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Combinatorial Number Theory and Additive Group Theory
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.
Number Theory
Number Theory has fascinated mathematicians from the most ancient of times. A remarkable feature of number theory is the fact that there is something in it for everyone from puzzle enthusiasts, problem solvers and amatcur mathematicians to professional scientists and technologists.
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Hobson-Jobson
Bungalow, pyjamas, tiffin, rickshaw, veranda, curry, cheroot, chintz, calico, gingham, mango, junk and catamaran are all words which have crept into the English language from the days of Britain's colonial rule of the Indian sub-continent and the Malaysian Peninsular. Hobson-Jobson (derived from the Islamic cry at the celebration of Muhurram 'Ya Hasan, ya Hosain' is shorthand for the assimilation of foreign words to the sound pattern of the adopting language. This dictionary, compiled in the late-19th century, is an invaluable source which has never been superseded. It is an essential book for all who are interested in English etymology and the development of the language. AUTHORS: Arthur Co...
Handbook of Number Theory II
This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.
Unsolved Problems in Number Theory
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.
