This book effectively integrates computing concepts into the number theory curriculum using a heuristic approach and strong emphasis on rigorous proofs. Its in-depth coverage of modern applications considers the latest trends and topics, such as elliptic curves—a subject that has seen a rise in popularity in the undergraduate curriculum.

1 Introduction
2 Divisibility and Primes
3 Modular Arithmetic
4 Fundamental Theorems of Modular Arithmetic
5 Cryptography
6 Primality Testing and Factoring
7 Primitive Roots
8 Applicatons
9 Quadratic Congruences
10 Applications
11 Continued Fractions
12 Factoring Methods
13 Diophantine Approximations
14 Diophantine Equations
15 Arithmetical Functions and Dirichles Series
16 Distribution of Primes
17 Quadratic Reciprocity Law
18 Binary Quadratic Forms
19 Elliptic Curves
A Mathematical Induction
B Binomial Theorem
C Algorithmic Complexity and O-notation
Answers and Hints
Index of Notation
Index

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