Mathematics in Cybersecurity

1Introduction to Sets

Concepts

• Definition of a set
• Elements of a set
• Cardinality of a set
• Notation (using braces, ellipsis, rosters, set builder notation)
• De Morgan's Laws

Augustus De Morgan (born June 27, 1806, Madura, India—died March 18, 1871, London, England) was an English mathematician and logician whose major contributions to the study of logic include the formulation of De Morgan's laws and work leading to the development of the theory of relations and the rise of modern symbolic, or mathematical, logic.

Encyclopedia Brittanica

1.1 Introduction

The landscape of history of mathematics, logic, and computer science is populated by gigantic figures: Sir Isaac Newton, Aristotle, Alan Turing, Galileo Galilei, Ludwig Wittgenstein, and countless others. As we embark on a journey to understand mathematics and its relationship to cybersecurity, we remark that not all of what we will discuss here will be straightforward (let alone simple!). Many of the results we present and use will be named after men and women of genius, and we will pause to honor them in our writing; it is to them that we all owe a measure of gratitude, awe, and respect.

We are, metaphorically speaking, walking in the footsteps of giants.

Be confident, however, that you are eminently capable of mastering the material we are about to present. You will emerge from the course with new ideas and techniques, new skills and insights, and a sense of accomplishment that will see you through the challenges that ...