Mathematical Masterpieces

Advanced undergraduates will find here an introduction to the excitement of mathematical discovery, through close examination of original historical sources. Each chapter is anchored by a different story sequence of selected primary sources showcasing a masterpiece of mathematical achievement, illustrated by mathematical exercises and historical photographs.


This book traces the historical development of four different mathematical concepts by presenting readers with the original sources, yielding 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 showcases a masterpiece of mathematical achievement, anchored around a sequence of selected primary sources. 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. The book includes exercises, numerous historical photographs, and an annotated bibliography.

This text has been developed and class tested for over 15 years Uses original sources to teach the history of mathematics Heavily illustrated with line drawings and half-tones, and each chapter is accompanied by exercises Each chapter is self-contained and could be used independently Includes supplementary material: sn.pub/extras

Zusammenfassung
Although teaching and learning with primary historical sources require a commitment of study, the investment yields the rewards of a deeper understanding of the subject, an appreciation of its details, and a glimpse into the direction research has taken.

Inhalt
The Bridge Between Continuous and Discrete.- Solving Equations Numerically: Finding Our Roots.- Curvature and the Notion of Space.- Patterns in Prime Numbers: The Quadratic Reciprocity Law.

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