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This book is issued from a 30 year experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are...
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"What's new in this edition? We have added new content and also tried to make improvements to the existing material. There are five new historical sketches, on: The tangent function and how it made its way into trigonometry. Logarithms, both decimal and natural. Conic sections: ellipses, parabolas, and hyperbolas. Irrational numbers. The derivative. As always, each of these come with Questions and Projects that try to address both the mathematics...
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"In this vibrant work, which is ideal for teaching and learning, Apoorva Khare and Anna Lachowska explain the mathematics essential for understanding and appreciating our quantitative world. They show with examples that mathematics is a key tool in the creation and appreciation of art, music, and literature, not just science and technology. The book covers basic mathematical topics from logarithms to statistics, but the authors eschew mundane finance...
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"In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard."--Publisher description.
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Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides...
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Princeton mathematical volume 49
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Benson Farb is professor of mathematics at the University of Chicago. He is the editor of Problems on Mapping Class Groups and Related Topics and the coauthor of Noncommutative Algebra. Dan Margalit is assistant professor of mathematics at Georgia Institute of Technology.
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book...
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An accessible history and philosophical commentary on our notion of infinity.
How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict...
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"The fascinating world of graph theory goes back several centuries and revolves around the study of graphs - mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics - and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit...
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Great Courses volume 9
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Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic—the kind we apply in daily life—is the gateway to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy’s equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army...
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Annals of mathematics studies volume no. 180
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Nicholas M. Katz is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; Rigid Local Systems; Twisted L-Functions and Monodromy; and Moments, Monodromy, and Perversity.
Convolution and Equidistribution explores...
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The updated new edition of the classic and comprehensive guide to the history of mathematics
For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind's relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat's Last Theorem and the Poincaré Conjecture, in addition to recent advances in...
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Mathematician John Allen Paulos employs his singular wit to guide us through an unlikely mathematical jungle--the pages of the daily newspaper. From the Senate and sex to celebrities and cults, Paulos takes stories that may not seem to involve math at all and demonstrates how mathematical naivete can put readers at a distinct disadvantage. Whether he's using chaos theory to puncture economic and environmental predictions, applying logic to clarify...
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"We are all doing math all the time, from the way we communicate with each other to the way we travel, from how we work to how we relax. Many of us are aware of this. But few of us really appreciate the full power of math - the extent to which its influence is not only in every office and every home, but also in every courtroom and hospital ward. In this eye-opening and extraordinary book, Kit Yates explores the true stories of life-changing events...
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What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers--for the sake of truth, beauty, and practical applications--this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.
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This book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a specified regression function of increments — linear or nonlinear. The statistical experiments are studied by the sample volume increasing, as well as in discrete-continuous time by the number of stages increasing for different...
