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Mathematical foundation of computer science

Author: Y N Singh
Publisher: New Delhi : New Age International, ©2005.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions℗ℓconcepts and  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Singh, Y.N.
Mathematical foundation of computer science.
New Delhi : New Age International, ©2005
(OCoLC)225590308
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Y N Singh
ISBN: 9788122422948 8122422942 1281788821 9781281788825
OCLC Number: 310971241
Description: 1 online resource (xv, 376 pages) : illustrations
Contents: Cover13; --
Copyright --
Preface --
Motivation13; --
Feature of the Book13; --
Acknowledgements13; --
Contents --
Chapter 1. Discrete Theory, Relations and Functions --
1.1 Introduction --
1.2 Elementary Theory of Sets 13; --
1.3 Set Rules and Sets Combinations --
1.3.1 Rule of Equality13; --
1.3.2 Study of Sets Combinations13; --
1.3.3 Power Set --
1.3.4 Multisets --
1.3.5 Ordered Sets --
1.3.6 Cartesian Products13; --
1.4 Relations --
1.4.1 Binary Relation --
1.4.2 Equivalence Relation --
1.4.3 Pictorial Representation of Relations --
1.4.4 Composite Relation --
1.4.5 Ordering Relation --
1.5 Function --
1.5.1 Classification of Functions13; --
1.5.2 Composition of Functions --
1.5.3 Inverse Functions --
1.5.4 Recursively Defined Functions --
1.6 Mathematical Induction and Piano's Axioms13; --
Chapter 2. Discrete Numeric Functions and Generating Functions --
2.1 Introduction --
2.2 Properties of Numeric Functions --
2.2.1 Addition of numeric functions13; --
2.2.2 Multiplication of Numeric Functions13; --
2.2.3 Multiplication with a Scalar Factor to Numeric Function13; --
2.2.4 Quotient of Numeric Functions --
2.2.5 Modulus of Numeric Function13; --
2.2.6. S1an and S1an13; --
2.2.7 Accumulated Sum of Numeric Fuctions13; --
2.2.8 Forward Difference & Backward Difference --
2.2.9 Convolution of Numeric Functions --
2.3 Asymptotic Behavior (Performance) of Numeric Functions13; --
2.3.1 Big-Oh (O) Notation13; --
2.3.2 Omega (937;) Notation 13; --
2.3.3 Theta (952;) Notation13; --
2.4 Generating Functions --
2.5 Application of Generating Function to Solve Combinatorial Problems --
Chapter 3. Recurrence Relations with Constant Coefficients --
3.1 Introduction --
3.2 Recurrence Relation for Discrete Numeric Functions --
3.3 Finding the Solution of LRRCC --
3.3.1 Method of Finding Homogenous Solution --
3.3.2 Method of Finding Particular Solution --
3.4 Alternate Method (Finding Solution of LRRCC by Generating Function) --
3.5 Common Recurrences from Algorithms --
3.6 Method for Solving Recurrences --
3.6.1 Iteration Method --
3.6.2 Master Theorem --
3.6.3 Substitution Method --
3.7 Matrix Multiplication --
Chapter 4. Algebraic Structure --
4.1 Introduction --
4.2 Groups --
4.3 Semi Subgroup --
4.4 Complexes --
4.5 Product Semigroups --
4.6 Permutation Groups --
4.7 Order of a Group --
4.8 Subgroups --
4.9 Cyclic Groups --
4.10 Cosets --
4.11 Group Mapping --
4.12 Rings --
4.13 Fields --
Chapter 5. Propositional Logic --
5.1 Introduction to Logic --
5.2 Symbolization of Statements --
5.3 Equivalence of Formula --
5.4 Propositional Logic --
5.4.1 Well Formed Formula (wff)13; --
5.4.2 Immediate Subformula --
5.4.3 Subformula --
5.4.4 Formation Tree of a Formula13; --
5.4.5 Truth Table --
5.5 Tautology --
5.6 Theory of Inference --
5.6.1 Validity by Truth Table --
5.6.2 Natural Deduction Method --
5.6.3 Analytical Tableaux Method (ATM) --
5.7 Predicate Logic --
5.7.1 Symbolization of Statements Using Predicate13; --
5.7.2 Variables and Quantifiers --
5.7.3 Free and Bound Variables13; --
5.8 Inference Theory of Predicate Logic --
Chapter 6. Lattice Theory --
6.1 Introduction --
6.2 Partial Ordere.
Responsibility: Y.N. Singh.

Abstract:

The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions℗ℓconcepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. T.

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