The Mathematical Career of Pierre de Fermat, 1601-1665
The Mathematical Career of Pierre de Fermat, 1601-1665

Author: Michael Sean Mahoney

Publisher: Princeton University Press

Published: 1994

Total Pages: 458

ISBN-13: 9780691036663

DOWNLOAD EBOOK

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

The Cambridge Descartes Lexicon
The Cambridge Descartes Lexicon

Author: Lawrence Nolan

Publisher: Cambridge University Press

Published: 2015-01-01

Total Pages: 1642

ISBN-13: 1316380939

DOWNLOAD EBOOK

The Cambridge Descartes Lexicon is the definitive reference source on René Descartes, 'the father of modern philosophy' and arguably among the most important philosophers of all time. Examining the full range of Descartes' achievements and legacy, it includes 256 in-depth entries that explain key concepts relating to his thought. Cumulatively they uncover interpretative disputes, trace his influences, and explain how his work was received by critics and developed by followers. There are entries on topics such as certainty, cogito ergo sum, doubt, dualism, free will, God, geometry, happiness, human being, knowledge, Meditations on First Philosophy, mind, passion, physics, and virtue, which are written by the largest and most distinguished team of Cartesian scholars ever assembled for a collaborative research project - 92 contributors from ten countries.

The Unfinished Game
The Unfinished Game

Author: Keith Devlin

Publisher:

Published: 2010-03-23

Total Pages: 210

ISBN-13: 0465018963

DOWNLOAD EBOOK

Before the mid-seventeenth century, scholars generally agreed that it was impossible to predict something by calculating mathematical outcomes. One simply could not put a numerical value on the likelihood that a particular event would occur. Even the outcome of something as simple as a dice roll or the likelihood of showers instead of sunshine was thought to lie in the realm of pure, unknowable chance. The issue remained intractable until Blaise Pascal wrote to Pierre de Fermat in 1654, outlining a solution to the "unfinished game" problem: how do you divide the pot when players are forced to.

The Mathematical Career of Pierre de Fermat, 1601-1665
The Mathematical Career of Pierre de Fermat, 1601-1665

Author: Michael Sean Mahoney

Publisher: Princeton University Press

Published: 2018-06-05

Total Pages: 455

ISBN-13: 0691187630

DOWNLOAD EBOOK

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

13 Lectures on Fermat's Last Theorem
13 Lectures on Fermat's Last Theorem

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 306

ISBN-13: 1468493426

DOWNLOAD EBOOK

Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.

Introduction to Probability
Introduction to Probability

Author: David F. Anderson

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 447

ISBN-13: 110824498X

DOWNLOAD EBOOK

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

The Geometry of René Descartes
The Geometry of René Descartes

Author: René Descartes

Publisher: Courier Corporation

Published: 2012-09-19

Total Pages: 275

ISBN-13: 0486158179

DOWNLOAD EBOOK

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.

How Euler Did Even More
How Euler Did Even More

Author: C. Edward Sandifer

Publisher: The Mathematical Association of America

Published: 2014-11-19

Total Pages: 254

ISBN-13: 0883855844

DOWNLOAD EBOOK

Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.

Making up Numbers: A History of Invention in Mathematics
Making up Numbers: A History of Invention in Mathematics

Author: Ekkehard Kopp

Publisher: Open Book Publishers

Published: 2020-10-23

Total Pages: 280

ISBN-13: 1800640978

DOWNLOAD EBOOK

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Imaginary Philosophical Dialogues
Imaginary Philosophical Dialogues

Author: Kenneth Binmore

Publisher: Springer Nature

Published: 2020-12-23

Total Pages: 209

ISBN-13: 3030653870

DOWNLOAD EBOOK

How would Plato have responded if his student Aristotle had ever challenged his idea that our senses perceive nothing more than the shadows cast upon a wall by a true world of perfect ideals? What would Charles Darwin have said to Karl Marx about his claim that dialectical materialism is a scientific theory of evolution? How would Jean-Paul Sartre have reacted to Simone de Beauvoir’s claim that the Marquis de Sade was a philosopher worthy of serious attention? This light-hearted book proposes answers to such questions by imagining dialogues between thirty-three pairs of philosophical sages who were alive at the same time. Sometime famous sages get a much rougher handling than usual, as when Adam Smith beards Immanuel Kant in his Konigsberg den. Sometimes neglected or maligned sages get a chance to say what they really believed, as when Epicurus explains that he wasn’t epicurean. Sometimes the dialogues are about the origins of modern concepts, as when Blaise Pascal and Pierre de Fermat discuss their invention of probability, or when John Nash and John von Neumann discuss the creation of game theory. Even in these scientific cases, the intention is that the protagonists come across as fallible human beings like the rest of us, rather than the intellectual paragons of philosophical textbooks.