This book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Although primary sources can be more demanding, the investment yields the rewards of a deeper understanding of the subject, an appreciation of the details, and a glimpse into the direction research has taken. Each chapter contains a different story, each anchored around a sequence of selected primary sources showcasing a masterpiece of mathematical achievement. The authors begin by studying the interplay between the discrete and continuous, with a focus on sums of powers. They proceed to the development of algorithms for finding numerical solutions of equations as developed by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, with its roots in the emerging calculus of the 17th century, while the final chapter ends with an exploration of the elusive properties of prime numbers, and the patterns found therein. This book emerged from a course taught at New Mexico State University to juniors and seniors majoring in mathematics. The intended audience is juniors and seniors majoring in mathematics, as well as anyone pursuing independent study. The authors have included exercises, numerous historical photographs, and an annotated bibliography.
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