This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

Book of Proof

Science & Math

Richard Hammack

Mathematics

Virginia Commonwealth Universi

Lightning Source, Inc.

Handbook of Product Graphs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products and their subgraphs and explores the relationship between graph parameters of the product and factors. Extensively revised and expanded, the handbook presents full proofs of many important results as well as up-to-date research and conjectures. Results and Algorithms New to the Second Edition: <ul>
<li>Cancellation results </li> <li>A quadratic recognition algorithm for partial cubes </li> <li>Results on the strong isometric dimension </li> <li>Computing the Wiener index via canonical isometric embedding </li> <li>Connectivity results </li> <li>A fractional version of Hedetniemi’s conjecture </li> <li>Results on the independence number of Cartesian powers of vertex-transitive graphs </li> <li>Verification of Vizing’s conjecture for chordal graphs </li> <li>Results on minimum cycle bases </li> <li>Numerous selected recent results, such as complete minors and nowhere-zero flows </li> </ul> The second edition of this classic handbook provides a thorough introduction to the subject and an extensive survey of the field. The first three parts of the book cover graph products in detail. The authors discuss algebraic properties, such as factorization and cancellation, and explore interesting and important classes of subgraphs. The fourth part presents algorithms for the recognition of products and related classes of graphs. The final two parts focus on graph invariants and infinite, directed, and product-like graphs. Sample implementations of selected algorithms and other information are available on the book’s website, which can be reached via the authors’ home pages.

Handbook of Product Graphs (Discrete Mathematics and Its Applications)

Computers & Technology

Sandi Klavzar

Wilfried Imrich

Operating Systems

CRC-Press

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Books by Richard Hammack