A textbook for an undergraduate course at lower-level without and at upper-level with optional sections on applications. Assumes no background in computer science and no mathematics past solid high-school level. Combines elementary number theory with algebraic number theory and applications such as those in cryptology. Begins with the arithmetic of the rational integers and proceeds through quadratic orders to an introduction of algebraic number theory. Also briefly traces the history of number theory from the earliest inscriptions. Annotation c. by Book News, Inc., Portland, Or.
Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to
cryptography
factoring
primality testing
complexity analysis
computer arithmetic
computational number theory
Fundamental Number Theory with Applications also covers:
Carmichael numbers
Dirichlet products
Jacobsthal sums
Mersenne primes
perfect numbers
powerful numbers
self-contained numbers
Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material.
Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.
