Author: Daniel J. Velleman
Publisher: Cambridge University Press
Release Date: 2006-01-16
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
This series of books deals with the mathematical modeling and computational simulation of complex wave propagation phenomena in science and engineering. This first volume of the series introduces the basic mathematical and physical fundamentals, and it is mainly intended as a reference guide and a general survey for scientists and engineers. It presents a broad and practical overview of the involved foundations, being useful as much in industrial research, development, and innovation activities, as in academic labors.
Author: John M. Lee
Publisher: American Mathematical Soc.
Release Date: 2013-04-10
The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P.  of cover.
Author: Donald Yau
Publisher: American Mathematical Soc.
Release Date: 2016-02-29
Genre: Algebra, Homological
The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Author: Rowan Garnier
Publisher: Taylor & Francis
Release Date: 2009-11-09
Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content. New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors. Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.
Author: Charles Rich
Publisher: Morgan Kaufmann Pub
Release Date: 1986
For AI, programming is a domain that stimulates fundamental research in knowledge representation and automated reasoning. This volume collects thirty-four important papers covering a wide spectrum of work in this area.
Author: Norman Biggs
Publisher: Oxford University Press
Release Date: 2002-12-19
The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics includes new chapters on statements and proof, logical framework, natural numbers and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.Key Features:* Contains nine new introductory chapters, in addition to updated chapters from the previous edition* Contains over 1000 individual exercises and selected solutions* Companion website www.oup.com/mathematics/discretemath contains hints and solutions to all exercisesContents:The Language of Mathematics1. Statements and proofs2. Set notation3. The logical framework4. Natural numbers5. Functions6. How to count 7. Integers8. Divisibility and prime numbers9. Fractions and real numbersTechniques10. Principles of counting11. Subsets and designs12. Partition, classification and distribution13. Modular arithmeticAlgorithms and Graphs14. Algorithms and their efficiency15. Graphs16. Trees, sorting and searching17. Bipartite graphs and matching problems18. Digraphs, networks and flows19. Recursive techniquesAlgebraic Methods20. Groups21. Groups of permutations22. Rings, fields and polynomials23. Finite fields and some applications24. Error-correcting codes25. Generating functions26. Partitions of a positive integer27. Symmetry and counting
Author: Catherine Winder
Publisher: Taylor & Francis
Release Date: 2012-11-12
You have a useful library of books covering the tools, techniques and aesthetics of animation, but you've been asked to put your production and creative skills to the test to produce a theatrical feature film or to deliver 52 episodes of a television series with only 18 months in the schedule. Producing Animation is your answer. Written by Catherine Winder and Zahra Dowlatabadi and edited by Tracey Miller-Zarneke, Producing Animation is a comprehensive guide to the production industry. Already a relied upon resource by professionals and students alike, this book covers the process from script to screen while defining the role of the producer at each phase. The second edition features new content such as sidebars on key topics from industry experts, discussions on CG, 2D and stereoscopic production processes, and an overview on marketing and distributing your project. The companion website provides access to sample tables, templates and workflow outlines for CG and 2D animation production.