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This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics. The first two parts, which form the bulk of the volume, contain the two main advanced courses, Additive Group Theory and Non-Unique Factorizations by Alfred Geroldinger, and Sumsets and Structure by Imre Z. Ruzsa. The first part centers on the interaction between non-unique factorization theory and additive group theory. The main objective of factorization theory is a systematic treatment of phenomena related to the non-uniqueness of factorizations in monoids and domains. This part introduces basic concepts of factorization theory such as sets of lengths, and outlines the translation of arithmetical questions in Krull monoids into combinatorial questions on zero-sum sequences over the class group. Using methods from additive group theory such as the theorems of Kneser and of Kemperman-Scherk, classical zero-sum constants are studied, including the Davenport constant and the Erdös-Ginzburg-Ziv constant. Finally these results are applied again to the starting arithmetical problems. The second part is a course on the basics of combinatorial number theory (or additive combinatorics): cardinality inequalities (Plünnecke's graph theoretical method), Freiman's theorem on the structure of sets with a small sumset, inequalities for the Schnirelmann and asymptotic density of sumsets, analogous results for the measure of sumsets of reals, the connection with the Bohr topology. The third part of the volume collects some of the seminars which accompanied the main courses. It contains contributions by C. Elsholtz, G. Freiman, Y. O. Hamidoune, N. Hegyvari, G. Karolyi, M. Nathanson, J. Solymosi and Y. Stanchescu.

Discrete mathematics --- discrete wiskunde

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Van Basis tot Limiet (VBTL) is een totaalmethode wiskunde voor het secundair onderwijs. VBTL is er voor de 1e graad A-stroom, het materiaal voor de 2e graad wordt aangepast volgens de hervormingen van het secundair onderwijs voor doorstroom- en dubbele finaliteit. Voor de 3e graad is VBTL geschikt voor ASO, TSO en KSO. VBTL is al jaar en dag dé referentie in wiskundeonderwijs in Vlaanderen. Het is een kwaliteitsvolle methode met sterke handboeken en een ruim aanbod aan randproducten. VBTL laat verschillende onderwijsstijlen en didactische aanpakken toe en stelt de expertise van de leerkracht centraal. Leerkrachtgestuurd onderwijs Groot gamma aan leermaterialen en ruim aanbod aan randmateriaal Duidelijke structuur Enorme hoeveelheid oefenmateriaal op verschillende beheersingsniveaus Stimuleert competentiegericht en probleemoplossend denken Extra aandacht aan rekenvaardigheden, wiskundetaal en ICT-vaardigheden Sluit perfect aan bij de eindtermen en de leerplannen Naar aanleiding van de nieuwe eindtermen wordt VBTL jaar per jaar volledig vernieuwd.

Discrete wiskunde. --- Secundair onderwijs.

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The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerous list of identities that are derived in the body of the book. The mathematics in the book is derived from first principles. On only one occasion does it rely on a result not derived within the text. Since the book does not require calculus or advanced techniques, it should be accessible to advanced high school students and undergraduates in math or computer science. Senior mathematicians might be unfamiliar with some of the topics addressed in its pages or find interest in the book's unified approach to discrete math.

Discrete mathematics --- discrete wiskunde

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This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb's insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study. Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems. Solomon Golomb's Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book's many entertaining challenges.

Discrete mathematics --- discrete wiskunde

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Discrete mathematics --- grafieken --- discrete wiskunde