The Resource A course in discrete mathematical structures, L. R. Vermani, Shalini Vermani

A course in discrete mathematical structures, L. R. Vermani, Shalini Vermani

Label
A course in discrete mathematical structures
Title
A course in discrete mathematical structures
Statement of responsibility
L. R. Vermani, Shalini Vermani
Creator
Contributor
Subject
Language
eng
Cataloging source
BTCTA
http://library.link/vocab/creatorName
Vermani, L. R.
Dewey number
511.6
Illustrations
illustrations
Index
index present
LC call number
QA76.9.M35
LC item number
V47 2012
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Vermani, Shalini
http://library.link/vocab/subjectName
Computer science
Label
A course in discrete mathematical structures, L. R. Vermani, Shalini Vermani
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 613-614) and index
Contents
  • Venn Diagrams
  • Solution by the method of generating functions
  • 5.2.4.
  • Some typical examples
  • 5.2.5.
  • Recurrence relations reducible to linear recurrence relations
  • 6.
  • Partially Ordered Sets
  • 6.1.
  • Preliminaries
  • 6.2.
  • 1.4.
  • Hasse Diagrams
  • 6.3.
  • Chains and Antichains in Posets
  • 7.
  • Graphs
  • 7.1.
  • Preliminaries and Graph Terminology
  • 7.1.1.
  • Some typical examples
  • 7.2.
  • Power Set
  • Paths and Circuits
  • 7.3.
  • Shortest Path in Weighted Graphs
  • 7.4.
  • Eulerian Paths and Circuits
  • 7.5.
  • Hamiltonian Paths and Circuits
  • 7.6.
  • Planar Graphs
  • 7.6.1.
  • 1.5.
  • Applications
  • 7.6.2.
  • Some further examples
  • 7.6.3.
  • Graph colouring
  • 7.7.
  • Matrix Representations of Graphs
  • 7.7.1.
  • Adjacency matrix
  • 8.
  • Countable Sets
  • Trees
  • 8.1.
  • Introduction and Elementary Properties
  • 8.2.
  • Rooted Trees
  • 8.3.
  • Tree Searching or Traversing a Tree
  • 8.4.
  • Applications of Trees
  • 8.4.1.
  • 1.6.
  • Prefix codes
  • 8.4.2.
  • Binary search trees
  • 8.4.3.
  • On counting trees
  • 8.4.4.
  • Some further examples
  • 8.5.
  • Spanning Trees and Cut-Sets
  • 8.6.
  • Some Special Maps (Functions)
  • Minimal/Minimum/Shortest Spanning Tree
  • 9.
  • Groups
  • 9.1.
  • Groups: Preliminaries
  • 9.2.
  • Subgroups
  • 9.2.1.
  • Lagrange's theorem
  • 9.3.
  • 1.6.1.
  • Quotient Groups
  • 9.4.
  • Symmetric Groups
  • 10.
  • Rings
  • 10.1.
  • Rings
  • 10.2.
  • Polynomial Rings
  • 10.3.
  • characteristic function
  • Quotient Rings and Homomorphisms
  • 11.
  • Fields and Vector Spaces
  • 11.1.
  • Fields
  • 11.1.1.
  • Field extensions and minimal polynomial
  • 11.1.2.
  • Characteristic of a field
  • 11.1.3.
  • 1.7.
  • Splitting field
  • 11.2.
  • Vector Spaces
  • 11.2.1.
  • Basis of a vector space
  • 11.2.2.
  • Subspaces and quotient spaces
  • 11.2.3.
  • Linear transformations
  • 12.
  • Machine generated contents note:
  • Partitions of Sets
  • Lattices and Boolean Algebra
  • 12.1.
  • Lattices
  • 12.2.
  • Lattices as Algebraic Systems
  • 12.3.
  • Sublattices and Homomorphisms
  • 12.4.
  • Distributive and Modular Lattices
  • 12.5.
  • 1.8.
  • Complemented Lattices
  • 12.6.
  • Boolean Algebras
  • 12.7.
  • Boolean Polynomials and Boolean Functions
  • 12.8.
  • Switching (or Logical) Circuits
  • 13.
  • Matrices, Systems of Linear Equations and Eigen Values
  • 13.1.
  • Minset and Maxset Normal Forms
  • Linear System of Equations
  • 13.1.1.
  • Rank of a matrix
  • 13.1.2.
  • Linear system of equations
  • 13.2.
  • Elementary Row Operations, Gaussian Elimination
  • 13.2.1.
  • Elementary row operations
  • 13.2.2.
  • 1.9.
  • Gaussian elimination in matrix form
  • 13.2.3.
  • Gaussian elimination method
  • 13.2.4.
  • Direct methods for the solution of linear system of equations
  • 13.2.5.
  • Method of factorization
  • 13.2.6.
  • Some additional examples
  • 13.3.
  • Multisets
  • Eigen Values
  • 13.3.1.
  • Eigen values and eigen vectors
  • 2.
  • Propositional Calculus and Logic
  • 2.1.
  • Propositions
  • 2.2.
  • 1.
  • Compositions of Propositions
  • 2.3.
  • Truth Tables and Applications
  • 2.4.
  • Some Further Applications of Logic
  • 2.5.
  • Functionally Complete Set of Connectives
  • 2.6.
  • Connectives NAND and NOR
  • 3.
  • Sets
  • More on Sets
  • 3.1.
  • Principle of Inclusion and Exclusion
  • 3.2.
  • Pigeonhole Principle
  • 3.2.1.
  • Some typical applications of the pigeonhole principle
  • 3.3.
  • Binary Relations
  • 3.3.1.
  • 1.1.
  • Relations
  • 3.3.2.
  • Equivalence relations
  • 3.3.3.
  • Union, intersection and inverse of relations
  • 3.3.4.
  • Composition of relations
  • 3.3.5.
  • matrix of a relation
  • 3.3.6.
  • Preliminaries
  • Closure operations on relations
  • 4.
  • Some Counting Techniques
  • 4.1.
  • Principle of Mathematical Induction
  • 4.2.
  • Strong Induction
  • 4.3.
  • Arithmetic, Geometric and Arithmetic-Geometric Series
  • 4.4.
  • 1.2.
  • Permutations and Combinations
  • 4.4.1.
  • Rules of product and sum
  • 4.4.2.
  • Permutations
  • 4.4.3.
  • arrangements of objects that are not all distinct
  • 4.4.4.
  • Combinations
  • 4.4.5.
  • Algebra of Sets
  • Generation of permutations and combinations
  • 5.
  • Recurrence Relations
  • 5.1.
  • Partial Fractions
  • 5.1.1.
  • Rational functions
  • 5.1.2.
  • Partial fractions
  • 5.1.3.
  • 1.3.
  • Procedure for resolving into partial fractions
  • 5.1.4.
  • Some solved examples
  • 5.2.
  • Recurrence Relations: Preliminaries
  • 5.2.1.
  • Homogeneous solutions
  • 5.2.2.
  • Particular solutions
  • 5.2.3.
Dimensions
23 cm.
Extent
xiv, 626 p.
Isbn
9781848167070
Other physical details
ill.
System control number
  • (CaMWU)u2541324-01umb_inst
  • 2560094
  • (Sirsi) i9781848166967
  • (OCoLC)659769725
Label
A course in discrete mathematical structures, L. R. Vermani, Shalini Vermani
Publication
Bibliography note
Includes bibliographical references (p. 613-614) and index
Contents
  • Venn Diagrams
  • Solution by the method of generating functions
  • 5.2.4.
  • Some typical examples
  • 5.2.5.
  • Recurrence relations reducible to linear recurrence relations
  • 6.
  • Partially Ordered Sets
  • 6.1.
  • Preliminaries
  • 6.2.
  • 1.4.
  • Hasse Diagrams
  • 6.3.
  • Chains and Antichains in Posets
  • 7.
  • Graphs
  • 7.1.
  • Preliminaries and Graph Terminology
  • 7.1.1.
  • Some typical examples
  • 7.2.
  • Power Set
  • Paths and Circuits
  • 7.3.
  • Shortest Path in Weighted Graphs
  • 7.4.
  • Eulerian Paths and Circuits
  • 7.5.
  • Hamiltonian Paths and Circuits
  • 7.6.
  • Planar Graphs
  • 7.6.1.
  • 1.5.
  • Applications
  • 7.6.2.
  • Some further examples
  • 7.6.3.
  • Graph colouring
  • 7.7.
  • Matrix Representations of Graphs
  • 7.7.1.
  • Adjacency matrix
  • 8.
  • Countable Sets
  • Trees
  • 8.1.
  • Introduction and Elementary Properties
  • 8.2.
  • Rooted Trees
  • 8.3.
  • Tree Searching or Traversing a Tree
  • 8.4.
  • Applications of Trees
  • 8.4.1.
  • 1.6.
  • Prefix codes
  • 8.4.2.
  • Binary search trees
  • 8.4.3.
  • On counting trees
  • 8.4.4.
  • Some further examples
  • 8.5.
  • Spanning Trees and Cut-Sets
  • 8.6.
  • Some Special Maps (Functions)
  • Minimal/Minimum/Shortest Spanning Tree
  • 9.
  • Groups
  • 9.1.
  • Groups: Preliminaries
  • 9.2.
  • Subgroups
  • 9.2.1.
  • Lagrange's theorem
  • 9.3.
  • 1.6.1.
  • Quotient Groups
  • 9.4.
  • Symmetric Groups
  • 10.
  • Rings
  • 10.1.
  • Rings
  • 10.2.
  • Polynomial Rings
  • 10.3.
  • characteristic function
  • Quotient Rings and Homomorphisms
  • 11.
  • Fields and Vector Spaces
  • 11.1.
  • Fields
  • 11.1.1.
  • Field extensions and minimal polynomial
  • 11.1.2.
  • Characteristic of a field
  • 11.1.3.
  • 1.7.
  • Splitting field
  • 11.2.
  • Vector Spaces
  • 11.2.1.
  • Basis of a vector space
  • 11.2.2.
  • Subspaces and quotient spaces
  • 11.2.3.
  • Linear transformations
  • 12.
  • Machine generated contents note:
  • Partitions of Sets
  • Lattices and Boolean Algebra
  • 12.1.
  • Lattices
  • 12.2.
  • Lattices as Algebraic Systems
  • 12.3.
  • Sublattices and Homomorphisms
  • 12.4.
  • Distributive and Modular Lattices
  • 12.5.
  • 1.8.
  • Complemented Lattices
  • 12.6.
  • Boolean Algebras
  • 12.7.
  • Boolean Polynomials and Boolean Functions
  • 12.8.
  • Switching (or Logical) Circuits
  • 13.
  • Matrices, Systems of Linear Equations and Eigen Values
  • 13.1.
  • Minset and Maxset Normal Forms
  • Linear System of Equations
  • 13.1.1.
  • Rank of a matrix
  • 13.1.2.
  • Linear system of equations
  • 13.2.
  • Elementary Row Operations, Gaussian Elimination
  • 13.2.1.
  • Elementary row operations
  • 13.2.2.
  • 1.9.
  • Gaussian elimination in matrix form
  • 13.2.3.
  • Gaussian elimination method
  • 13.2.4.
  • Direct methods for the solution of linear system of equations
  • 13.2.5.
  • Method of factorization
  • 13.2.6.
  • Some additional examples
  • 13.3.
  • Multisets
  • Eigen Values
  • 13.3.1.
  • Eigen values and eigen vectors
  • 2.
  • Propositional Calculus and Logic
  • 2.1.
  • Propositions
  • 2.2.
  • 1.
  • Compositions of Propositions
  • 2.3.
  • Truth Tables and Applications
  • 2.4.
  • Some Further Applications of Logic
  • 2.5.
  • Functionally Complete Set of Connectives
  • 2.6.
  • Connectives NAND and NOR
  • 3.
  • Sets
  • More on Sets
  • 3.1.
  • Principle of Inclusion and Exclusion
  • 3.2.
  • Pigeonhole Principle
  • 3.2.1.
  • Some typical applications of the pigeonhole principle
  • 3.3.
  • Binary Relations
  • 3.3.1.
  • 1.1.
  • Relations
  • 3.3.2.
  • Equivalence relations
  • 3.3.3.
  • Union, intersection and inverse of relations
  • 3.3.4.
  • Composition of relations
  • 3.3.5.
  • matrix of a relation
  • 3.3.6.
  • Preliminaries
  • Closure operations on relations
  • 4.
  • Some Counting Techniques
  • 4.1.
  • Principle of Mathematical Induction
  • 4.2.
  • Strong Induction
  • 4.3.
  • Arithmetic, Geometric and Arithmetic-Geometric Series
  • 4.4.
  • 1.2.
  • Permutations and Combinations
  • 4.4.1.
  • Rules of product and sum
  • 4.4.2.
  • Permutations
  • 4.4.3.
  • arrangements of objects that are not all distinct
  • 4.4.4.
  • Combinations
  • 4.4.5.
  • Algebra of Sets
  • Generation of permutations and combinations
  • 5.
  • Recurrence Relations
  • 5.1.
  • Partial Fractions
  • 5.1.1.
  • Rational functions
  • 5.1.2.
  • Partial fractions
  • 5.1.3.
  • 1.3.
  • Procedure for resolving into partial fractions
  • 5.1.4.
  • Some solved examples
  • 5.2.
  • Recurrence Relations: Preliminaries
  • 5.2.1.
  • Homogeneous solutions
  • 5.2.2.
  • Particular solutions
  • 5.2.3.
Dimensions
23 cm.
Extent
xiv, 626 p.
Isbn
9781848167070
Other physical details
ill.
System control number
  • (CaMWU)u2541324-01umb_inst
  • 2560094
  • (Sirsi) i9781848166967
  • (OCoLC)659769725

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