Mathematical Masterpieces Further Chronicles by the Explorers
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Description: 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 17 th 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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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $59.99
Copyright year: 2007
Publication date: 8/14/2007
Size: 6.25" wide x 9.25" long x 0.75" tall
|The Bridge Between Continuous and Discrete|
|Archimedes Sums Squares to Find the Area Inside a Spiral|
|Fermat and Pascal Use Figurate Numbers, Binomials, and the Arithmetical Triangle to Calculate Sums of Powers|
|Jakob Bernoulli Finds a Pattern|
|Euler's Summation Formula and the Solution for Sums of Powers|
|Euler Solves the Basel Problem|
|Solving Equations Numerically: Finding Our Roots|
|Qin Solves a Fourth-Degree Equation by Completing Powers|
|Newton's Proportional Method|
|Simpson's Fluxional Method|
|Smale Solves Simpson|
|Curvature and the Notion of Space|
|Huygens Discovers the Isochrone|
|Newton Derives the Radius of Curvature|
|Euler Studies the Curvature of Surfaces|
|Gauss Defines an Independent Notion of Curvature|
|Riemann Explores Higher-Dimensional Space|
|Patterns in Prime Numbers: The Quadratic Reciprocity Law|
|Euler Discovers Patterns for Prime Divisors of Quadratic Forms|
|Lagrange Develops a Theory of Quadratic Forms and Divisors|
|Legendre Asserts the Quadratic Reciprocity Law|
|Gauss Proves the "Fundamental Theorem"|
|Eisenstein's Geometric Proof|
|Gauss Composes Quadratic Forms: The Class Group|
|Appendix on Congruence Arithmetic|