Summary: This is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples which are ...show more analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results.
Provides a low key introduction to Number Theory.
Encourages students to make mathematical discoveries on their own through five basic steps: experimentation, pattern recognition, hypothesis formation, hypothesis testing, and formal proof.
Covers material not usually presented at this level, such as the RSA cryptosystem, elliptic curves, and an overview of Wiles' proof of Fermat's Last Theorem.
All the core text problems are built into the text and must be worked by all students.