MATH/CMSC H395: Introduction to Discrete Mathematics

Lecture

TBA

MW 1:00–2:15pm

Office hours

KINSC H207D

TBA

This course introduces three fundamental aspects of discrete mathematics: enumeration, graph theory and discrete probability. Our introduction to enumeration covers basic counting, basic approximations, bijective arguments, double-counting arguments, recurrence relations, generating functions, the pigeonhole principle, inclusion-exclusion, etc. Our introduction to graph theory includes topics such as connectivity, trees, matchings, colorings, Ramsey theory, etc. Our introduction to discrete probability includes linearity of expectation, the law of averages, Markov’s inequality, Chebyshev’s inequality, etc. We will see how discrete probability can be used to prove the existence of surprising discrete structures.

Syllabus

Schedule and Assignments

Homework assignments must be written in \(\LaTeX\) and can be submitted either in-person or by email. If you email me your assignment, the subject line should read MATH H395 <LAST NAME> HW<HOMEWORK NUMBER> and the email should include a .pdf version of your work titled <LAST NAME>_<HOMEWORK NUMBER>.pdf. If you wish to include a picture as part of a solution, the picture need not be typeset; a legible photograph of a hand-drawn picture is acceptable.

Homework assignments are due at the beginning of lecture (12:30pm) on the date by which they are posted in the following table. If you cannot attend class when an assignment is due, you are responsible for emailing me your assignment. For each minute the assignment is late, your assignment grade will be reduced by 1%. For example, an assignment which would score 85% but was submitted at 12:35pm would instead receive an 80%.