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CD3281 Data Structures and Algorithms Laboratory

CD3281 Data Structures and Algorithms Laboratory

Anna University – CD3281 Data Structures and Algorithms Laboratory Regulation 2021 Syllabus, Notes, Lab Manual Important Questions, Question Paper with Answers, Previous Year Question Paper.

LIST OF EXPERIMENTS: CD3281 Data Structures and Algorithms Laboratory

1. Implement simple ADTs as Python classes
2. Implement recursive algorithms in Python
3. Implement List ADT using Python arrays
4. Linked list implementations of List
5. Implementation of Stack and Queue ADTs
6. Applications of List, Stack and Queue ADTs
7. Implementation of sorting and searching algorithms
8. Implementation of Hash tables
9. Tree representation and traversal algorithms
10. Implementation of Binary Search Trees
11. Implementation of Heaps Lab Manual
12. Graph representation and Traversal algorithms
13. Implementation of single source shortest path algorithm
14. Implementation of minimum spanning tree algorithms

COURSE OUTCOMES: CD3281 Data Structures and Algorithms Laboratory

At the end of the course, the student should be able to:
CO1:Implement ADTs as Python classes
CO2:Design, implement, and analyse linear data structures, such as lists, queues, and stacks, according to the needs of different applications Lab Manual
CO3:Design, implement, and analyse efficient tree structures to meet requirements such as searching, indexing, and sorting
CO4:Model problems as graph problems and implement efficient graph algorithms to solve them

COURSE OBJECTIVES: CD3281 Data Structures and Algorithms Laboratory

 To implement ADTs in Python
 To design and implement linear data structures – lists, stacks, and queues
 To implement sorting, searching and hashing algorithms

Syllabus Click Here
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Previous Year Question Paper Click Here
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TEXT BOOK: CD3281 Data Structures and Algorithms Laboratory

1. Michael T. Goodrich, Roberto Tamassia, and Michael H. Goldwasser, “Data Structures & Algorithms in Python”, John Wiley & Sons Inc., 2013

REFERENCES: CD3281 Data Structures and Algorithms Laboratory

1. Rance D. Necaise, “Data Structures and Algorithms Using Python”, John Wiley & Sons, 2011
2. Aho, Hopcroft, and Ullman, “Data Structures and Algorithms”, Pearson Education, 1983. Lab Manual
3. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, “Introduction to Algorithms”, Second Edition, McGraw Hill, 2002.
4. Mark Allen Weiss, “Data Structures and Algorithm Analysis in C++”, Fourth Edition, Pearson Education, 2014

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Important question Notes question bank Question Paper R-2021 Syllabus

CD3291 Data Structures and Algorithms

CD3291 Data Structures and Algorithms Study Materials

Anna University – CD3291 Data Structures and Algorithms Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I ABSTRACT DATA TYPES CD3291 Data Structures and Algorithms Syllabus

Abstract Data Types (ADTs) – ADTs and classes – introduction to OOP – classes in Python – inheritance – namespaces – shallow and deep copying
Introduction to analysis of algorithms – asymptotic notations – divide & conquer – recursion – analyzing recursive algorithms

UNIT II LINEAR STRUCTURES CD3291 Data Structures and Algorithms Notes

List ADT – array-based implementations – linked list implementations – singly linked lists – circularly linked lists – doubly linked lists – Stack ADT – Queue ADT – double ended queues – applications

UNIT III SORTING AND SEARCHING CD3291 Data Structures and Algorithms Important Questions

Bubble sort – selection sort – insertion sort – merge sort – quick sort – analysis of sorting algorithms – linear search – binary search – hashing – hash functions – collision handling – load factors, rehashing, and efficiency

UNIT IV TREE STRUCTURES CD3291 Data Structures and Algorithms Question Paper

Tree ADT – Binary Tree ADT – tree traversals – binary search trees – AVL trees – heaps – multi-way search trees

UNIT V GRAPH STRUCTURES CD3291 Data Structures and Algorithms Question Bank

Graph ADT – representations of graph – graph traversals – DAG – topological ordering – greedy algorithms – dynamic programming – shortest paths – minimum spanning trees – introduction to complexity classes and intractability

Syllabus Click Here
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TEXT BOOK: CD3291 DSA Notes

1. Michael T. Goodrich, Roberto Tamassia, and Michael H. Goldwasser, “Data Structures & Algorithms in Python”, An Indian Adaptation, John Wiley & Sons Inc., 2021

REFERENCES: CD3291 DSA Important Questions

1. Lee, Kent D., Hubbard, Steve, “Data Structures and Algorithms with Python” Springer Edition 2015
2. Rance D. Necaise, “Data Structures and Algorithms Using Python”, John Wiley & Sons, 2011
3. Aho, Hopcroft, and Ullman, “Data Structures and Algorithms”, Pearson Education, 1983.
4. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, “Introduction to Algorithms”, Second Edition, McGraw Hill, 2002.
5. Mark Allen Weiss, “Data Structures and Algorithm Analysis in C++”, Fourth Edition, Pearson Education, 2014

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CS3361 Data Science Laboratory

CS3361 Data Science Laboratory Study Materials

Anna University – CS3361 Data Science Laboratory Regulation 2021 Syllabus, Notes, Lab Manual Important Questions, Question Paper with Answers, Previous Year Question Paper.

COURSE OBJECTIVES: CS3361 Data Science Laboratory
 To understand the python libraries for data science
 To understand the basic Statistical and Probability measures for data science.
 To learn descriptive analytics on the benchmark data sets.
 To apply correlation and regression analytics on standard data sets.
 To present and interpret data using visualization packages in Python.

LIST OF EXPERIMENTS:
1. Download, install and explore the features of NumPy, SciPy, Jupyter, Statsmodels and Pandas packages.
2. Working with Numpy arrays
3. Working with Pandas data frames
4. Reading data from text files, Excel and the web and exploring various commands for doing descriptive analytics on the Iris data set. CS3361 Data Science Laboratory
5. Use the diabetes data set from UCI and Pima Indians Diabetes data set for performing the following:
a. Univariate analysis: Frequency, Mean, Median, Mode, Variance, Standard Deviation, Skewness and Kurtosis.
b. Bivariate analysis: Linear and logistic regression modeling
c. Multiple Regression analysis
d. Also compare the results of the above analysis for the two data sets.

6. Apply and explore various plotting functions on UCI data sets.
a. Normal curves
b. Density and contour plots
c. Correlation and scatter plots
d. Histograms CS3361 Data Science Laboratory Lab Manual
e. Three dimensional plotting
7. Visualizing Geographic Data with Basemap

Syllabus Click Here
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COURSE OUTCOMES: CS3361 Data Science Laboratory

At the end of this course, the students will be able to:
CO1: Make use of the python libraries for data science
CO2: Make use of the basic Statistical and Probability measures for data science. Lab Manual
CO3: Perform descriptive analytics on the benchmark data sets.
CO4: Perform correlation and regression analytics on standard data sets CS3361 Data Science Laboratory
CO5: Present and interpret data using visualization packages in Python.

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CS3381 Object Oriented Programming Laboratory

CS3381 Object Oriented Programming Laboratory

Anna University – CS3381 Object Oriented Programming Laboratory Regulation 2021 Syllabus, Notes, Lab Manual Important Questions, Question Paper with Answers, Previous Year Question Paper.

COURSE OBJECTIVES: CS3381 Object Oriented Programming Laboratory

 To build software development skills using java programming for real-world applications.
 To understand and apply the concepts of classes, packages, interfaces, inheritance, exception handling and file processing.
 To develop applications using generic programming and event handling

LIST OF EXPERIMENTS: CS3381 Object Oriented Programming Laboratory

1. Solve problems by using sequential search, binary search, and quadratic sorting algorithms (selection, insertion)
2. Develop stack and queue data structures using classes and objects.
3. Develop a java application with an Employee class with Emp_name, Emp_id, Address, Mail_id, Mobile_no as members. Inherit the classes, Programmer, Assistant Professor, Associate Professor and Professor from employee class. Add Basic Pay (BP) as the member of all the inherited classes with 97% of BP as DA, 10 % of BP as HRA, 12% of
BP as PF, 0.1% of BP for staff club funds. Generate pay slips for the employees with their gross and net salary.
4. Write a Java Program to create an abstract class named Shape that contains two integers and an empty method named printArea(). Provide three classes named Rectangle, Triangle and Circle such that each one of the classes extends the class Shape. Each one of the classes contains only the method printArea( ) that prints the area of the given shape.
5. Solve the above problem using an interface.
6. Implement exception handling and creation of user defined exceptions. CS3381 Object Oriented Programming Laboratory Lab Manual

7. Write a java program that implements a multi-threaded application that has three threads. First thread generates a random integer every 1 second and if the value is even, the second thread computes the square of the number and prints. If the value is odd, the third thread will print the value of the cube of the number.
8. Write a program to perform file operations.
9. Develop applications to demonstrate the features of generics classes. CS3381 Object Oriented Programming Laboratory Lab Manual
10. Develop applications using JavaFX controls, layouts and menus.
11. Develop a mini project for any application using Java concepts.
Lab Requirements: for a batch of 30 students
Operating Systems: Linux / Windows
Front End Tools: Eclipse IDE / Netbeans IDE

Syllabus Click Here
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Previous Year Question Paper Click Here
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COURSE OUTCOMES: CS3381 Object Oriented Programming Laboratory

On completion of this course, the students will be able to
CO1 : Design and develop java programs using object oriented programming concepts
CO2 : Develop simple applications using object oriented concepts such as package, exceptions
CO3: Implement multithreading, and generics concepts
CO4 : Create GUIs and event driven programming applications for real world problems
CO5: Implement and deploy web applications using Java

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CS3311 Data Structures Laboratory

CS3311 Data Structures Laboratory

Anna University – CS3311 Data Structures Laboratory Regulation 2021 Syllabus, Notes, Lab Manual Important Questions, Question Paper with Answers, Previous Year Question Paper.

LIST OF EXERCISES: CS3311 Data Structures Laboratory

1. Array implementation of Stack, Queue and Circular Queue ADTs
2. Implementation of Singly Linked List
3. Linked list implementation of Stack and Linear Queue ADTs
4. Implementation of Polynomial Manipulation using Linked list
5. Implementation of Evaluating Postfix Expressions, Infix to Postfix conversion Lab Manual

6. Implementation of Binary Search Trees
7. Implementation of AVL Trees
8. Implementation of Heaps using Priority Queues
9. Implementation of Dijkstra’s Algorithm
10. Implementation of Prim’s Algorithm
11. Implementation of Linear Search and Binary Search
12. Implementation of Insertion Sort and Selection Sort
13. Implementation of Merge Sort
14. Implementation of Open Addressing (Linear Probing and Quadratic Probing)

COURSE OUTCOMES: CS3311 Data Structures Laboratory Lab Manual

At the end of this course, the students will be able to:
CO1: Implement Linear data structure algorithms.
CO2: Implement applications using Stacks and Linked lists
CO3: Implement Binary Search tree and AVL tree operations.
CO4: Implement graph algorithms.
CO5: Analyze the various searching and sorting algorithms.

Syllabus Click Here
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Previous Year Question Paper Click Here
Question Bank Click Here

COURSE OBJECTIVES: CS3311 Data Structures Laboratory

To demonstrate array implementation of linear data structure algorithms.
To implement the applications using Stack. Lab Manual
To implement the applications using Linked list
To implement Binary search tree and AVL tree algorithms.
To implement the Heap algorithm.
To implement Dijkstra’s algorithm.
To implement Prim’s algorithm
To implement Sorting, Searching and Hashing algorithms.

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Important question Notes question bank Question Paper R-2021 Syllabus

CS3391 Object Oriented Programming

CS3391 Object Oriented Programming Study Materials

Anna University – CS3391 Object Oriented Programming Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I INTRODUCTION TO OOP AND JAVA CS3391 Object Oriented Programming Syllabus

Overview of OOP – Object oriented programming paradigms – Features of Object Oriented Programming – Java Buzzwords – Overview of Java – Data Types, Variables and Arrays – Operators – Control Statements – Programming Structures in Java – Defining classes in Java – Constructors-Methods -Access specifiers – Static members- Java Doc comments

UNIT II INHERITANCE, PACKAGES AND INTERFACES CS3391 Object Oriented Programming Notes

Overloading Methods – Objects as Parameters – Returning Objects –Static, Nested and Inner Classes. Inheritance: Basics– Types of Inheritance -Super keyword -Method Overriding – Dynamic Method Dispatch –Abstract Classes – final with Inheritance. Packages and Interfaces: Packages – Packages and Member Access –Importing Packages – Interfaces.

UNIT III EXCEPTION HANDLING AND MULTITHREADING CS3391 Object Oriented Programming Important Questions

Exception Handling basics – Multiple catch Clauses – Nested try Statements – Java’s Built-in Exceptions – User defined Exception. Multithreaded Programming: Java Thread Model–Creating a Thread and Multiple Threads – Priorities – Synchronization – Inter Thread Communication- Suspending –Resuming, and Stopping Threads –Multithreading. Wrappers – Auto boxing.

UNIT IV I/O, GENERICS, STRING HANDLING CS3391 Object Oriented Programming Question Bank

I/O Basics – Reading and Writing Console I/O – Reading and Writing Files. Generics: Generic Programming – Generic classes – Generic Methods – Bounded Types – Restrictions and Limitations. Strings: Basic String class, methods and String Buffer Class.

UNIT V JAVAFX EVENT HANDLING, CONTROLS AND COMPONENTS CS3391 Object Oriented Programming Question paper

JAVAFX Events and Controls: Event Basics – Handling Key and Mouse Events. Controls: Checkbox, ToggleButton – RadioButtons – ListView – ComboBox – ChoiceBox – Text Controls – ScrollPane. Layouts – FlowPane – HBox and VBox – BorderPane – StackPane – GridPane. Menus – Basics – Menu – Menu bars – MenuItem.

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TEXT BOOKS: OOP Notes Important Questions

1. Herbert Schildt, “Java: The Complete Reference”, 11 th Edition, McGraw Hill Education, New Delhi, 2019
2. Herbert Schildt, “Introducing JavaFX 8 Programming”, 1 st Edition, McGraw Hill Education, New Delhi, 2015

REFERENCE: Question Paper

1. Cay S. Horstmann, “Core Java Fundamentals”, Volume 1, 11 th Edition, Prentice Hall, 2018.

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CS3301 Data Structures

CS3301 Data Structures Study Materials

Anna University – CS3301 Data Structures Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I LISTS CS3301 Data Structures Syllabus

Abstract Data Types (ADTs) – List ADT – Array-based implementation – Linked list implementation – Singly linked lists – Circularly linked lists – Doubly-linked lists – Applications of lists – Polynomial ADT – Radix Sort – Multilists.

UNIT II STACKS AND QUEUES CS3301 Data Structures Notes

Stack ADT – Operations – Applications – Balancing Symbols – Evaluating arithmetic expressions- Infix to Postfix conversion – Function Calls – Queue ADT – Operations – Circular Queue – DeQueue – Applications of Queues.

UNIT III TREES CS3301 Data Structures Important Questions

Tree ADT – Tree Traversals – Binary Tree ADT – Expression trees – Binary Search Tree ADT – AVL Trees – Priority Queue (Heaps) – Binary Heap.

UNIT IV MULTIWAY SEARCH TREES AND GRAPHS CS3301 Data Structures Question Paper

B-Tree – B+ Tree – Graph Definition – Representation of Graphs – Types of Graph – Breadth-first traversal – Depth-first traversal –– Bi-connectivity – Euler circuits – Topological Sort – Dijkstra’s algorithm – Minimum Spanning Tree – Prim’s algorithm – Kruskal’s algorithm

UNIT V SEARCHING, SORTING AND HASHING TECHNIQUES CS3301 Data Structures Question Bank

Searching – Linear Search – Binary Search. Sorting – Bubble sort – Selection sort – Insertion sort – Shell sort –. Merge Sort – Hashing – Hash Functions – Separate Chaining – Open Addressing –Rehashing – Extendible Hashing.

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TEXT BOOKS CS3301 Data Structures

1. Mark Allen Weiss, Data Structures and Algorithm Analysis in C, 2nd Edition, Pearson Education, 2005.
2. Kamthane, Introduction to Data Structures in C, 1st Edition, Pearson Education, 2007

REFERENCES

1. Langsam, Augenstein and Tanenbaum, Data Structures Using C and C++, 2nd Edition, Pearson Education, 2015.
2. Thomas H. Cormen, Charles E. Leiserson, Ronald L.Rivest, Clifford Stein, Introduction to Algorithms”, Fourth Edition, Mcgraw Hill/ MIT Press, 2022.
3. Alfred V. Aho, Jeffrey D. Ullman,John E. Hopcroft ,Data Structures and Algorithms, 1st edition, Pearson, 2002.
4. Kruse, Data Structures and Program Design in C, 2nd Edition, Pearson Education, 2006.

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CS3352 Foundations of Data Science

CS3352 Foundations of Data Science Study materials

Anna University – CS3352 Foundations of Data Science Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I INTRODUCTION CS3352 Foundations of Data Science Syllabus

Data Science: Benefits and uses – facets of data – Data Science Process: Overview – Defining research goals – Retrieving data – Data preparation – Exploratory Data analysis – build the model– presenting findings and building applications – Data Mining – Data Warehousing – Basic Statistical descriptions of Data

UNIT II DESCRIBING DATA CS3352 Foundations of Data Science Notes

Types of Data – Types of Variables -Describing Data with Tables and Graphs –Describing Data with Averages – Describing Variability – Normal Distributions and Standard (z) Scores

UNIT III DESCRIBING RELATIONSHIPS CS3352 Foundations of Data Science Important Questions

Correlation –Scatter plots –correlation coefficient for quantitative data –computational formula for correlation coefficient – Regression –regression line –least squares regression line – Standard error of estimate – interpretation of r2 –multiple regression equations –regression towards the mean

UNIT IV PYTHON LIBRARIES FOR DATA WRANGLING CS3352 Foundations of Data Science Question Bank

Basics of Numpy arrays –aggregations –computations on arrays –comparisons, masks, boolean logic – fancy indexing – structured arrays – Data manipulation with Pandas – data indexing and selection – operating on data – missing data – Hierarchical indexing – combining datasets – aggregation and grouping – pivot tables

UNIT V DATA VISUALIZATION CS3352 Foundations of Data Science Question Paper

Importing Matplotlib – Line plots – Scatter plots – visualizing errors – density and contour plots – Histograms – legends – colors – subplots – text and annotation – customization – three dimensional plotting – Geographic Data with Basemap – Visualization with Seaborn.

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TEXT BOOKS CS3352 Foundations of Data Science FDS

1. David Cielen, Arno D. B. Meysman, and Mohamed Ali, “Introducing Data Science”, Manning Publications, 2016. (Unit I)
2. Robert S. Witte and John S. Witte, “Statistics”, Eleventh Edition, Wiley Publications, 2017. (Units II and III)
3. Jake VanderPlas, “Python Data Science Handbook”, O’Reilly, 2016. (Units IV and V)

REFERENCES: FDS Study Materials

1. Allen B. Downey, “Think Stats: Exploratory Data Analysis in Python”, Green Tea Press,2014.

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CS3351 Digital Principles and Computer Organization

CS3351 Digital Principles and Computer Organization Study Materials

Anna University – CS3351 Digital Principles and Computer Organization Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I COMBINATIONAL LOGIC CS3351 Digital Principles and Computer Organization Syllabus

Combinational Circuits – Karnaugh Map – Analysis and Design Procedures – Binary Adder – Subtractor – Decimal Adder – Magnitude Comparator – Decoder – Encoder – Multiplexers – Demultiplexers

UNIT II SYNCHRONOUS SEQUENTIAL LOGIC CS3351 Digital Principles and Computer Organization Notes

Introduction to Sequential Circuits – Flip-Flops – operation and excitation tables, Triggering of FF, Analysis and design of clocked sequential circuits – Design – Moore/Mealy models, state minimization, state assignment, circuit implementation – Registers – Counters.

UNIT III COMPUTER FUNDAMENTALS CS3351 Digital Principles and Computer Organization Important Questions

Functional Units of a Digital Computer: Von Neumann Architecture – Operation and Operands of Computer Hardware Instruction – Instruction Set Architecture (ISA): Memory Location, Address and Operation – Instruction and Instruction Sequencing – Addressing Modes, Encoding of Machine Instruction – Interaction between Assembly and High Level Language.

UNIT IV PROCESSOR CS3351 Digital Principles and Computer Organization Questions Paper

Instruction Execution – Building a Data Path – Designing a Control Unit – Hardwired Control, Microprogrammed Control – Pipelining – Data Hazard – Control Hazards.

UNIT V MEMORY AND I/O CS3351 Digital Principles and Computer Organization Question Bank

Memory Concepts and Hierarchy – Memory Management – Cache Memories: Mapping and Replacement Techniques – Virtual Memory – DMA – I/O – Accessing I/O: Parallel and Serial Interface – Interrupt I/O – Interconnection Standards: USB, SATA

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TEXT BOOKS: CS3351 Digital Principles and Computer Organization DPCO

1. M. Morris Mano, Michael D. Ciletti, “Digital Design : With an Introduction to the Verilog HDL, VHDL, and System Verilog”, Sixth Edition, Pearson Education, 2018.
2. David A. Patterson, John L. Hennessy, “Computer Organization and Design, The Hardware/Software Interface”, Sixth Edition, Morgan Kaufmann/Elsevier, 2020.

REFERENCES: DPCO

1. Carl Hamacher, Zvonko Vranesic, Safwat Zaky, Naraig Manjikian, “Computer Organization and Embedded Systems”, Sixth Edition, Tata McGraw-Hill, 2012.
2. William Stallings, “Computer Organization and Architecture – Designing for Performance”, Tenth Edition, Pearson Education, 2016.
3. M. Morris Mano, “Digital Logic and Computer Design”, Pearson Education, 2016.

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MA3354 Discrete Mathematics

MA3354 Discrete Mathematics Study Materials

Anna University – MA3354 Discrete Mathematics Regulation 2021 Syllabus, Notes, Important Questions, Question Paper with Answers, Previous Year Question Paper.

UNIT I LOGIC AND PROOFS MA3354 Discrete Mathematics Syllabus

Propositional logic – Propositional equivalences – Predicates and quantifiers – Nested quantifiers – Rules of inference – Introduction to proofs – Proof methods and strategy.

UNIT II COMBINATORICS MA3354 Discrete Mathematics Notes

Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeonhole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.

UNIT III GRAPHS MA3354 Discrete Mathematics Important Questions

Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.

UNIT IV ALGEBRAIC STRUCTURES MA3354 Discrete Mathematics Question Bank

Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism’s – Normal subgroup and cosets – Lagrange’s theorem – Definitions and examples of Rings and Fields.

UNIT V LATTICES AND BOOLEAN ALGEBRA MA3354 Discrete Mathematics Question Paper

Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra – Sub Boolean Algebra – Boolean Homomorphism.

Syllabus Click Here
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TEXT BOOKS: MA3354 Discrete Mathematics

1. Rosen. K.H., “Discrete Mathematics and its Applications”, 7th Edition, Tata McGraw Hill Pub. Co. Ltd., New Delhi, Special Indian Edition, 2017.
2. Tremblay. J.P. and Manohar. R, “Discrete Mathematical Structures with Applications to Computer Science”, Tata McGraw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.

REFERENCES:

1. Grimaldi. R.P. “Discrete and Combinatorial Mathematics: An Applied Introduction”, 5thEdition, Pearson Education Asia, Delhi, 2013.
2. Koshy. T. “Discrete Mathematics with Applications”, Elsevier Publications, 2006.
3. Lipschutz. S. and Mark Lipson., “Discrete Mathematics”, Schaum’s Outlines, Tata McGraw Hill Pub. Co. Ltd., New Delhi, 3rd Edition, 2010.

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