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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First Sentence:
The first half of the nineteenth century was a time of tremendous change and upheavals all over the world. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
similar plane numbers, trichotomy principle, unit disk model, higher parabolas, set theory chapter, number theory chapter, power residues modulo, parallel postulate, added straight line, primitive triples, two square numbers, characteristic triangle, reduced equation, infinite descent, proposed equation, angle sum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Academy of Sciences, Continuum Hypothesis, Fundamental Theorem of Calculus, Euclid's Elements, Axiom of Choice, Ars Magna, Ecole Polytechnique, Georg Cantor, Hypothesis of the Acute Angle, Paradoxes of the Infinite, Pythagorean Theorem, Cavalieri's Principle, Fundamental Theorem of Arithmetic, Augustin-Louis Cauchy, Disquisitiones Arithmeticae, Ernst Kummer, Hypothesis of the Obtuse Angle, Sophie Germain's Theorem, University of Bologna, Andrew Wiles, Bernard Bolzano, Evariste Galois, Fermat's Little Theorem, Intermediate Value Theorem, Joseph Louis Lagrange New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The first half of the nineteenth century was a time of tremendous change and upheavals all over the world. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
similar plane numbers, trichotomy principle, unit disk model, higher parabolas, set theory chapter, number theory chapter, power residues modulo, parallel postulate, added straight line, primitive triples, two square numbers, characteristic triangle, reduced equation, infinite descent, proposed equation, angle sum Key Phrases - Capitalized Phrases (CAPs): (learn more)
Academy of Sciences, Continuum Hypothesis, Fundamental Theorem of Calculus, Euclid's Elements, Axiom of Choice, Ars Magna, Ecole Polytechnique, Georg Cantor, Hypothesis of the Acute Angle, Paradoxes of the Infinite, Pythagorean Theorem, Cavalieri's Principle, Fundamental Theorem of Arithmetic, Augustin-Louis Cauchy, Disquisitiones Arithmeticae, Ernst Kummer, Hypothesis of the Obtuse Angle, Sophie Germain's Theorem, University of Bologna, Andrew Wiles, Bernard Bolzano, Evariste Galois, Fermat's Little Theorem, Intermediate Value Theorem, Joseph Louis Lagrange New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 100
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49
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- History of Mathematics, Vol. I (Dover Books on Mathematics) by David E. Smith in Back Matter (1), Back Matter (2), and Back Matter (3)
- Sophie Germain: An Essay in the History of the Theory of Elasticity (Studies in the History of Modern Science) by L.L. Bucciarelli in Front Matter, Back Matter (1), and Back Matter (2)
- Analysis by Its History (Undergraduate Texts in Mathematics / Readings in Mathematics) by Ernst Hairer in Front Matter, Back Matter (1), and Back Matter (2)
- Abraham Robinson by Joseph Warren Dauben on page 150, Back Matter (1), and Back Matter (2)
- Mathematics: A Concise History and Philosophy (Undergraduate Texts in Mathematics / Readings in Mathematics) by W.S. Anglin in Front Matter, and Back Matter
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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
- Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever by Hal Hellman in Back Matter (1), and Back Matter (2)
- A Field Guide to Algebra (Undergraduate Texts in Mathematics) by Antoine Chambert-Loir in Back Matter
- Differential Equations: An Introduction with Mathematica® (Undergraduate Texts in Mathematics) by Clay C. Ross in Back Matter
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