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. |
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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 1
... proof of its reality was not long in coming . However , in the end this " negative " answer left mathematics a much richer subject . Instead of one geometry , there now was a rich variety of possible geometries , which found ...
... proof of its reality was not long in coming . However , in the end this " negative " answer left mathematics a much richer subject . Instead of one geometry , there now was a rich variety of possible geometries , which found ...
Σελίδα 2
... proof , Euclid builds up his geometrical edifice as a very beautiful and economical succession of theorems and proofs , each depending on the previous ones , with little that is superfluous . This structure was greatly influenced by the ...
... proof , Euclid builds up his geometrical edifice as a very beautiful and economical succession of theorems and proofs , each depending on the previous ones , with little that is superfluous . This structure was greatly influenced by the ...
Σελίδα 3
... proof , the facts shown in the case of other lines may direct our imagination the opposite way . And , though the controversial arguments against the meeting of the straight lines should contain much that is surpris- ing , is there not ...
... proof , the facts shown in the case of other lines may direct our imagination the opposite way . And , though the controversial arguments against the meeting of the straight lines should contain much that is surpris- ing , is there not ...
Σελίδα 4
... proof of Proposition 32. Much subsequent effort was focused on understanding the precise relationship between this result and the parallel postulate , as we will see later in the chapter . The other central consequence of the parallel ...
... proof of Proposition 32. Much subsequent effort was focused on understanding the precise relationship between this result and the parallel postulate , as we will see later in the chapter . The other central consequence of the parallel ...
Σελίδα 5
... proof depended only on the first four postulates . Finally , using invalid reasoning , he convinced himself that he had found the elusive contradiction , and concluded that the parallel postulate was valid after all . In 1733 , he ...
... proof depended only on the first four postulates . Finally , using invalid reasoning , he convinced himself that he had found the elusive contradiction , and concluded that the parallel postulate was valid after all . In 1733 , he ...
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