Mathematics in Berlin
Mathematics in Berlin

Author: Heinrich Begehr

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 204

ISBN-13: 3034887876

DOWNLOAD EBOOK

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

DOWNLOAD EBOOK

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.

Numerical Mathematics
Numerical Mathematics

Author: Alfio Quarteroni

Publisher: Springer

Published: 2017-01-26

Total Pages: 669

ISBN-13: 0387227504

DOWNLOAD EBOOK

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.

Matheon--mathematics for Key Technologies
Matheon--mathematics for Key Technologies

Author: Peter Deuflhard

Publisher: Susaeta

Published: 2014

Total Pages: 472

ISBN-13: 9783037191378

DOWNLOAD EBOOK

Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these; the last three of its facets are not well known, though. They have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities, MATHEON has become an international trademark. Its mission and its strategies for carrying out creative, application-driven research in mathematics and cooperating in the solution of complex problems in key technologies are by now a role model for the development of many other centers. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. At the same time, the innovation cycles get shorter and shorter. These simultaneous challenges can be mastered only by qualitatively and quantitatively rigorous methods. And that is where mathematics is indispensable. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization, open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as optimization, discrete mathematics, numerical analysis, scientific computing, applied analysis and stochastic analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in solving the challenging problems in key technologies. This book presents in seven chapters the research highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities, and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of ``showcases'' are presented that illustrate a few success stories.

Discrete Mathematics
Discrete Mathematics

Author: Martin Aigner

Publisher: American Mathematical Society

Published: 2023-01-24

Total Pages: 402

ISBN-13: 1470470632

DOWNLOAD EBOOK

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.

Combinatorial Theory
Combinatorial Theory

Author: Martin Aigner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 493

ISBN-13: 3642591019

DOWNLOAD EBOOK

This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen

Proofs from THE BOOK
Proofs from THE BOOK

Author: Martin Aigner

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 194

ISBN-13: 3662223430

DOWNLOAD EBOOK

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

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

DOWNLOAD EBOOK

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.