Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. The objects studied in discrete mathematics, such as integers, graphs, and statements in logic, are distinct and separated values. It is an important area of mathematics, and providing the mathematical basis for the understanding of computers and modern computation. In this course we stress the art of proof in the hope that computer scientists will learn to think formally and precisely. Almost every formula and theorem are proved in full. This course introduces second year students to the basic concepts of discrete mathematics, covering topics such as sets, proof techniques, counting methods, recurrence relations, induction and graph theory. The course provides important background for students pursuing a Computer Science degree. The content of the course includes four parts, part 1 on foundational concepts, part 2 on digraphs and graphs, part 3 on order notation and counting, and part 4 on modular arithmetic and cryptography.

[1] Harry Lewis, Rachel Zax, Essential Discrete Mathematics for Computer Science, Princeton University Press, 2019.
[2] Kenneth H. Rosen, Discrete Mathematics and its Applications, 7th edition, McGraw Hill Higher Education, 2012.
[3] W.D. Wallis, A Beginner’s Guide to Discrete Mathematics, Second Edition, Springer Science, 2012.
[4] Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd Edition, University of Northern Colorado, 2013.