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| Author | : Alex Iosevich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 154 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821843974 |
Based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.
| Author | : Mauro Di Nasso |
| Publisher | : Springer |
| Total Pages | : 211 |
| Release | : 2019-05-23 |
| Genre | : Mathematics |
| ISBN | : 3030179567 |
The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.
| Author | : George E. Andrews |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 144 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : 0821807161 |
Integrates developments and related applications in $q$-series with a historical development of the field. This book develops important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory.
| Author | : Alfred Geroldinger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 324 |
| Release | : 2009-04-15 |
| Genre | : Mathematics |
| ISBN | : 3764389613 |
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.
| Author | : Anthony Vazzana |
| Publisher | : CRC Press |
| Total Pages | : 530 |
| Release | : 2007-10-30 |
| Genre | : Computers |
| ISBN | : 1584889381 |
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
| Author | : Valérie Berthé |
| Publisher | : Cambridge University Press |
| Total Pages | : 637 |
| Release | : 2010-08-12 |
| Genre | : Mathematics |
| ISBN | : 0521515971 |
This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.
| Author | : Ross G. Pinsky |
| Publisher | : Springer |
| Total Pages | : 165 |
| Release | : 2014-08-09 |
| Genre | : Mathematics |
| ISBN | : 3319079654 |
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
| Author | : Melvyn B. Nathanson |
| Publisher | : Springer Nature |
| Total Pages | : 237 |
| Release | : 2019-12-10 |
| Genre | : Mathematics |
| ISBN | : 3030311066 |
Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
| Author | : János Pintz |
| Publisher | : Walter de Gruyter |
| Total Pages | : 418 |
| Release | : 2013-12-12 |
| Genre | : Mathematics |
| ISBN | : 3110282429 |
Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics. The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.
| Author | : Krishnaswami Alladi |
| Publisher | : Springer |
| Total Pages | : 289 |
| Release | : 2013-12-21 |
| Genre | : Mathematics |
| ISBN | : 1475745079 |
This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.
