Mathematical Expeditions: Chronicles by the ExplorersSpringer Science & Business Media, 1 Δεκ 2013 - 278 σελίδες This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics. |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 85.
Σελίδα ix
... Prove the Parallel Postulate Lobachevskian Geometry 1.5 Poincaré's Euclidean Model for Non - Euclidean Geometry Set Theory : Taming the Infinite 2.1 Introduction 2.2 Bolzano's Paradoxes of the Infinite 2.3 Cantor's Infinite Numbers ...
... Prove the Parallel Postulate Lobachevskian Geometry 1.5 Poincaré's Euclidean Model for Non - Euclidean Geometry Set Theory : Taming the Infinite 2.1 Introduction 2.2 Bolzano's Paradoxes of the Infinite 2.3 Cantor's Infinite Numbers ...
Σελίδα 1
... prove that the geometry laid out by Euclid around 300 B.C.E. in his Elements was the " true " and only one , and provided a description of the physical universe we live in . Not until the end of the eighteenth century did it occur to ...
... prove that the geometry laid out by Euclid around 300 B.C.E. in his Elements was the " true " and only one , and provided a description of the physical universe we live in . Not until the end of the eighteenth century did it occur to ...
Σελίδα 2
... prove it using the other postulates or to replace it by a more fundamental truth , possibly based on a different definition of parallelism . Proclus himself says : This ought even to be struck out of the Postulates altogether ; for it ...
... prove it using the other postulates or to replace it by a more fundamental truth , possibly based on a different definition of parallelism . Proclus himself says : This ought even to be struck out of the Postulates altogether ; for it ...
Σελίδα 3
... proved by Euclid himself as a theorem . It may be that some would be deceived and would think it proper to place ... proving even the most basic facts . Thus , given an angle with sides / and l ' , we want to draw the same angle with ...
... proved by Euclid himself as a theorem . It may be that some would be deceived and would think it proper to place ... proving even the most basic facts . Thus , given an angle with sides / and l ' , we want to draw the same angle with ...
Σελίδα 4
... proved without using the parallel postulate . It is used , however , in Euclid's proof of Proposition 32. Much subsequent ... prove the parallel postulate . An interesting approach was proposed by the Englishman John Wallis ( 1616–1703 ) ...
... proved without using the parallel postulate . It is used , however , in Euclid's proof of Proposition 32. Much subsequent ... prove the parallel postulate . An interesting approach was proposed by the Englishman John Wallis ( 1616–1703 ) ...
Περιεχόμενα
1 | |
Taming the Infinite | 54 |
3 | 69 |
Calculating Areas and Volumes | 89 |
1 | 95 |
4 | 123 |
5 | 129 |
7 | 150 |
Fermats Last Theorem | 156 |
The Search for an Elusive Formula | 204 |
References | 259 |
Credits | 269 |
Άλλες εκδόσεις - Προβολή όλων
Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Περιορισμένη προεπισκόπηση - 2000 |
Mathematical Expeditions Reinhard Laubenbacher,David Pengelley Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1998 |
Συχνά εμφανιζόμενοι όροι και φράσεις
aggregate algebraic analysis angle sum Archimedes arithmetic Axiom Axiom of Choice called Cantor Cardano cardinal number Cauchy Cauchy's Cavalieri's century coefficients complex numbers Continuum Hypothesis cube curve definition divisor elements equal equations of degree equivalent Euclid Euclid's Euclid's Elements Euclidean Euclidean geometry Euler Exercise exponent factors Fermat equation Fermat's Last Theorem FIGURE finite follows formula functions Fundamental Theorem Galois Gauss Germain given Greek hyperbolic geometry Hypothesis indivisibles infinite sets infinitesimal Lagrange Legendre Leibniz Lemma Lobachevsky mathematicians mathematics method natural numbers non-Euclidean non-Euclidean geometry number theory one-to-one correspondence parabola parallel postulate perpendicular PHOTO Poincaré polynomial prime numbers problem proof proposed equation Proposition prove Pythagorean triples Quadrature rational numbers real numbers reduced equation relatively prime result right angles roots segment set theory sides solution solve square straight line tangent triangle FDC values variable Zermelo's