Axioms and Hulls (Lecture Notes in Computer Science, #606)
by Donald E. Knuth
One way to advance the science of computational geometry is to make a comprehensive study of fundamental operations that are used in many different algorithms. This monograph attempts such an investigation in the case of two basic predicates: the counterclockwise relation pqr, which states that the circle through points (p, q, r) is traversed counterclockwise when we encounter the points in cyclic order p, q, r, p,...; and the incircle relation pqrs,...
Flowers GRAYSCALE Landscape Coloing Books Volume 3 (Flowers Grayscale Landscape Coloing Books, #3)
by Jane T Berrios
This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and e...
Principles of Combinatorics (Mathematics in Science & Engineering)
by Claude Berge
Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell ho...
50 Jahre Bundeswettbewerb Mathematik
Dieses Buch wird alle Liebhaber der Mathematik (und die es werden wollen) durch eine Fulle von reizvollen und unterhaltsamen Problemstellungen aus Algebra, Geometrie, Kombinatorik und Zahlentheorie begeistern. Vierzig ausgewahlte Aufgaben aus 50 Jahren Bundeswettbewerb Mathematik werden mit ausfuhrlichen Loesungen, Einblicken in das mathematische Umfeld und inhaltlichen Variationen reich illustriert prasentiert. Von der Mathematik geht fur viele seit jeher eine besondere Faszination aus. Wer t...
Numerical Ocean Acoustic Propagation In Three Dimensions
by Ding Lee, Martin H Schultz, and W L Siegmann
This book introduces a comprehensive mathematical formulation of the three-dimensional ocean acoustic propagation problem by means of functional and operator splitting techniques in conjunction with rational function approximations. It presents various numerical solutions of the model equation such as finite difference, alternating direction and preconditioning. The detailed analysis of the concept of 3D, N x 2D and 2D problems is very useful not only mathematically and physically, but also comp...
Graphen Algorithmen Programme
by Hansjoachim Walther and Gunter Nagler
Graphentheorie ist eine junge mathematische Disziplin, 1936 erschien das erste Lehrbuch yom ungarischen Mathematiker DENES KONIG. Mit der stiirmischen Ent- wicklung der Operationsforschung erlebte auch die Graphentheorie eine ungeahnte Bliite, so daB die Zahl der Biicher zur Graphentheorie heute schon Legion ist. Das Gros der Autoren setzt jedoch beim Leser einen relativ hohen mathematischen Aus- bildungsgrad sowie ein hohes Abstraktionsvermogen voraus. Wir verlangen yom Leser im allgemeinen nic...
Combinatorial Set Theory (Springer Monographs in Mathematics)
by Lorenz J Halbeisen
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated techniq...
Seminaire De Theorie DES Nombres, 1990-1991 (Progress in Mathematics, #108)
by S David
Based on the lectures given at the Seminaire de Theorie des Nombres de Paris in 1990-1991, this collection of papers reflects work in many areas of number theory, including: cubic exponential sums; Riemann's period relations; and Galois representations attached to points on Shimura varieties.
Introduction to Closure Systems (Discrete Mathematics and Its Applications)
by Robert E. Jamison
The notion of closure pervades mathematics, especially in the fields of topology and projective geometry. Demonstrating this pervasiveness in the field, this graduate-level book provides a complete introduction to closure systems. With an emphasis on finite spaces and algebraic closures, the text covers graph theory, ordered sets, lattices, projective geometry, and formal logic as they apply to the study of closures. Each chapter presents a vignette to illustrate the topic covered. The author al...
Graphs, Algorithms, and Optimization, Second Edition (Discrete Mathematics and Its Applications)
by William Kocay and Donald L. Kreher
The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.
Algebra und Diskrete Mathematik geh ren zu den wichtigsten Grundlagen der Informatik. Umfassend und lebendig f hrt das zweib ndige Lehrbuch in den Themenkomplex ein. Klar herausgearbeitete L sungsalgorithmen, viele Beispiele, ausf hrliche Beweise und die Hervorhebung wichtiger Kerninhalte machen den Lehrstoff leicht zug nglich. Die umfangreiche Sammlung von bungsaufgaben der 2., korrigierten Auflage hilft beim aktiven Lernen und zeigt die unterschiedlichsten Anwendungsm glichkeiten des erarbeite...
Based on both theoretical investigations and industrial experience, this book provides an extensive approach to support the planning and optimization process for modern communication networks. The book contains a thorough survey and a detailed comparison of state-of-the-art numerical algorithms in the matrix-geometric field.
Categories and Functors (Pure & Applied Mathematics S.) (Pure and Applied Mathematics)
by B Pareigis
Representation Theory of Symmetric Groups (Discrete Mathematics and Its Applications)
by Pierre-Loic Meliot
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial a...
This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.
Scale-Isometric Polytopal Graphs in Hypercubes and Cubic Lattices
by Michel-marie Deza, Viacheslav Grishukhin, and Mikhail I Shtogrin
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical Structures and Proofs is a textbook intended for such a course, or for self-study. This book introduces an array of fundamental mathematical structures. It also explores the delicate balance of intuition and rigor—and the flexible thinking—requi...
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools fr...