Description
Wiley Wiley Acing The Gate: Computer Science And Information Technology, 2Ed (Combo) by Anil Kumar Verma
The book uses a precise and systematic approach to present the subject of computer science and information technology for GATE (CS). The content of the book is built after thorough analysis of concepts asked in previous year question papers, and thus emerges as a fully competent book to cater to the needs of the GATE aspirants. Difficult topics such as theory of computation, compiler design, operating systems are clarified using simple steps and illustrations as well as supported by a large number of problems for practice; as these form the major portion of the GATE syllabus. Using this book, the aspirants would be able to revise their fundamentals of the subject and test their preparedness level through multitude of problems, thereby developing the aptitude required for success in GATE.
Wiley Acing the GATE: Engineering Mathematics and General Aptitude is intended to be the complete book for those aspiring to compete in the Graduate Aptitude Test in Engineering (GATE) in various engineering disciplines, including Electronics and Communication, Electrical, Mechanical, Computer Science, Civil, Chemical and Instrumentation, comprehensively covering all topics as prescribed in the syllabus in terms of study material and an elaborate question bank. The book presents the subjects of Engineering Mathematics and General Aptitude in a systematic, structured and precise manner.
About the Author
Anil Kumar Verma is currently working as an Associate Professor in the Department of CSE
Table of Contents
Preface
About the Authors
Acing the GATE
About GATE
Attributes for Success in Examination
1 Digital Logic
·Introduction
·Number System
·Boolean Logic
·Digital Circuits
2 Computer Organization and Architecture
·Introduction
·Computer Architecture
·Machine Instructions and Addressing Modes
·Arithmetic Logic Unit
·CPU Control Design
·I/O Interface (Interrupt and DMA Mode)
·Instruction Pipelining
·Memory Hierarchy
3 Programming and Data Structures
·Introduction
·Basic Terminology
·Stack
·Queue
·Linked List
·Trees
4 Algorithms
·Introduction
·Algorithm
·Hashing
·Binary Heap
·Searching and Sorting
·Graph
·Greedy Approach
·Graph Traversa
·Dynamic Programming
·All-Pair Shortest Path
·Concepts of Complexity Classes
5 Theory of Computation
·Introduction
·Finite Automata
·Finite Automata and Regular Language
·Pushdown Automata
·Context-Free Grammar and Languages
·Turing Machine
6 Compiler Design
·Introduction
·Compilers and Interpreters
·Lexical Analyzer
·Parser
·Syntax-Directed Translation
·Runtime Environment
·Intermediate Code Generation
·Code Optimization
7 Operating System
·Introduction
·Types of Operating System
·Process Management
·CPU Scheduling
·Process Synchronization
·Deadlocks
·Threads
·Memory Management
·File System
·I/O Systems
·Protection and Security
8 Databases
·Introduction
·Components of Database Systems
·DBMS Architecture
·Data Models
·Database Design
·Query Languages (SQL)
·File Structures
·Transactions and Concurrency Control
9 Information Systems and Software Engineering*
·Introduction
·Information Systems
·Software
·Process Models
·Measurement of Metrics
·Risk Analysis
·Software Development Life Cycle
10 Computer Networks
·Introduction
·Network
·LAN Technologies
·ISO/OSI Stack
·Layer 4: Transport Layer
·Layer 5: Session Layer
·Layer 6: Presentation Layer
·Layer 7: Application Layer
·Devices
·Network Security
·Basic of WiFi
11 Web Technologies*
·Introduction
·HTML
·Cascading Style Sheets
·Basic Concepts of Client— Server Computing
·J2EE platform
12 Discrete Mathematics
·Introduction
·Propositional Logic and First Order Logic
·Set Theory
·Relations
·Group
·Permutation
·Combinatorics
·Graph Theory
Important Formulas
Solved Examples
GATE Previous Years’ Questions
Practice Exercises
Answers to Practice Exercises
Index
Preface
Engineering Mathematics
1 Linear Algebra
Matrix
Determinants
Solutions of Simultaneous Linear Equations
Augmented Matrix
Gauss Elimination Method
Cayley—Hamilton Theorem
Eigenvalues and Eigenvectors
2 Calculus
Limits
Properties of Limits
Continuity and Discontinuity
Differentiability
Mean Value Theorems
Fundamental Theorem of Calculus
Differentiation
Applications of Derivatives
Partial Derivatives
Integration
Methods of Integration
Definite Integrals
Improper Integrals
Double Integration
Change of Order of Integration
Triple Integrals
Applications of Integrals
Fourier Series
Vectors
Line Integrals
Surface Integrals
Stokes’ Theorem
Green’s Theorem
Gauss Divergence Theorem
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
3 Differential Equations
Introduction
Solution of a Differential Equation
Linear Differential Equation
Particular Integrals
Homogeneous Linear Equation
Bernoulli’s Equation
Euler—Cauchy Equations
Solving Differential Equations Using Laplace Transforms
Variation of Parameters Method
Separation of Variables Method
One-Dimensional Diffusion (Heat Flow) Equation
Second Order One-Dimensional Wave Equation
Two-Dimensional Laplace Equation
Solved Examples
Practice Exercises
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
4 Complex Variables
Introduction
Complex Functions
Exponential Function of Complex Variables
Circular Function of Complex Variables
Hyperbolic Functions of Complex Variables
Logarithmic Function of Complex Variables
Limit and Continuity of Complex Functions
Derivative of Complex Variables
Cauchy—Riemann Equations
Integration of Complex Variables
Cauchy’s Theorem
Cauchy’s Integral Formula
Taylor’s Series of Complex Variables
Laurent’s Series of Complex Variables
Zeros and Poles of an Analytic Function
Residues
Residue Theorem
Calculation of Residues
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
5 Probability and Statistics
Fundamentals of Probability
Types of Events
Approaches to Probability
Axioms of Probability
Conditional Probability
Geometric Probability
Rules of Probability
Statistics
Arithmetic Mean
Median
Mode
Relation between Mean, Median and Mode
Geometric Mean
Harmonic Mean
Range
Mean Deviation
Standard Deviation
Coefficient of Variation
Probability Distributions
Random Variable
Properties of Discrete Distribution
Properties of Continuous Distribution
Types of Discrete Distribution
Types of Continuous Distribution
Correlation and Regression Analyses
Correlation
Lines of Regression
Hypothesis Testing
Hypothesis Testing Procedures for Some Common Statistical Problems
Hypothesis Testing of a Proportion
Hypothesis Testing of a Mean
Hypothesis Testing of Difference Between Proportions
Hypothesis Testing of Difference Between Means
Bayes’ Theorem
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
6 Numerical Methods
Introduction
Numerical Solution of System of Linear Equations
Gauss Elimination Method
Matrix Decomposition Methods (LU Decomposition Method)
Gauss—Jordan Method
Iterative Methods of Solution
Numerical Solution of Algebraic and Transcendental Equations
Bisection Method
Regula—Falsi Method (Method of False Position Method)
Newton—Raphson Method
Secant Method
Jacobian
Numerical Integration
Newton—Cotes Formulas (General Quadrature)
Rectangular Rule
Trapezoidal Rule
Simpson’s Rule
Numerical Solution of Ordinary Differential Equation (O.D.E.)
Picard’s Method
Euler’s Method
Runge—Kutta Method
Euler’s Predictor—Corrector Method
Accuracy and Precision
Classification of Errors
Significant Figures
Measuring Error
Propagation of Errors
Method of Least Square Approximation
Lagrange Polynomials
Numerical Differentiation
Newton’s Forward Formula
Newton’s Backward Formula
Stirling’s or Bessel’s Formula
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
7 Mathematical Logic
Introduction
Statements
Atomic Statements
Molecular Statements
Truth Table
Truth Values
Connectives
Types of Connectives
Well-Formed Formulas
Duality Law
Equivalent Well-Formed Formula
Logical Identities
Normal Form
Disjunction Normal Form
Conjunctive Normal Form
Propositional Calculus
Rules of Inference
Predicate Calculus
Predicates
Quantifier
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
8 Set Theory and Algebra
Introduction to Set Theory
Subsets and Supersets
Equal Sets
Comparable Sets
Universal Set
Power Set
Types of Sets
Operations on Sets
Important Laws and Theorems
Venn Diagrams
Operations on Sets Using Venn Diagrams
Application of Sets
Cartesian product of Sets
Relations
Types of Relations
Properties of Relation
Functions
Types of Functions
Compositions of Functions
Introduction to Algebra
Semigroups
Some Important Theorems
Group
Some Important Theorems
Residue Classes
Residue Class Addition
Residual Class Multiplication
Partial Ordering
Hasse Diagram
Lattice
Sublattice
Bounds
Boolean algebra of Lattices
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
9 Combinatory
Introduction
Counting
Fundamental Principle of Addition
Fundamental Principle of Multiplication
Permutations
Conditional Permutations
Permutations when all Objects are not Distinct
Circular Permutations
Combinations
Properties of Combinations
Conditional Combinations
Generating Functions
Ordinary Generating Function
Exponential Generating Function
Poisson Generating Function
Recurrence Relation
Logistic Map
Fibonacci Numbers
Binomial Coefficients
Summation
Asymptotic Analysis
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
10 Graph Theory
Introduction
Fundamental Concepts of Graph
Common Terminologies
Degree of a Vertex
Multigraph
Walks, Paths and Connectivity
Subgraph
Types of Graphs
Complete Graph
Regular Graph
Bipartite Graph
Tree Graph
Trivial Graph
Cycle
Operations on Graphs
Matrix Representation of Graphs
Adjacent Matrix
Incidence Matrix
Cuts
Spanning Trees and Algorithms
Kruskal’s Algorithm
Prim’s Algorithm
Binary Trees
Euler Tours
Konigsberg Bridge Problem
Hamiltonian Graphs
Closure of a Graph
Graph Isomorphism
Homeomorphic Graphs
Planar Graphs
Matching
Covering
Independent Set
Graph Coloring
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
Chapter 11 Transform Theory
Introduction
Laplace Transform
Laplace Transform of Common Signals
Properties of Laplace Transform
Inverse Laplace Transform
z -Transform
z -Transform of Common Sequences
Properties of z -Transform
Inverse z-Transform
Relationship between z-Transform and Laplace Transform
Fourier Transform
Convergence of Fourier Transforms
Properties of Fourier Transform
Solved Examples
Practice Exercise
Answers
Explanations and Hints
Solved GATE Previous Years’ Questions
General Aptitude: Verbal Ability
1 English Grammar
Articles
Noun
Use of Nouns in Singular Form
Use of Nouns in Plural Form
Conversion of Nouns from Singular to Plural
Collective Nouns
Pronoun
Personal Pronoun
Reflexive and Emphatic Pronoun
Demonstrative Pronoun
Indefinite Pronoun
Distributive Pronoun
Relative Pronoun
Interrogative Pronoun
Use of Pronouns
Adjective
Use of Adjectives
Preposition
Preposition of Time
Preposition of Position
Preposition of Direction
Other Uses of Preposition
Verbs
Use of Verb
Use of Infinitives
Use of Gerunds
Tenses
Use of Tenses
Adverbs
Practice Exercise
2 Synonyms
Tips to Solve Synonym Based Questions
3 Antonyms
Graded Antonyms
Complementary Antonyms
Relational Antonyms
Practice Exercise
4 Sentence Completion
Tips to Solve Sentence Completion Based Questions
5 Verbal Analogies
Types of Analogies
Tips to Solve Verbal Analogies Questions
6 Word Groups
7 Verbal Deduction
Tips and Tricks to Solve Verbal Deduction Questions
General Aptitude: Numerical Ability
Unit 1: Basic Arithmetic
1 Number System
Numbers
Classification of Numbers
Progressions
Arithmetic Progressions
Geometric Progressions
Infinite Geometric Progressions
Averages, Mean, Median and Mode
Relation between AM, GM and HM
Some Algebraic Formulas
The Remainder Theorem
The Polynomial Factor Theorem
Base System
Counting Trailing Zeros
Inequations
Quadratic Equations
Even and Odd Numbers
Prime Numbers and Composite Numbers
HCF and LCM of Numbers
Cyclicity
Test for Divisibility
2 Percentage
Introduction
Some Important Formulae
3 Profit and Loss
Introduction
Some Important Formulae
Margin and Markup
4 Simple Interest and Compound Interest
Introduction
Some Important Formulae
5 Time and Work
Introduction
Important Formulas and Concepts
6 Average, Mixture and Alligation
Average
Weighted Average
Mixture and Alligation
7 Ratio, Proportion and Variation
Ratio
Proportion
Variation
8 Speed, Distance and Time
Introduction
Some Important Formulas
Unit 2: Algebra
1 Permutation and Combination
Permutation
Combination
Partitions
Counting
Fundamental Principle of Addition
Fundamental Principle of Multiplication
2 Progression
Arithmetic Progression
Geometric Progression
Infinite Geometric Progression
Harmonic Series
Relation between AM, GM and HM
3 Probability
Introduction
Some Basic Concepts of Probability
Some Important Theorems
4 Set Theory
Introduction
Venn Diagrams
Operation on Sets
Venn Diagram with Two Attributes
Venn Diagram with Three Attributes
5 Surds, Indices and Logarithms
Surds
Logarithm
Unit 3: Reasoning and Data Interpretation
1 Cubes and Dices
Cubes
Dices
2 Line Graph
Introduction
3 Tables
Introduction
4 Blood Relationship
Introduction
Standard Coding Technique
5 Bar Diagram
Introduction
6 Pie Chart
Introduction
Types of Pie Charts
3-D Pie Chart
Doughnut Chart
Exploded Pie Chart
Polar Area Chart
Ring Chart/Multilevel Pie Chart
7 Puzzles
Introduction
Types of Puzzles
8 Analytical Reasoning
Introduction
General Aptitude: Solved Gate Previous Years’ Questions