Mathematical Excursions, 2nd Edition

Book Preface

Mathematical Excursions is about mathematics as a system of knowing or understanding our surroundings. It is similar to an English literature textbook, an Introduction to Philosophy textbook, or perhaps an Introductory Psychology textbook. Each of those books provide glimpses into the thoughts and perceptions of some of the world’s greatest writers, philosophers, and psychologists. Reading and studying their thoughts enables us to better understand the world we inhabit.

In a similar way, Mathematical Excursions provides glimpses into the nature of mathematics and how it is used to understand our world. This understanding, in conjunction with other disciplines, contributes to a more complete portrait of our world. Our contention is that ancient Greek architecture is quite dramatic but even more so when the “Golden Ratio” is considered. That I. M. Pei’s work becomes even more interesting with a knowledge of elliptical shapes. That the challenges of sending information across the Internet is better understood by examining prime numbers.

That the perils of radioactive waste take on new meaning with a knowledge of exponential functions. That generally, a knowledge of mathematics strengthens the way we know, perceive, and understand our surroundings.

The central purpose of Mathematical Excursions is to explore those facets of mathematics that will strengthen your quantitative understandings of our environs. We hope you enjoy the journey.

New to This Edition

â–  Reading and interpreting graphs has been expanded to allow students more practice with this important topic.
â–  Chapter 8, Geometry, has been expanded to include the Pythagorean Theorem and congruent triangles.
â–  An introduction to right triangle trigonometry has been added to Chapter 8, Geometry.
â–  Chapter 10, Finance, has expanded coverage of stocks, bonds, and annuities.
â–  There is an Algebra Review Appendix that can be downloaded from the web as a PDF.
â–  All the exercise sets have been reviewed and new, contemporary problems have been added.