Before moving on from these preliminaries and our introductory Prologue, let’s step back. What will we cover in this text?
We have started by exploring basic integer questions, and will continue looking at basic integers at first (Chapter 1–Chapter 3).
We’ll be essentially forced to move to the concepts of congruences and primes by the material (Chapter 4–Chapter 7).
Next, we’ll explore a more advanced point of view of the concepts of integers and congruences, including groups, to attack cryptography efficiently (Chapter 8–Chapter 12).
About halfway through, we’ll introduce the ways in which geometry infiltrates number theory (Chapter 13–Chapter 17).
Finally, functions and limits will help us illuminate primes in depth, as well as show us how the ideas of calculus really do show up in number theory quite naturally (Chapter 18–Chapter 24), concluding with an introduction to the legendary Riemann Hypothesis in Chapter 25.
Let’s get ready for an exciting exploration of number theory!