Alex Kasman – författare
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2 produkter
2 produkter
Häftad, Engelska, 2005
436 kr
Skickas inom 11-20 vardagar
Where can you hear an old man in a nursing home tell of how he disproved Goldbach's Conjecture as part of an undergraduate research project? Get inside the mind of James Clerk Maxwell as he discovers electro-magnetic waves? Witness the 19th century's greatest mathematician finally get the credit she was denied by sexism and murder? In Reality Conditions, a collection of short stories spanning a variety of genres, you can share in these and other fictional mathematical experiences.Each story is a mathematical journey designed to entertain, educate and tantalize. There is something here for everyone: humor, drama, the little details to the big picture, science fiction to true histories. Through these stories, those with little mathematical background will encounter some of the most interesting parts of the field of mathematics for the first time. Even professional mathematicians will be captivated by ideas that take us to the limits of knowledge, addressing the questions of how mathematics is related to the human mind and how it is related to reality. The book is perfect for leisure reading. Join one of the leading experts in the area of mathematical fiction as he takes us on a whirlwind tour of mathematics, both real and imaginary.
Häftad, Engelska, 2023
691 kr
Skickas inom 5-8 vardagar
Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity.Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous.Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $\wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians.Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of MathematicaR to facilitate computation and animate solutions.The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.