| 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: |
Monday, Wednesday, Friday 1:25-2:15pm, in-person in Vincent Hall 211 |
| COVID policy: | The University currently requires all students, staff, faculty to wear masks when indoors regardless of vaccination status. As your instructor, I should be wearing either a face shield or mask when in front of the room. The University strongly encourages all members of its community to get vaccinated. Resources are available for accessing vaccines. Please stay home if you experience symptoms of COVID-19, and consult with your healthcare provider about an appropriate course of action. An absence due to symptoms of COVID-19 is an excused absence, and I will work with you to find the best course of action for missed work and/or class experiences. |
| Office hours: |
Wed 12:20pm in VinH 256 Tues 9:05am, Thur 9:05am at this Zoom link. |
| Class Discord server: |
Here is our Discord server. Let me know if you have ideas for channels, particularly those that could facilitate some study groups. |
| 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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| What this course is NOT: |
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 likely be 6 homework assignments due in the class Canvas site by midnight on
Wednesdays, generally every other week,
except for
Late homework will not be accepted. Early homework is fine, and can be left in my mailbox in the School of Math mailroom near Vincent Hall 105. 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. 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 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. 22 |
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 (moved 3.05 to HW 2) 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. 6 |
From Garrett's text: 2.04 3.05 4.01, 4.02, 4.04, 4.05, 4.06, 4.11 |
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| Midterm exam 1 | Wed. Oct. 13 | Midterm 1, to be turned in at the class Canvas site. | |
| Homework 3 | Wed Oct. 27 |
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. 10 |
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. 17 | Midterm 2, to be turned in at the class Canvas site. | |
| Homework 5 | Wed Dec. 1 |
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. 8 (note 1-week due date!) |
From Garrett's text: 11.04, 11.05 14.02, 05 15.03, 13 | |
| Final exam | Wed. Dec. 15 | Final exam, to be turned in at the class Canvas site. |