Mathematicians do not know in advance if their assertions are true, so they need to verify assertions with rigorous proofs or produce counterexamples, then attempt to salvage the assertions by transforming them into theorems. Extending the Frontiers of Mathematics: Inquiries into Proof and Argumentation invites readers to experience this progression of mathematical discovery. Burger's informal, humorous writing style and intriguing puzzles engage readers throughout the learning process. The innovative text offers a discovery-based approach that is ideal.

Activity-Based Statistics helps build real statistical understanding through a set of innovative hands-on activities that can be used each day in conjunction with other texts. The second edition continues to emphasize discovery by motivating readers to apply the skills they have learned to discover the everyday relevance of statistics. There are over 45 activities and five long-term projects that have been updated and extended to encourage readers to experience statistics in context. While the second edition includes updated technology extensions for Fathom, technology is used throughout the...

Sweet Reason is a unique introductory logic text that covers both the basic rudiments of formal and informal logic as well as the real world where the discipline of logic adds substance and meaning to human discourse. As the text alternately discusses, instructs, questions, teases and challenges, readers will find themselves absorbing the fundamentals of the discipline, becoming fluent in the language of logic, understanding how logic works in the real world, and enjoying logic's ability to entertain, surprise, discover, and enlighten.

A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include...