Synopses & Reviews
The spirit of this book is based on the study of original historical sources to learn great mathematics via the rich insights and motivation provided by original sources. Both the nature and structure of this book are similar to that of the authors' previous UTM, Mathematical Expeditions. However, the level and mathematical emphasis in the new book is different. Mathematical Expeditions contained material from a freshman and sophomore level course, while this new book is taken from a junior and senior level course. At the same time, the focus of the new book is more on modern mathematics than was the case with Mathematical Expeditions. The new book is more about mathematics than it is about its history. The authors' goal is to throw light on the mathematical world in which we live, and in the process, to introduce students to the exciting world of mathematical discovery, to get across the thrill of exploring the unkonwn that motivates most mathematicians.
Review
From the reviews: "This book is closely related to courses of mathematics held for students at New Mexico State University ... . An important aspect of the book is the numerous exercises, which should help students to gain a deeper insight into the presented material. Numerous references and well-organized indices make the book easy to use. It can be recommended for university libraries and students with an interest in the history of mathematics presented from a modern point of view." (EMS Newsletter, September, 2008) "This book consists of four chapters, each of which presents a 'sequence of selected primary sources' leading up to a 'masterpiece of mathematical achievement'. ... Each chapter contains ... lots of historical comments sketching the further development of the topic. There are also a lot of exercises. ... This is a well written and entertaining book that can (and should) be used in seminars or reading courses." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1140, 2008)
Synopsis
In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J. Gould writes: W]e acquire a surprising source of rich and apparently limitless novelty from the primary documents of great thinkers throughout our history. But why should any nuggets, or even ?akes, be left for int- lectual miners in such terrain? Hasn t the Origin of Species been read untold millions of times? Hasn t every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sources certainly not in necessary depth and completion, and often not at all. . . . I can attest that all major documents of science remain cho- full of distinctive and illuminating novelty, if only people will study them in full and in the original editions. Why would anyone not yearn to read these works; not hunger for the opportunity? 99, p. 6f] It is in the spirit of Gould s insights on an approach to science based on p- mary texts that we o?er the present book of annotated mathematical sources, from which our undergraduate students have been learning for more than a decade. 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. Our students read sequences of primary sources."
Synopsis
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.
Synopsis
Intended for juniors and seniors majoring in mathematics, as well as anyone pursuing independent study, this book traces the historical development of four different mathematical concepts by presenting readers with the original sources. Each chapter showcases a masterpiece of mathematical achievement, anchored to a sequence of selected primary sources. The authors examine the interplay between the discrete and continuous, with a focus on sums of powers. They then delineate the development of algorithms by Newton, Simpson and Smale. Next they explore our modern understanding of curvature, and finally they look at the properties of prime numbers. The book includes exercises, numerous photographs, and an annotated bibliography.
Synopsis
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.
Synopsis
Experience the discovery of mathematics by reading the original work of some of the greatest minds throughout history. Here are the stories of four mathematical adventures, including the Bernoulli numbers as the passage between discrete and continuous phenomena, the search for numerical solutions to equations throughout time, the discovery of curvature and geometric space, and the quest for patterns in prime numbers. Each story is told through the words of the pioneers of mathematical thought. Particular advantages of the historical approach include providing context to mathematical inquiry, perspective to proposed conceptual solutions, and a glimpse into the direction research has taken. The text is ideal for an undergraduate seminar, independent reading, or a capstone course, and offers a wealth of student exercises with a prerequisite of at most multivariable calculus.
Table of Contents
Preface.- The Bridge Between the Continuous and the Discrete.- Solving Equations Numerically: Finding our Roots.- Curvature and the Notion of Space.- Patterns in Prime Numbers: The Quadratic Reciprocity Law.- References.- Credits.