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Old and New Problems and Results in Combinatorial Number Theory
Author: Paul Erdös
Publisher:
Published: 1999
Total Pages: 250
ISBN-13: 9780387984605
DOWNLOAD EBOOK →This book discusses various problems in elementary number theory, most of which have a combinatorial flavor. In general classical problems are avoided and almost no proofs are given for the presented problems. Both the difficulty and importance of the problems discussed are very variable in some are only exercises while others are very difficult or even hopeless and may have important consequences or their eventual solution may lead to important advances and the discovery of new methods. This new edition is the joint work of the late Paul Erdys, Ron Graham, and as new co-authors, Melvin Nathanson and Xingde Jia.
Unsolved Problems in Number Theory
Author: Richard Guy
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 455
ISBN-13: 0387266771
DOWNLOAD EBOOK →Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
Combinatorial Number Theory and Additive Group Theory
Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
Published: 2009-04-15
Total Pages: 324
ISBN-13: 3764389613
DOWNLOAD EBOOK →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.
Old and New Unsolved Problems in Plane Geometry and Number Theory
Author: Victor Klee
Publisher: American Mathematical Soc.
Published: 2020-07-31
Total Pages: 333
ISBN-13: 1470454610
DOWNLOAD EBOOK →Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.
Theory and Problems of Combinatorics
Author: C. Vasudev
Publisher: New Age International
Published: 2005
Total Pages: 11
ISBN-13: 8122417051
DOWNLOAD EBOOK →Combinatorics Is The Mathematics Of Counting, Selecting And Arranging Objects. Combinatorics Include The Theory Of Permutations And Combinations. These Topics Have An Enormous Range Of Applications In Pure And Applied Mathematics And Computer Science. These Are Processes By Which We Organize Sets So That We Can Interpret And Apply The Data They Contain. Generally Speaking, Combinatorial Questions Ask Whether A Subset Of A Given Set Can Be Chosen And Arranged In A Way That Conforms With Certain Constraints And, If So, In How Many Ways It Can Be Done. Applications Of Combinatorics Play A Major Role In The Analysis Of Algorithms.For Example, It Is Often Necessary In Such Analysis To Count The Average Number Of Times That A Particular Portion Of An Algorithm Is Executed Over All Possible Data Sets. This Topic Also Includes Solution Of Difference Equations. Differences Are Required For Analysis Of Algorithmic Complexity, And Since Computers Are Frequently Used In The Numerical Solution Of Differential Equations Via Their Discretized Versions Which Are Difference Equations. It Also Deals With Questions About Configurations Of Sets, Families Of Finite Sets That Overlap According To Some Prescribed Numerical Or Geometrical Conditions. Skill In Using Combinatorial Techniques Is Needed In Almost Every Discipline Where Mathematics Is Applied.Salient Features * Over 1000 Problems Are Used To Illustrate Concepts, Related To Different Topics, And Introduce Applications. * Over 1000 Exercises In The Text With Many Different Types Of Questions Posed. * Precise Mathematical Language Is Used Without Excessive Formalism And Abstraction. * Precise Mathematical Language Is Used Without Excessive Formalism And Abstraction. * Problem Sets Are Started Clearly And Unambiguously And All Are Carefully Graded For Various Levels Of Difficulty.
Combinatorics and Number Theory of Counting Sequences
Author: Istvan Mezo
Publisher: CRC Press
Published: 2019-08-19
Total Pages: 480
ISBN-13: 1351346385
DOWNLOAD EBOOK →Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
Author: Mauro Di Nasso
Publisher: Springer
Published: 2019-05-23
Total Pages: 206
ISBN-13: 3030179567
DOWNLOAD EBOOK →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.
Combinatorial Number Theory
Author: Bruce Landman
Publisher: Walter de Gruyter
Published: 2011-12-22
Total Pages: 501
ISBN-13: 3110925095
DOWNLOAD EBOOK →This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics.
The Mathematical Coloring Book
Author: Alexander Soifer
Publisher: Springer Science & Business Media
Published: 2008-10-13
Total Pages: 619
ISBN-13: 0387746420
DOWNLOAD EBOOK →This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
