CMSC 37110-1: Discrete Mathematics


What's new | Course description | Course info | Text | Grading, tests | Policy on collaboration | Homework | Statistics | prior years

What's new?

The final exam has been posted. Solve it on your own quiet time. (See below, or click "Grading, tests" on the banner.) (Posted Dec 11.)

FINAL EXAM: Friday, December 11, 10:30 - 12:30, Ry-277

Homework statistics posted. Click "statistics" on the banner. (Posted Dec 10.)

Pre-final tutorial: Wed, Dec 9, 4:30 pm, Ry-277.

Statistics posted (fourth quiz and adjusted cumulative test scores). Click "statistics" on the banner. (Posted Dec 11.)

The fourth quiz has been posted. Solve it on your own quiet time. (See below, or click "Grading, tests" on the banner.)

Please report any errors on this website by email to the instructor. Those who are first to report significant errors receive homework bonus points.

Questionnaire

Please send email to the instructor with answers to these questions, even if you are only sitting in on the class, did not register, or have an unusual status. Your answers to these questions will help me better to plan the course. Please write "CMSC 37110 data" in the subject.

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Old news

This site is up.

Remember: LAST CLASS: Friday, December 4. Attendance mandatory.

The sixteenth homework set has been posted. Click "Homework" on the banner. Due Friday, Dec 4. Posted Wed, Dec 2, 7:40am. (Solve homework set #15 first.)

Remember: LAST CLASS: Friday, December 4. Attendance mandatory.

The fifteenth homework set has been posted. Click "Homework" on the banner. Due Wednesday, Dec 2. Posted Mon, Nov 30, 7:30pm.

The fourteenth homework set has been posted. Click "Homework" on the banner. Due Monday, Nov 30. Posted Thu, Nov 26, 5pm.

The thirteenth homework set has been posted. Click "Homework" on the banner. Due Wednesday, Nov 25. Posted Mon, Nov 23, 10:10pm.

The twelfth homework set has been posted. Click "Homework" on the banner. Due Friday, Nov 20. Posted Mon, Nov 16, 7pm. Some of the problems in the set are only due Monday, Nov 23, but require reading a chapter from MN, so take an early start.

The eleventh homework set has been posted. Click "Homework" on the banner. Due Monday, Nov 16. Posted Sun, Nov 15, 11am. Problems were announced in Friday's class.

The tenth homework set has been posted. Click "Homework" on the banner. Due Friday, Nov 13. Posted Wed, Nov 11, 2:30pm.

The ninth homework set has been posted. Click "Homework" on the banner. Due Monday, Nov 9, the same day as the eighth set except that the "DO" exercises are due Tuesday before the tutorial. Posted Fri, Nov 6, 3pm. Make sure you solve the eighth homework set first.

Cumulative test scores posted. Click "statistics" on the banner. (Nov 4, 8:15pm)

The eighth homework set has been posted. Click "Homework" on the banner. Due Monday, Nov 9. Posted Wed, Nov 4, 7:50pm. Make sure you solve the sixth and seventh homework sets first.

The seventh homework set has been posted. Click "Homework" on the banner. Due Friday, Nov 6. Posted Mon, Nov 2, 5pm. Make sure you solve the sixth homework set first.

The sixth homework set has been posted. Click "Homework" on the banner. Due Wednesday, Nov 4. Posted Mon, Nov 2, 2pm. "DO" exercises, due Tuesday, Nov 3, before the tutorial, posted Mon, Nov 2, 3:30 pm.

Midterm statistics has been posted. Click "statistics" on the banner. (Oct 29, 1pm)

The midterm has been posted. (See below, or click "Grading, tests" on the banner.) Solve the problems without the time pressure.

The fifth homework set has been posted. Click "Homework" on the banner. Due Monday, Oct 26. (Posted Wed, Oct 21, 7:30pm.)

The fourth homework set has been posted. Click "Homework" on the banner. Due Friday, Oct 23. (Posted Tue, Oct 20, 8pm.)

Statistics of quizzes 1 and 2 posted. Click "statistics" on the banner. (Posted Oct 20, updated Oct 21.)

Second quiz has been posted. (See below, or click "Grading, tests" on the banner.)

The first quiz has been posted. Click "Grading, tests" on the banner and then "first quiz." DO: Solve all problems without the time pressure (by Monday, October 12)

Test dates have been posted. (See below, or click "Grading, tests" on the banner.) First quiz: Friday, October 9 (in class, 20 minutes, closed book - no text, no notes)

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Course description

This course intends to introduce the students into the ways of mathematical thinking, from intuition to formal statement and proof, through a number of interconnected elementary subjects most of which should be both entertaining and useful in their many connections to classical mathematics as well as to real-world applications.

Through a long series of examples, we practice how to formalize mathematical ideas and learn the nuts and bolts of proofs.

High-school level familiarity with sets, functions, and relations will be assumed.

The list of subjects includes quantifier notation, number theory, methods of counting, generating functions, finite probability spaces, undirected and directed graphs, basic linear algebra, finite Markov Chains (a class of stochastic processes).

Sequences of numbers will be a recurring theme throughout. Our primary interest will be the rate of growth of such a sequence (asymptotic analysis). From calculus, the notion of limits (especially at infinity) is required background. "Asymptotic thinking" about sequences is also the bread and butter of the analysis of algorithms, the subject of a course offered in Winter.

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Course information

Instructor: László Babai     Ryerson 164     e-mail: laci(at)cs(dot)uchicago(dot)edu.

Office hours: by appointment (please send e-mail)


Teaching assistant:

Raghav Kulkarni    raghav(at)cs(dot)uchicago(dot)edu.

The TA holds office hours Thursday 5:00-6:00pm in Ry-162 (the "Theory Lounge").


Classes: MWF 11:30 - 12:20, Ry-277

Tutorial: Tue 4:30 - 5:20 pm, Ry-277. Attendance mandatory unless waived by instructor. The main theme is solving problems, especially homework and test problems.

LAST CLASS: Friday, December 4. Attendance mandatory.

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Text

Your primary text will be your course notes, so please make sure you don't miss classes. If you do, you should copy somebody's class notes and discuss the class with them.

Instructor's Discrete Mathematics Lecture Notes (PDF)

Instructor's Linear Algebra lecture notes (PDF)

Printed text:

J. Matoušek, J. Nešetříl: "Invitation to Discrete Mathematics," published by Oxford University Press, ISBN# 098502079.

(Note: the second edition of this text appeared in 2009. You may also use the first edition. The numbering of chapters has changed; I will post the correspondence.)

Recommended reference (undergraduate text):

Kenneth H. Rosen: Discrete Mathematics and its Applications (n-th edition, n=2,3,4,5,...)

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Grading

Grades are based on homework (25%), a midterm (16%), four quizzes (1st quiz 4%, the other three 6% each), class participation (5%) and the final exam (32%).

The tests are closed-book; no notes permitted. Calculators are permitted for basic arithmetic (multiplication, division) but not for more advanced functions such as g.c.d. Calculators will seldom be of any use: the problems tend to involve very little numerical calculation.

Test dates

October 9 Friday: first quiz (4%)

October 16 Friday: second quiz (6%)

October 28 Wednesday: midterm (16%)

November 11 Wednesday: third quiz (6%)

December 2 Wednesday: fourth quiz (6%)

December 4, Friday: LAST CLASS. Attendance mandatory.

December 11 Friday, 10:30 - 12:30: final exam (32%)

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Rules on HOMEWORK

Unless otherwise stated, homework is always due the next class (before class). Please check the website for updates. The problems will be posted shortly after class. However, errors may occur, so please recheck the website, especially if you suspect an error. If you find an error or something that looks suspicious in an assignment, please notify the instructor (by email). If you are the first to point out an error, you may receive bonus points. "DO" problems are meant to check your understanding of the concepts. Do them but do not hand them in. If you encounter any difficulties, please check with teh TA during office hours. Challenge problems don't have a specific deadline except they cease to be problems once they have been discussed in class. If you are working on a challenge problem, please send email to the instructor so as to avoid the problem being discussed before you handed in the solution. Solutions to Challenge problems don't earn you credit toward your grade but they do earn you the instructor's respect, in addition to giving you valuable experience.

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Policy on collaboration

Studying in groups is strongly encouraged. Collaboration on current homework is discouraged but not prohibited. If you do collaborate, state it at the beginning of your solution (give name of collaborator). DO NOT COPY someone else's solution: after the discussion, throw away any written records. Understand the ideas discussed and give your own rendering. The same applies to other sources such as the Web: give the source (URL), but DO NOT COPY. Understand; then write your own version without looking at the source or your notes.

View the instructor's class material from previous years

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