your own.
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| Exams |
There will be a take-home midterm exam and a take home final exam in place of the weekly homework assignments due Thursday, October 22 and Friday, December 18, respectively. You must complete these exams entirely on your own, using only the textbook, your course notes, and your homeworks as references. Extensions may be granted only in extraordinary circumstances at the discretion of the professor and must be negotated before the exams are due. |
| Project |
Each student or pair of students will do an independent project, writing approximately 5 pages (single spaced) and giving a 15 minute in-class presentation during the final week of the semester. Pairs of students must write 10 pages and give a 30 minute presentation. In order to obtain full credit, students must meet the following milestones:
October 26: Professor Landweber will give out a list of proposed projects.
November 2: Project proposal due.
November 9: You must have met with Professor Landweber to discuss your project.
November 23: One-page outline due, describing what will be in your paper and presentation.
December 7: Rough draft of your paper due.
December 14: Final draft of your paper due.
December 14, 16: Presentations in class.
Project Suggestions
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| Grading |
40% Homework
40% Exams (2 @ 20% each)
20% Project
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| Schedule |
August 31
September 2 | Linear Algebra | Sections 1.1, 1.2 |
Section 1.2: Exercises 1, 2, 3
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| September 7, 9 | Weights | Sections 1.3, 1.4 |
Section 1.3: Exercises 4, 5, 6
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| September 14, 16 | Building Codes | Sections 1.4, 1.5 |
Section 1.4: Exercises 11, 14, 22
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| September 21, 23 | Equivalence | Sections 1.5, 1.6 |
Section 1.5: Exercises 23, 26, 31
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| September 30 | Hamming Codes | Section 1.8 |
Section 1.6: Exercises 37, 39, 41
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| October 7 | Encodign and Decoding | Section 1.5.5 |
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| October 14 | Reed-Muller Codes | Sections 1.10, 1.11 |
Section 1.5: Exercise 33
Section 1.8: Exercise 55
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| October 19, 21 | Review | |
Take-Home Midterm
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| October 26, 28 | Finite Fields | Section 3.1 |
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| November 2, 4 | Finite Fields | Sections 3.2, 3.3, 3.4 |
Section 3.1: Exercise 150
Section 3.2: Exercise 159 |
| November 9, 11 | Cyclic Codes | Sections 3.5, 3.6, 3.7 |
Section 3.2: Exercise 156
Sectiom 3.4: Exercises 168, 173a,b
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| November 16 | BHC Codes | Sections 4.1, 4.2 |
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| November 23 | Reed-Solomon Codes | Sections 4.3, 4.4, 4.5 |
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November 30
December 2 | Compact Discs | Chapter 5 |
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| December 7, 9 | Projects | |
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| December 14, 16 | Projects | |
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