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.
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.
Preface; 1. The Ancient Greeks; 2. Zeno's Paradox and the concept of limit; 3. The mystical mathematics of Hypatia; 4. The Islamic world and the development of algebra; 5. Cardano, Abel, Galois, and the solving of equations; 6. Rene Descartes and the idea of coordinates; 7. The invention of differential calculus; 8. The great Isaac Newton; 9. Complex numbers and polynomials; 10. The prince of mathematics; 11. Sophie Germain and Fermat's Problem; 12. Cauchy and the foundations of analysis; 13. The prime numbers; 14. Dirichlet and how to count; 15. Riemann and the geometry of surfaces; 16. Georg Cantor and the orders of infinity; 17. The natural numbers; 18. Henri Poincaré, child phenomenon; 19. Sonya Kovalevskaya and mechanics; 20. Emmy Noether and algebra; 21. Methods of proof; 22. Alan Turing and cryptography; Bibliography; Index.
A series of snapshots of the history of mathematics from ancient times to the twentieth century.
Steven G. Krantz received his BA from the University of California, Santa Cruz, and his Ph.D. from Princeton University. He has taught at UCLA, Princeton University, Penn State University, and Washington University in St Louis. He has directed 17 Ph.D. theses, authored over 50 books, and over 150 scholarly papers. He has served on several editorial boards, and is Editor-in-Chief of three journals. Krantz is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Foundation Award.
This important work is not as detailed as Howard Eves's An
Introduction to the History of Mathematics, but it is more
manageable and better suited to teaching the subject. Krantz
selects key eras and topics to illustrate how mathematics in the
Western world evolved from the ancient Greeks to the early modern
era...The carefully written work contains numerous examples, an
excellent selection of problems and projects, and an extensive
bibliography. Useful for history of mathematics or senior capstone
courses. Highly recommended."" - R.L. Pour for CHOICE Magazine
""This is a remarkable book. It is exactly what the title promises
it to be. It is a history of mathematics that teaches the student
what mathematics is about through problem solving. Through
biographical data and anecdotes the reader gets a feeling for the
historical dimension of mathematics while at the same time the well
chosen subjects and the exercises bring across the exciting
character of mathematics and its development. Excellent stuff for
undergraduate students and future teachers."" - Teun Koetsier for
Zentrallblatt
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