| Prerequisites: |
Single-variable calculus, and a solid background in linear algebra. Some familiarity with modular arithmetic might help, but is not required. We will eventually understanding something about finite fields, their structure, and matrices/linear algebra using them. For this reason, the course has a slightly higher mathematical level than Math 5248. |
| Instructor: | Victor Reiner (You can call me "Vic"). |
| Office: Vincent Hall 256 Telephone (with voice mail): (612) 625-6682 E-mail: reiner@math.umn.edu |
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| Classes: |
12:20-2:15 PM on Mondays, Wednesdays
in-person in Vincent Hall 211 |
| Office hours: |
To be determined. Initial proposal: Mon, Tues 4:40-5:30 in my office, and via this Zoom link. |
| Class Discord server: | Use our class Discord server to introduce yourself, ask questions, form study groups, etc. |
| Course content: |
This is an introductory course in the mathematics of codes for communication designed to achieve compression of information and error-detecting/correction. We intend to cover much of the text by Garrett listed below, including treatment of
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Some student learning outcomes: |
By the end of the course, among other things, we would like you to know ...
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What this course is NOT about: |
This course should not be confused with a course in
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| Text, materials, resources: |
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| Homework and exams: | There will be 6 homework assignments due in the class Canvas site by midnight on
Wednesdays, generally every other week,
except for
The take-home midterms and final exam are open-book, open-library, open-web, but no collaboration or consultation of human sources is allowed. You must name any sources that you used, beyond Garrett's text, including AI sources such as ChatGPT. Use your judgement when consulting such AI sources, as they sometimes spout nonsense, and relying on them too much will hamper your own learning. Late homework will not be accepted. Early homework is fine. Collaboration is encouraged as long as everyone collaborating understands the solution thoroughly, and you write up the solution in your own words, along with a note at the top of the homework indicating with whom you've collaborated. This includes AI sources such as ChatGPT. Homework solutions should be well-explained-- the grader will be told not to give credit for an unsupported answer. |
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| Grading: |
Homework = 50% of grade Each of 2 midterms = 15% of grade Final exam 20% of grade. Complaints about the grading should be brought to Vic. |
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| Policy on incompletes: | Incompletes will be given only in exceptional circumstances, where the student has completed almost the entire course with a passing grade, but something unexpected happens to prevent completion of the course. Incompletes will never be made up by taking the course again later. You must talk to me before the final exam if you think an incomplete may be warranted. | |||||||||||||||||||||||||||||
| Other expectations | This is a 4-credit course, so I would guess that the
average student should spend about 8 hours per week outside
of class to get a decent grade. Part of this time each week
would be well-spent making a first pass through the material
in the book and the posted lecture notes that we anticipate to cover in class that week,
so that you can bring your questions/confusions to class
and ask about them.
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| Assignment or Exam |
Due date by midnight at the course Canvas site |
Problems due, mainly from Garrett's text |
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| Homework 1 | Wed Sept 18 |
From Garrett's text: 1.28, 1.31, 1.33 (In Problem 1.31, assume drawing with replacement, that is, after each time you draw a ball of either color, you put it back into the urn before doing the next drawing.) 2.03 3.02 Not from text: A. Consider a source W={A,B,C,D,E} and encoding maps f:W→Ci mapping the 5 letters in order onto these three collections C1, C2, C3 of codewords: C1={0,10,110,1110,1111} C2={0,10,110,1110,1101} C3={0,01,011,0111,1111} Indicate for each (with explanation) whether or not f is (a) uniquely decipherable, (b) prefix (=instantaneous). B. Does there exist a binary code which is instantaneous and has code words with lengths (1,2,3,3)? If not, prove it. If so, construct one. |
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| Homework 2 | Wed Oct 2 |
From Garrett's text: 2.04 3.05 4.01, 4.02, 4.04, 4.05, 4.06, 4.11 In Problem 4.05, a minor typo correction: after parity bits are added, the codewords should be 00, 101, 1100, 11101, 11110. Also, in the same problem, before adding the extra parity bit, any digit that gets flipped in transmission is considered an undetected error. |
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| Midterm exam 1 | Wed Oct 9 | Midterm 1, to be turned in at the class Canvas site. | |
| Homework 3 | Wed Oct 23 |
From Garrett's text: 5.01, 5.02, 5.03, 5.04, 5.05, 5.08 6.01, 6.03, 6.07, 6.22, 6.37, 6.49, 6.50, 6.57, 6.52, 6.80, 6.81 8.17 |
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| Homework 4 | Wed Nov 6 |
From Garrett's text: 6.30, 6.31 9.11, 9.12 10.04, 10.08, 10.11 11.11 12.06, 12.10, 12.12, 12.14, 12.15 |
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| Midterm exam 2 | Wed Nov 13 | Midterm 2, to be turned in at the class Canvas site. | |
| Homework 5 | Wed Nov 27 |
From Garrett's text: 12.01, 12.02, 12.04, 12.17, 12.19, 12.20 13.02, 13.05, 13.07, 13.09, 13.10 |
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| Homework 6 | Wed Dec 4 (note 1-week due date!) |
From Garrett's text: 11.04, 11.05 14.02, 05 (In 14.02, assume the matrix has entries in F2.) 15.03, 13 | |
| Final exam | Wed. Dec 11 |
Final exam will appear here in PDF, to be turned in at the class Canvas site. |