Discrete Mathematics

A discrete mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this teaching material stresses mathematical reasoning and the different ways problems are solved. Five important themes are interwoven in this teaching material: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling. A successful discrete mathematics course should carefully blend and balance all the above themes.This teaching material covers sets, functions, sequences, matrices, logic, elementary counting principle, recurrence relation, undirected graphs, directed graphs and weighted graphs. There are exercises at the end of each section. Appendices contain some important symbols, answers to selected exercises and references.