{"product_id":"discrete-and-combinatorial-mathematics-9781292022796","title":"Discrete and Combinatorial Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePART 1. FUNDAMENTALS OF DISCRETE MATHEMATICS.\u003c\/b\u003e \u003c\/p\u003e \u003cb\u003e1. Fundamental Principles of Counting.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Rules of Sum and Product. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003ePermutations. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eCombinations: The Binomial Theorem. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eCombinations with Repetition. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Catalan Numbers (Optional). \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e2. Fundamentals of Logic.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eBasic Connectives and Truth Tables. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eLogical Equivalence: The Laws of Logic. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eLogical Implication: Rules of Inference. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Use of Quantifiers. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eQuantifiers, Definitions, and the Proofs of Theorems. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e3. Set Theory.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eSets and Subsets. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSet Operations and the Laws of Set Theory. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eCounting and Venn Diagrams. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eA First Word on Probability. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Axioms of Probability (Optional). \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eConditional Probability: Independence (Optional). \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eDiscrete Random Variables (Optional). \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e4. Properties of the Integers: Mathematical Induction.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Well-Ordering Principle: Mathematical Induction. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eRecursive Definitions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Division Algorithm: Prime Numbers. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Greatest Common Divisor: The Euclidean Algorithm. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Fundamental Theorem of Arithmetic. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e5. Relations and Functions.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eCartesian Products and Relations. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eFunctions: Plain and One-to-One. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eOnto Functions: Stirling Numbers of the Second Kind. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSpecial Functions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Pigeonhole Principle. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eFunction Composition and Inverse Functions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eComputational Complexity. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eAnalysis of Algorithms. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e6. Languages: Finite State Machines.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eLanguage: The Set Theory of Strings. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eFinite State Machines: A First Encounter. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eFinite State Machines: A Second Encounter. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e7. Relations: The Second Time Around.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eRelations Revisited: Properties of Relations. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eComputer Recognition: Zero-One Matrices and Directed Graphs. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003ePartial Orders: Hasse Diagrams. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eEquivalence Relations and Partitions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eFinite State Machines: The Minimization Process. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART 2. FURTHER TOPICS IN ENUMERATION.\u003c\/b\u003e \u003c\/p\u003e \u003cb\u003e8. The Principle of Inclusion and Exclusion.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Principle of Inclusion and Exclusion. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eGeneralizations of the Principle. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eDerangements: Nothing Is in Its Right Place. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eRook Polynomials. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eArrangements with Forbidden Positions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e9. Generating Functions.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eIntroductory Examples. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eDefinition and Examples: Calculational Techniques. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003ePartitions of Integers. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Exponential Generating Functions. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eThe Summation Operator. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003eSummary and Historical Review. \u003cp\u003e \u003c\/p\u003e \u003cb\u003e10. Recurrence Relations.\u003c\/b\u003e","brand":"Pearson Education","offers":[{"title":"Default Title","offer_id":51019577622871,"sku":"9781292022796","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292022796.jpg?v=1750780681","url":"https:\/\/bookcurl.com\/products\/discrete-and-combinatorial-mathematics-9781292022796","provider":"Book Curl","version":"1.0","type":"link"}