Mathematical Masterpieces Further Chronicles by the Explorers

Name: Mathematical Masterpieces Further Chronicles by the Explorers
Price: 35.53 USD
Availability: InStock
ISBN: 9780387330617

ISBN-10: 0387330615

ISBN-13: 9780387330617

Edition: 2007

Authors: Art Knoebel, Reinhard Laubenbacher, Jerry Lodder, David Pengelley

List price: $54.99

This item qualifies for FREE shipping.

30 day, 100% satisfaction guarantee!

Buy new: $56.69

Marketplace

4 new & used from $35.53

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

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…

Book details

List price: $54.99
Copyright year: 2007
Publisher: Springer New York
Publication date: 8/14/2007
Binding: Paperback
Pages: 340
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.100
Language: English



Preface



The Bridge Between Continuous and Discrete



Introduction



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



Introduction



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



Introduction



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



Introduction



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


References


Credits


Name Index


Subject Index