Additive Combinatorics

Author: Terence Tao
Publisher: Cambridge University Press
ISBN: 9781139458344
Release Date: 2006-09-14
Genre: Mathematics

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Additive Combinatorics

Author: Bela Bajnok
Publisher: CRC Press
ISBN: 9781351137607
Release Date: 2018-04-27
Genre: Mathematics

Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods.

Combinatorial Number Theory and Additive Group Theory

Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
ISBN: 9783764389611
Release Date: 2009-04-15
Genre: Mathematics

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Mathematics

Author: Ida Kantor
Publisher: American Mathematical Soc.
ISBN: 9781470422615
Release Date: 2015-08-27
Genre: MATHEMATICS

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

Geometric Analysis

Author: Peter Li
Publisher: Cambridge University Press
ISBN: 9781107020641
Release Date: 2012-05-03
Genre: Mathematics

Basic techniques for researchers interested in the field of geometric analysis.

Wahrscheinlichkeit

Author: Alʹbert Nikolaevich Shiri︠a︡ev
Publisher:
ISBN: UOM:39015015715181
Release Date: 1988
Genre: Probabilities


Numerische lineare Algebra

Author: Folkmar Bornemann
Publisher: Springer-Verlag
ISBN: 9783658128845
Release Date: 2016-03-16
Genre: Mathematics

Dieses Buch führt anhand grundlegender Problemstellungen der linearen Algebra in das algorithmisch-numerische Denken ein. Die Beschränkung auf die lineare Algebra sichert dabei eine stärkere thematische Kohärenz als sie sonst in einführenden Vorlesungen zur Numerik zu finden ist. Die Darstellung betont die Zweckmäßigkeit von Matrixpartitionierungen gegenüber einer komponentenweisen Betrachtung, was sich nicht nur in einer übersichtlicheren Notation und kürzeren Algorithmen auszahlt, sondern angesichts moderner Computerarchitekturen auch zu signifikanten Laufzeitgewinnen führt. Die Algorithmen und begleitenden numerischen Beispiele werden in der Programmierumgebung MATLAB angegeben, zusätzlich aber in einem Anhang auch in der zukunftsweisenden, frei zugänglichen Programmiersprache Julia. Das vorliegende Buch eignet sich für eine zweistündige Vorlesung über numerische lineare Algebra ab dem zweiten Semester des Bachelorstudiengangs Mathematik.

Feierabend

Author: Vanna Vannuccini
Publisher: Riemann Verlag
ISBN: 9783641105181
Release Date: 2013-04-15
Genre: Art

Eine Liebeserklärung an die Deutschen – und ein unverstellter Blick in ihre Seele. Feiertage, das sind Ostern, Weihnachten oder Neujahr. Holidays. Wie aber erklärt man einem Engländer „Feierabend“? Eine wilde Party nach Büroschluss? Oder ist es ein magisches Wort, beim dem sofort alle Stifte fallen, das Licht ausgeht und die Maschinen stillstehen? Die Sprache ist die Seele eines Landes. Und die deutsche Sprache ist komplex. Sie ist vielschichtig und detailverliebt. Die beiden italienischen Autorinnen widmen sich den unübersetzbaren Wörtern wie Weltanschauung, Feierabend, Zweisamkeit oder Schadenfreude. Sie beobachten, wie Land und Leute davon geprägt sind, wie sich die deutsche Mentalität darin widerspiegelt. Indem die Begriffe verbunden werden mit historischen Ereignissen, Literatur und Politik, entsteht ein facettenreiches Gesellschaftsporträt, das tief in die deutsche Seele blicken lässt. Und es ist ein liebevoller Blick von außen auf uns: klug und kritisch, überraschend und mit feinsinnigem Humor. Ohne Häme und platte Vorurteile wie wir es sonst gewohnt sind. Nahezu eine Hymne.