ISBN : 9780198846734
Number theory is one of the oldest branches of mathematics that is primarily concerned with positive integers. While it has long been studied for its beauty and elegance as a branch of pure mathematics, it has seen a resurgence in recent years with the advent of the digital world for its modern applications in both computer science and cryptography.
Number Theory: Step by Step is an undergraduate-level introduction to number theory that assumes no prior knowledge, but works to gradually increase the reader's confidence and ability to tackle more difficult material.
The strength of the text is in its large number of examples and the step-by-step explanation of each topic as it is introduced to help aid understanding the abstract mathematics of number theory.
It is compiled in such a way that allows self-study, with explicit solutions to all the set of problems freely available online via the companion website. Punctuating the text are short and engaging historical profiles that add context for the topics covered and provide a dynamic background for the subject matter.
1 A Survey of Divisibility
2 Primes and Factorization
3 Theory of Modular Arithmetic
4 A Survey of Modular Arithmetic with Prime Moduli
5 Euler's Generalization of Fermat's Theorem
6 Primitive Roots and Indices
7 Quadratic Residues
8 Non-Linear Diophantine Equations