Mathematics in Berlin
Mathematics in Berlin

Author: Heinrich Begehr

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 204

ISBN-13: 3034887876

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This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.

Mathematics Everywhere
Mathematics Everywhere

Author: Martin Aigner

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 346

ISBN-13: 0821843494

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The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" understandable and enjoyable.

Foundations of Constructive Mathematics
Foundations of Constructive Mathematics

Author: M.J. Beeson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 484

ISBN-13: 3642689523

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This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.

Numerical Mathematics
Numerical Mathematics

Author: Alfio Quarteroni

Publisher: Springer

Published: 2017-01-26

Total Pages: 669

ISBN-13: 0387227504

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The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

Building Bridges
Building Bridges

Author: Martin Grötschel

Publisher: Springer Science & Business Media

Published: 2010-05-28

Total Pages: 536

ISBN-13: 3540852212

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Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.

Visualization and Mathematics
Visualization and Mathematics

Author: H.-C. Hege

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 391

ISBN-13: 3642591957

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Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.

Discrete Mathematics
Discrete Mathematics

Author: Martin Aigner

Publisher: American Mathematical Society

Published: 2023-01-24

Total Pages: 402

ISBN-13: 1470470632

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The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition… This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics. —Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Günter M. Ziegler has been an international success with translations into 12 languages.

Mathematics in Science and Technology
Mathematics in Science and Technology

Author: A. H. Siddiqi

Publisher: World Scientific

Published: 2011

Total Pages: 558

ISBN-13: 9814338818

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This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate ? independent hysteresis, numerical analysis of Hamilton Jacobi ? Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference.

Control of Self-Organizing Nonlinear Systems
Control of Self-Organizing Nonlinear Systems

Author: Eckehard Schöll

Publisher: Springer

Published: 2016-01-22

Total Pages: 478

ISBN-13: 3319280287

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The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.

Kolmogorov's Heritage in Mathematics
Kolmogorov's Heritage in Mathematics

Author: Eric Charpentier

Publisher: Springer Science & Business Media

Published: 2007-09-13

Total Pages: 326

ISBN-13: 3540363513

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In this book, several world experts present (one part of) the mathematical heritage of Kolmogorov. Each chapter treats one of his research themes or a subject invented as a consequence of his discoveries. The authors present his contributions, his methods, the perspectives he opened to us, and the way in which this research has evolved up to now. Coverage also includes examples of recent applications and a presentation of the modern prospects.