Computer Science ~ Contents - McGraw-Hill Books

Computer ScienceFEATURES• Clarity and Precision – Rosen’s writing style is direct andpragmatic. Care has been taken to balance the mix of notation andwords in mathematical statements. All definitions and theorems inthis text are stated extremely carefully so that students will appreciatethe precision of language and rigor needed in discrete mathematics.Proofs are motivated and developed slowly; their steps are allcarefully justified. Recursive definitions are explained and usedextensively.CONTENTSPreface. The MathZone Companion Website To the Student. 1 The Foundations:Logic and Proofs. 1.1 Propositional Logic 1.2 Propositional Equivalences1.3 Predicates and Quantifiers 1.4 Nested Quantifiers1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and StrategyEnd-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences and Sums2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations End-of-Chapter Material 3 The Fundamentals: Algorithms, the Integers, and Matrices 3.1Algorithms 3.2 The Growth of Functions 3.3 Complexity of Algorithms 3.4 TheIntegers and Division 3.5 Integers and Algorithms 3.6 Applications of NumberTheory 3.7 Matrices End-of-Chapter Material 4 Induction and Recursion 4.1Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 RecursiveDefinitions and Structural Induction 4.4 Recursive Algorithms 4.5 ProgramCorrectness End-of-Chapter Material 5 Counting 5.1 The Basics of Counting5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 BinomialCoefficients 5.5 Generalized Permutations and Combinations 5.6 GeneratingPermutations and Combinations End-of-Chapter Material 6 Discrete Probability6.1 An Introduction to Discrete Probability 6.2 Probability Theory 6.3 Bayes’Theorem 6.4 Expected Value and Variance End-of-Chapter Material 7 AdvancedCounting Techniques 7.1 Recurrence Relations 7.2 Solving Recurrence Relations7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 GeneratingFunctions 7.5 Inclusion-Exclusion 7.6 Applications of Inclusion-Exclusion End-of-Chapter Material 8 Relations 8.1 Relations and Their Properties 8.2 n-ary Relationsand Their Applications 8.3 Representing Relations 8.4 Closures of Relations 8.5Equivalence Relations 8.6 Partial Orderings End-of-Chapter Material 9 Graphs 9.1Graph Terminology and Models 9.2 Special Graphs 9.3 Representing Graphs andGraph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems 9.7 Planar Graphs 9.8 Graph Coloring End-of-Chapter Material 10Trees 10.1 Introduction to Trees 10.2 Applications of Trees 10.3 Tree Traversal10.4 Spanning Trees 10.5 Minimum Spanning Trees End-of-Chapter Material11 Boolean Algebra 11.1 Boolean Functions 11.2 Representing BooleanFunctions 11.3 Logic Gates 11.4 Minimization of Circuits End-of-Chapter Material12 Modeling Computation. 12.1 Languages and Grammars. 12.2 Finite-StateMachines with Output. 12.3 Finite-State Machines with No Output. 12.4 LanguageRecognition. 12.5 Turing Machines. End-of-Chapter Material. Appendixes.A.1 Axioms for Real Numbers and Integers. A.2 Exponential and LogarithmicFunctions. A.3 Pseudocode. Suggested Readings. Answers to Odd-NumberedExercises. Photo Credits. Index of Biographies. IndexInternational EditionDISCRETE MATHEMATICS BY EXAMPLEby Andrew Simpson, Ox ford Brookes2002 / 450pagesISBN-13: 978-0-07-709840-7 / MHID: 0-07-709840-4ISBN-13: 978-0-07-122914-2 / MHID: 0-07-122914-0 [IE](McGraw-Hill UK Title)CONTENTS1 Introduction. 2 Num bers. 3 Propositional logic. 4 Set theory. 5 Boolean algebra.6 Typed set theory. 7 Predicate logic. 8 Relations. 9 Func tions. 10 Sequences. 11Induction. 12 Graph theory. 13 Combinatorics. 14 Modelling. 15 AnalysisInternational EditionSCHAUM’S OUTLINE OF ESSENTIAL COMPUTERMATHEMATICSby Seymour Lipschutz, Temple University1982 / 256 pagesISBN-13: 978-0-07-037990-9 / MHID: 0-07-037990-4ISBN-13: 978-0-07-099132-3 / MHID: 0-07-099132-4 [IE]Schaum's PublicationCONTENTSBinary Number System. Com put er Codes. Computer Arith metic. Logic. Flowcharts.Sets and Relations. Boolean Al ge bra, Logic Gates. Simplifying Logic Circuits,Karnaugh Maps. Vectors, Matrices, Subscripted Vari ables. Linear Equations.Com bi na t o rics. Probability. Sta tis tics, Random Variables. Graph Theory. Trees,Directed Graphs, Machines.Programming Languages andProgram DesignInternational EditionNEWPROGRAMMING LANGUAGESSecond Editionby Allen B. Tucker, Bowdoin College, and Robert Noonan, Collegeof William and Mary2007 (August 2006) / Hardcover / 640 pagesISBN-13: 978-0-07-286609-4 / MHID: 0-07-286609-8ISBN-13: 978-0-07-125439-7 / MHID: 0-07-125439-0 [IE]Browse http://www.mhhe.com/tuckerTucker and Noonan's new approach emphasizes a thorough,hands-on treatment of key issues in programming languagedesign, providing a balanced mix of explanation andexperimentation. Opening chapters present the fundamentalprincipals of programming languages, while optionalcompanion chapters provide implementation-based, hands-onexperience that delves even deeper. This edition also includesa greatly expanded treatment of the four major programmingparadigms, incorporating a number of the most currentlanguages such as Perl and Python. Special topics presentedinclude event-handling, concurrency, and an all-new chapteron correctness. Overall, this edition provides both broad anddeep coverage of language design principles and the majorparadigms, allowing users the flexibility of choosing whattopics to emphasize.NEW TO THIS EDITION• Depth of coverage & currency: in-depth coverage of core topicsincludes both modern and historical example languages, including C,Ada, Perl, Java, Smalltalk, Python, Scheme, Haskell, and Prolog• The authors' approach offers unique coverage of event-handling,concurrent programming and program correctness, with specialchapters on each of these topics.• The authors emphasize a hands-on approach for implementationbasedproblems and exercises and include expanded coverage oflanguage design principles and trade-offs.• Introduces Clite (C Lite), a subset of the language C, as a basis forillustrating the principles of language design.FEATURES• Flexibile organization and coverage gives instructors the option ofadding implementation-based coverage to the principles chapters viaoptional companion chapters.3615-60_CompSc.indd 3611/15/06 5:05:21 PM