An Episodic History of Mathematics: Mathematical Culture Through Problem Solving (Mathematical Association of America Textbooks)

An Episodic History of Mathematics delivers a series of snapshots of the history of mathematics from ancient times to the twentieth century. The intent is not to be an encyclopedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book abounds with stories, and personalities play a strong role. The book will introduce readers to some of the genesis of mathematical ideas. Mathematical history is exciting and rewarding, and is a significant slice of the intellectual pie. A good education consists of learning different methods of discourse, and certainly mathematics is one of the most well-developed and important modes of discourse that we have. The focus in this text is on getting involved with mathematics and solving problems. Every chapter ends with a detailed problem set that will provide the student with many avenues for exploration and many new entrees into the subject. An Episodic History Of Mathematics Delivers A Series Of Snapshots Of Mathematics And Mathematicians From Ancient Times To The Twentieth Century. Giving Readers A Sense Of Mathematical Culture And History, The Book Also Acquaints Readers With The Nature And Techniques Of Mathematics Via Exercises. It Introduces The Genesis Of Key Mathematical Concepts. For Example, While Krantz Does Not Get Into The Intricate Mathematical Details Of Andrew Wiles's Proof Of Fermat's Last Theorem, He Does Describe Some Of The Streams Of Thought That Posed The Problem And Led To Its Solution. The Focus In This Text, Moreover, Is On Doing - Getting Involved With The Mathematics And Solving Problems. Every Chapter Ends With A Detailed Problem Set That Will Provide Students With Avenues For Exploration And Entry Into The Subject. It Recounts The History Of Mathematics; Offers Broad Coverage Of The Various Schools Of Mathematical Thought To Give Readers A Wider Understanding Of Mathematics; And Includes Exercises To Help Readers Engage With The Text And Gain A Deeper Understanding Of The Material.--publisher's Description. The Ancient Greeks And The Foundations Of Mathematics -- Zeno's Paradox And The Concept Of Limit -- The Mystical Mathematics Of Hypatia -- The Islamic World And The Development Of Algebra -- Cardano, Abel, Galois, And The Solving Of Equations -- René Descartes And The Idea Of Coordinates -- Pierre De Fermat And The Invention Of Differential Calculus -- The Great Isaac Newton -- The Complex Numbers And The Fundamental Theorem Of Algebra -- Carl Friedrich Gauss: The Prince Of Mathematics -- Sophie Germain And The Attack On Fermat's Last Problem -- Cauchy And The Foundations Of Analysis -- The Prime Numbers -- Dirichlet And How To Count -- Bernhard Riemann And The Geometry Of Surfaces -- Georg Cantor And The Orders Of Infinity -- The Number Systems -- Henri Poincaré, Child Phenomenon -- Sonya Kovalevskaya And The Mathematics Of Mechanics -- Emmy Noether And Algebra -- Methods Of Proof -- Alan Turing And Cryptography. Steven G. Krantz. Includes Bibliographical References (p. 365-369) And Index. An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematics-both classical and modern. Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincaré, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists. This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practical-getting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on. This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process. Preface The Ancient Greeks and the foundations of Mathematics Zeno's Paradox and the Concept of Limit The Mystical mathematics of Hypatia The Islamic World and the Development of Algebra Cardano, Abel, Galois, and the Solving of Equations Rene Descartes and the Idea of Coordinates Pierre de Fermat and the Invention of Differential Calculus The Great Isaac Newton The Complex Numbers and the Fundamental Theorem of Algebra Carl Friedrich Gauss: The Prince of Mathematics Sophie Germain and the Attack on Fermat's Last Problem Cauchy and the Foundations of Analysis The Prime Numbers Dirichlet and How to Count Bernard Riemann and the Geometry of Surfaces Georg Cantor and the Orders of Infinity The Number Systems Henri Poincare, Child Phenomenon Sonya Kovalevskaya and the Mathematics of Mechanics Emmy Noether and Algebra Methods of Proof Alan Turing and Cryptography Bibliography Index About the Author An Episodic History of Mathematics delivers a series of snapshots of the history of mathematics from ancient times to the twentieth century. The intent is not to provide an encyclopaedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book also acquaints the reader with the nature and techniques of mathematics through its exercises. The book introduces the genesis of many mathematical ideas. For example, while Krantz does not get into the nuts and bolts of Andrew Wiles's solution of Fermat's Last Theorem, he does describe some of the stream of thought that created the problem and led to its solution. The focus in this text is on doing - getting involved with the mathematics and solving problems. Every chapter ends with a detailed problem set that will provide the student with many avenues for exploration and many new entrees into the subject.