Discrete mathematics is the opposite of continuous mathematics. Calculus is continuous mathematics. Discrete mathematics is, roughly speaking, the study of concepts and applications built atop set theory and the integers.
The book is the Third Edition of Goodaire and Parmenter.
Roughly, we will cover these sections from the book: §2.1-5, §3.1-2, §4.1-5, §5.1-3, §6.1-3, §7.1-3, §7.5, §8.2, §9.1-3, §10.1-4, §11.1-3, and we will cover finite algebraic structures and finite state machines (not in the book.)