Tag Archives: Mathematicians

Category Theory for the Sciences

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Category Theory for the Sciences by David I. Spivak
2014 | ISBN: 0262028131 | English | 496 pages | PDF | 7 MB

Category Theory for the Sciences
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs — categories in disguise. After explaining the "big three" concepts of category theory — categories, functors, and natural transformations — the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with selected solutions. is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
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101st Airborne: The Screaming Eagles in World War II by Mark Bando

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101st Airborne: The Screaming Eagles in World War II by Mark Bando
English | Sep 15, 2007 | ISBN: 0760329842 | 256 Pages | PDF | 177,5 MB

101st Airborne: The Screaming Eagles in World War II by Mark Bando
In 1942, the 82nd Infantry Division at Camp Claiborne, Louisiana, was split in two. One of the new divisions began intense preparations and training for a surprise landing on the Nazi-occupied European continent. The location was Normandy, France; the date was June 6, 1944; and the division was the 101st Airborne: the legendary "band of brothers."

This is the story of that divisions heroic performance on D-Day, and right up to the Allied victory in Europe. Filled with historic images, many never before published, it is also a tribute to the fallen men of the 101st–the artists and athletes, scientists and mathematicians, architects and builders whose sacrifice secured the future but left the human race much diminished. Theirs is an accomplishment well-known but rarely so dramatically depicted: Here is the 101st landing on Utah Beach, coming in by parachute, or glider, or from the sea. Stirring words and pictures capture the landing, linking the Utah and Omaha beachheads; the divisions breaking of the German drive to the coast; and their brilliant stand at Bastogne; a refusal to yield so famously summed up in the commanders reply to a German call for surrender: "Nuts."
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A Course on Borel Sets by S. M. Srivastava

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A Course on Borel Sets by S. M. Srivastava
English | April 13, 1998 | ISBN: 0387984127 | 271 Pages | PDF | 1 MB
A thorough introduction to Borel sets and measurable selections, acting as a stepping stone to descriptive set theory by presenting such important techniques as universal sets, prewellordering, scales, etc.

A Course on Borel Sets by S. M. Srivastava
It contains significant applications to other branches of mathematics and serves as a self-contained reference accessible by mathematicians in many different disciplines.
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Mathematics and Music: A Diderot Mathematical Forum

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Mathematics and Music: A Diderot Mathematical Forum by Gerard Assayag
English | Aug 26, 2002 | ISBN: 3540437274 | 288 Pages | PDF | 20 MB
In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means.

Mathematics and Music: A Diderot Mathematical Forum
Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.
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Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis

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Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis
English | Sep 1, 2001 | ISBN: 0393322297 | 268 Pages | PDF | 55 MB
Computers are ubiquitous yet to many they remain objects of irreducible mystery. This text looks at the question of how today's computers can perform such a variety of tasks if computing is just glorified arithmetic. The author illustrates how the answer lies in the fact that computers are essentially engines of logic and that their hardware and software embody concepts developed over centuries by logicians.

Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis
"Engines of Logic" gives the reader a clear explanation of how and why computers work.
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Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis

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Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis
English | Sep 1, 2001 | ISBN: 0393322297 | 268 Pages | PDF | 55 MB
Computers are ubiquitous yet to many they remain objects of irreducible mystery. This text looks at the question of how today's computers can perform such a variety of tasks if computing is just glorified arithmetic. The author illustrates how the answer lies in the fact that computers are essentially engines of logic and that their hardware and software embody concepts developed over centuries by logicians.

Engines of Logic: Mathematicians and the Origin of the Computer by Martin Davis
"Engines of Logic" gives the reader a clear explanation of how and why computers work.
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Wave Motion

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Wave Motion By J. Billingham, A. C. King
2006 | 476 Pages | ISBN: 0521632579 , 0521634504 | PDF | 12 MB

Wave Motion
Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.
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Stability Analysis of Impulsive Functional Differential Equations

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Ivanka M. Stamova, "Stability Analysis of Impulsive Functional Differential Equations"
2009 | pages: 240 | ISBN: 3110221810 | PDF | 1 mb

Stability Analysis of Impulsive Functional Differential Equations
This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time, the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
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Elliptic Mixed, Transmission and Singular Crack Problems

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Elliptic Mixed, Transmission and Singular Crack Problems By Gohar Harutyunyan, B.-Wolfgang Schulze
2007 | 777 Pages | ISBN: 303719040X | PDF | 6 MB

Elliptic Mixed, Transmission and Singular Crack Problems
Mixed, transmission, or crack problems belong to the analysis of boundary value problems on manifolds with singularities. The Zaremba problem with a jump between Dirichlet and Neumann conditions along an interface on the boundary is a classical example. The central theme of this book is to study mixed problems in standard Sobolev spaces as well as in weighted edge spaces where the interfaces are interpreted as edges. Parametrices and regularity of solutions are obtained within a systematic calculus of boundary value problems on manifolds with conical or edge singularities. This calculus allows singularities on the interface and homotopies between mixed and crack problems. Additional edge conditions are computed in terms of relative index results. In a detailed final chapter, the intuitive ideas of the approach are illustrated, and there is a discussion of future challenges. A special feature of the text is the inclusion of many worked-out examples which help the reader to appreciate the scope of the theory and to treat new cases of practical interest. This book is addressed to mathematicians and physicists interested in models with singularities, associated boundary value problems, and their solvability strategies based on pseudo-differential operators. The material is also useful for students in higher semesters and young researchers, as well as for experienced specialists working in analysis on manifolds with geometric singularities, the applications of index theory and spectral theory, operator algebras with symbolic structures, quantisation, and asymptotic analysis.
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