The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers 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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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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algebraic analysis, similar plane numbers, trichotomy principle, higher parabolas, unit disk model, set theory chapter, number theory chapter, parallel postulate, power residues modulo, primitive triples, added straight line, two square numbers, larger cardinality, characteristic triangle, infinite descent, reduced equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Last Theorem, Elusive Formula, Quadrature of the Parabola, Continuum Hypothesis, Euclid's Elements, Taming the Infinite, Fundamental Theorem of Calculus, Axiom of Choice, Ars Magna, Academy of Sciences, Georg Cantor, Ecole Polytechnique, Hypothesis of the Acute Angle, Disquisitiones Arithmeticae, Cantor's Infinite Numbers, Galois Ends the Story, Theory of Parallels, Hypothesis of the Obtuse Angle, Joseph Liouville, Leonhard Euler, Lobachevskian Geometry, Lagrange's Theory of Equations, Sophie Germain, Ernst Kummer, Paradoxes of the Infinite Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
algebraic analysis, similar plane numbers, trichotomy principle, higher parabolas, unit disk model, set theory chapter, number theory chapter, parallel postulate, power residues modulo, primitive triples, added straight line, two square numbers, larger cardinality, characteristic triangle, infinite descent, reduced equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fermat's Last Theorem, Elusive Formula, Quadrature of the Parabola, Continuum Hypothesis, Euclid's Elements, Taming the Infinite, Fundamental Theorem of Calculus, Axiom of Choice, Ars Magna, Academy of Sciences, Georg Cantor, Ecole Polytechnique, Hypothesis of the Acute Angle, Disquisitiones Arithmeticae, Cantor's Infinite Numbers, Galois Ends the Story, Theory of Parallels, Hypothesis of the Obtuse Angle, Joseph Liouville, Leonhard Euler, Lobachevskian Geometry, Lagrange's Theory of Equations, Sophie Germain, Ernst Kummer, Paradoxes of the Infinite Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
50
books
cite this book:
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- The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh on 5 pages
- The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh on 5 pages
- Mathematical Expeditions: Chronicles by the Explorers (Undergraduate Texts in Mathematics) by Reinhard Laubenbacher in Front Matter, and Back Matter
- Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever by Hal Hellman in Back Matter (1), and Back Matter (2)
- Differential Equations: An Introduction with Mathematica® (Undergraduate Texts in Mathematics) by Clay C. Ross in Back Matter
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