Calendar Description

COMP2804 Discrete Structures II

Introduction to discrete mathematics and discrete structures. Topics include: counting, sequences and sums, discrete probability (including random variables, expectation, linearity of expectation, dependence, concentration results, distributions), recurrence relations. Material is illustrated through examples from computing.

Assumed Background

COMP 1805 (Minimum grade of B-?)
MATH 1007
MATH 1104
COMP 1406

Learning Objectives

To learn basic tools and techniques from combinatorics and probability theory which are used in several areas in CS. To learn basic counting techniques, asymptotic analysis, probability and statistics. Design and analysis of several simple randomized algorithms will be discussed during the course. Statistical ...

Topics

Counting: Permutations, Combinations, Binomial Coefficients, Pigeon-Hole Principle, Inclusion-Exclusion.
Asymptotic Complexity: O, Theta, Solving recurrence relations.
Probability: Random Variables, Expected Value, Indicator, Markov Inequality, Chernoff Bounds.
Randomized Algorithms: Median, Quicksort, Binary Search Trees, Skip Lists, 2-dimensional Linear Programming.
Statistics: Confidence tests and Intervals, Hypothesis Testing, p-values, chi square, ANOVA (Analysis of Variance)
Probability distributions: Poisson, normal, power laws (Zipf's law)