Noah Halford's solutions to the last problem set posted. Study them for style and ideas.
Quiz-2, cumulative test score, and homework statistics posted. Click "Statistics" on the navigation bar.
Fourteenth problem set posted (Dec 2, 6am) Due Thursday, Dec 4.
Second quiz posted. Click "Grading, tests" on the navigation bar and then "Second quiz."
Midterm and homework statistics posted. Click "Statistics" on the navigation bar.
Thirteenth problem set posted (Nov 25, 3am) Due Tuesday, Nov 25.
Twelfth problem set posted (Nov 18, 11:55am) Due Thursday, Nov 20.
Midterm posted. Click "Grading, tests" on the navigation bar and then "Midterm."
Tenth problem set, first and second batch posted (Nov 7, 9pm; 10:20pm) Due Tuesday, Nov 11.
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.
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.
Office hours: by appointment (please send e-mail)
Classes: TuTh 9:00 - 11:20, Ry-251
Tutorial: Th 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: Thursday, December 4. Attendance mandatory.
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)
DM Lecture Notes by Morgan Sonderegger and Lars Bergstrom (PDF) (detailed notes based on the 2007 class, but not proofread by instructor)
Problem sheets from instructor's 2012 REU course (including linear algebra problems and "puzzle problems")
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,...)
Grades are based on homework (27%), a midterm (20%), two quizzes (first quiz: 8%, second quiz: 5%), class participation (5%) and the final exam (35%).
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.
October 16 Thursday: first quiz (8%)
November 18 Tuesday: midterm (20%)
December 2 Tuesday: second quiz (5%)
December 5, Thursday: LAST CLASS. Attendance mandatory.
December 11 Thursday, 8:00 - 10:00: final exam (35%)