This course is an introduction to discrete mathematics, a field concerned with studying object with distinct or disconnected elements (as opposed to continuous, which is what one finds in calculus). The kinds of problems solved using discrete mathematics involve counting, studying relations between finite or infinite sets, analysis of processes that involve a finite number of steps, and many others.
Since strong emphasis in this course will be placed on developing proof-writing and proof-reading skills, we will begin by introducing and reviewing various basic proof techniques, properties of functions, sets, and logic. We will then spend some time studying counting problems before moving on to topics such as probability, equivalence relations, generating functions, and recurrence relations. Last few weeks of the course will be devoted to graph theory where many of the applications of discrete mathematics will be studied.
After completing this course, you will have a working knowledge of various problems and problem-solving techniques in discrete mathematics and will be equipped to take more advanced courses on number theory, probability, abstract algebra, graph theory, data structures, algorithms, and many others.
The more general objective of this course is to continue providing you with a deeper understanding and working knowledge of mathematics, while in the process strengthening your analytical skills, increasing your ability to communicate mathematics symbolically and orally, making you comfortable with reading and understanding mathematics on your own, and developing an appreciation for mathematics as one of the greatest intellectual tools that can be applied in a variety of real-life situations.