Kategoria BISAC: Mathematics >> Discrete Mathematics

This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community.

We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite...

Eine Gruppe, deren Mitglieder sich zwischen mehreren zur Wahl stehenden Alternativen entscheiden mussen, hat eine grosse Anzahl von Moglichkeiten, aus den Praferenzen der Einzelnen eine von der Gemeinschaft getragene Entscheidung zu ermitteln. Wie lasst sich sicherstellen, dass diese gemeinschaftliche Entscheidung den Willen der Gruppe sinnvoll widerspiegelt?

Die Untersuchung von Methoden, die die vielen individuellen Meinungen zu einer einzigen Entscheidung fur die gesamte Gruppe zusammenfassen, und die Darstellung der wichtigsten Eigenschaften dieser Verfahren sind Inhalt dieses...

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and...

Computer Arithmetic and Formal Proofs: Floating-point Algorithms with the Coq System explores floating-point arithmetic, a tool that is ubiquitous in modern computing as the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and cause numerous failures. This book explains how to avoid this and increase confidence in floating-point software by using the computer-assisted verification of correctness proof (the Coq proof assistant), the tool that is comprehensively discussed throughout this book.

This Second Edition continues to distill the abstract ideas of wavelet theory to a level accessible to undergraduates, and at the same time, introduces readers to the theory via an applications first approach. With extensive graphical displays, this self-contained book integrates concepts from calculus and linear algebra into the construction of wavelet transformations and their various applications, including data compression, edge detection in images, and signal and image denoising. The new edition has been thoroughly revised to include new applications including image...

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the...

This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of...

Written for mathematicians working with the theory of graph spectra, this (primarily theoretical) book presents relevant results considering the spectral properties of regular graphs. The book begins with a short introduction including necessary terminology and notation. The author then proceeds with basic properties, specific subclasses of regular graphs (like distance-regular graphs, strongly regular graphs, various designs or expanders) and determining particular regular graphs. Each chapter contains detailed proofs, discussions, comparisons, examples, exercises and also indicates...

This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.

The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations...