Logic and Discrete Mathematics A Concise Introduction.

Detalles Bibliográficos
Autor principal: Conradie, Willem
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2015.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Title Page
  • Copyright
  • Table of Contents
  • List of Boxes
  • Preface
  • Acknowledgements
  • About the Companion Website
  • Chapter 1: Preliminaries
  • 1.1 Sets
  • 1.2 Basics of logical connectives and expressions
  • 1.3 Mathematical induction
  • Chapter 2: Sets, Relations, Orders
  • 2.1 Set inclusions and equalities
  • 2.2 Functions
  • 2.3 Binary relations and operations on them
  • 2.4 Special binary relations
  • 2.5 Equivalence relations and partitions
  • 2.6 Ordered sets
  • 2.7 An introduction to cardinality
  • 2.8 Isomorphisms of ordered sets. Ordinal numbers
  • 2.9 Application: relational databases
  • Chapter 3: Propositional Logic
  • 3.1 Propositions, logical connectives, truth tables, tautologies
  • 3.2 Propositional logical consequence. Valid and invalid propositional inferences
  • 3.3 The concept and use of deductive systems
  • 3.4 Semantic tableaux
  • 3.5 Logical equivalences. Negating propositional formulae
  • 3.6 Normal forms. Propositional resolution
  • Chapter 4: First-Order Logic
  • 4.1 Basic concepts of first-order logic
  • 4.2 The formal semantics of first-order logic
  • 4.3 The language of first-order logic: a deeper look
  • 4.4 Truth, logical validity, equivalence and consequence in first-order logic
  • 4.5 Semantic tableaux for first-order logic
  • 4.6 Prenex and clausal normal forms
  • 4.7 Resolution in first-order logic
  • 4.8 Applications of first-order logic to mathematical reasoning and proofs
  • Chapter 5: Number Theory
  • 5.1 The principle of mathematical induction revisited
  • 5.2 Divisibility
  • 5.3 Computing greatest common divisors. Least common multiples
  • 5.4 Prime numbers. The fundamental theorem of arithmetic
  • 5.5 Congruence relations
  • 5.6 Equivalence classes and residue systems modulo n
  • 5.7 Linear Diophantine equations and linear congruences
  • 5.8 Chinese remainder theorem
  • 5.9 Euler's function. Theorems of Euler and Fermat
  • 5.10 Wilson's theorem. Order of an integer
  • 5.11 Application: public key cryptography
  • Chapter 6: Combinatorics
  • 6.1 Two basic counting principles
  • 6.2 Combinations. The binomial theorem
  • 6.3 The principle of inclusion-exclusion
  • 6.4 The Pigeonhole Principle
  • 6.5 Generalized permutations, distributions and the multinomial theorem
  • 6.6 Selections and arrangements with repetition
  • distributions of identical objects
  • 6.7 Recurrence relations and their solution
  • 6.8 Generating functions
  • 6.9 Recurrence relations and generating functions
  • 6.10 Application: classical discrete probability
  • Chapter 7: Graph Theory
  • 7.1 Introduction to graphs and digraphs
  • 7.2 Incidence and adjacency matrices
  • 7.3 Weighted graphs and path algorithms
  • 7.4 Trees
  • 7.5 Eulerian graphs and Hamiltonian graphs
  • 7.6 Planar graphs
  • 7.7 Graph colourings
  • Index
  • End User License Agreement

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