210241: Discrete Mathematics

Credit 04

Unit I Set Theory and Logic 
Introduction and significance of Discrete Mathematics, Sets– Naïve Set Theory (Cantorian Set Theory), Axiomatic Set Theory, Set Operations, Cardinality of set, Principle of inclusion and exclusion. Types of Sets – Bounded and Unbounded Sets, Diagonalization Argument, Countable and Uncountable Sets, Finite and Infinite Sets, Countably Infinite and Uncountably Infinite Sets, Power set, Propositional Logic- logic, Propositional Equivalences, Application of Propositional Logic- Translating English Sentences, Proof by Mathematical Induction and Strong Mathematical Induction

#Exemplar/Case Studies Know about the great philosophers- Georg Cantor, RichardM Dedekind and Aristotle

Mapping of Course Outcomes for Unit I CO1, CO3

Unit II Relations and Functions 
Relations and their Properties, n-ary relations and their applications, Representing relations , Closures of relations, Equivalence relations, Partial orderings, Partitions, Hasse diagram, Lattices, Chains and Anti-Chains, Transitive closure and Warshall‘s algorithm. Functions- Surjective, Injective and Bijective functions, Identity function, Partial function, Invertible function, Constant function, Inverse functions and Compositions of functions, The Pigeonhole Principle.
#Exemplar/Case Studies Know about the great philosophers-Dirichlet
Mapping of Course Outcomes for Unit II CO2

Unit III Counting Principles 
The Basics of Counting, rule of Sum and Product, Permutations and Combinations, Binomial Coefficients and Identities, Generalized Permutations and Combinations, Algorithms for generating Permutations and Combinations.
#Exemplar/Case Studies Study Sudoku solving algorithms and algorithm for generation of new SUDOKU. Study Hank-shake Puzzle and algorithm to solve it

Mapping of Course Outcomes for Unit III

Unit IV Graph Theory 
Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, the handshaking lemma, Single source shortest path- Dijkstra's Algorithm, Planar Graphs, Graph Colouring.

#Exemplar/Case Studies Three utility problem, Web Graph, Google map
Mapping of Course Outcomes for Unit IV CO4

Unit V Trees 
Introduction, properties of trees, Binary search tree, tree traversal, decision tree, prefix codes and Huffman coding, cut sets, Spanning Trees and Minimum Spanning Tree, Kruskal‘s and Prim‘s algorithms, The Max flow- Min Cut Theorem (Transport network).
#Exemplar/Case Studies Algebraic Expression tree, Tic-tac-toe game tree
Mapping of Course Outcomes for Unit V CO4, CO5

Unit VI Algebraic Structures and Coding Theory
The structure of algebra, Algebraic Systems, Semi Groups, Monoids, Groups, Homomorphism and Normal Subgroups, and Congruence relations, Rings, Integral Domains and Fields, Coding theory, Polynomial Rings and polynomial Codes, Galois Theory –Field Theory and Group Theory.
#Exemplar/Case Studies Cryptography used in world war II
Mapping of Course Outcomes for Unit VI CO6

Learning Resources

Text Books:
1. C. L. Liu, ―Elements of Discrete Mathematics‖, TMH, ISBN 10:0-07-066913-9.
2. N. Biggs, --“Discrete Mathematics”, 3rd Ed, Oxford University Press, ISBN 0 –19-850717–8.
Reference Books:
1. Bernard Kolman, Robert C. Busby and Sharon Ross, ―Discrete Mathematical Structures‖, Prentice-Hall of India /Pearson, ISBN: 0132078457, 9780132078450.
2. Narsingh Deo, “Graph with application to Engineering and Computer Science”, Prentice Hall of India, 1990, 0 – 87692 – 145 – 4.
3. Eric Gossett, “Discrete Mathematical Structures with Proofs”, Wiley India Ltd, ISBN:978-81-265-2758-8.
4. Sriram P & Steven S., “Computational Discrete Mathematics”, Cambridge University Press, ISBN 13: 978-0-521-73311-3.
5. Kenneth H. Rosen, ―Discrete Mathematics and its Applications‖, Tata McGraw-Hill, ISBN 978-0-07-288008-3

210242: Fundamentals of Data Structures

Credit 03

Unit I Introduction to Algorithm and Data Structures 
Introduction: From Problem to Data Structure (Problem, Logic, Algorithm, and Data Structure).
Data Structures: Data, Information, Knowledge, and Data structure, Abstract Data Types (ADT), Data
Structure Classification (Linear and Non-linear, Static and Dynamic, Persistent and Ephemeral data
structures)
Algorithms: Problem Solving, Introduction to algorithm, Characteristics of algorithm, Algorithm design
tools: Pseudo-code and flowchart
Complexity of algorithm: Space complexity, Time complexity, Asymptotic notation- Big-O, Theta and
Omega, Finding complexity using step count method, Analysis of programming constructs-Linear,
Quadratic, Cubic, Logarithmic.
Algorithmic Strategies- Introduction to algorithm design strategies- Divide and Conquer, and Greedy
strategy.
#Exemplar/Case Studies Multiplication technique by the mathematician Carl Friedrich Gauss and Karatsuba algorithm for fast multiplication.

Mapping of Course Outcomes for Unit I CO3, CO5, CO6

Unit II Linear Data Structure Using Sequential Organization
Concept of Sequential Organization, Overview of Array, Array as an Abstract Data Type, Operations
on Array, Merging of two arrays, Storage Representation and their Address Calculation: Row major
and Column Major, Multidimensional Arrays: Two-dimensional arrays, n-dimensional arrays. Concept
of Ordered List, Single Variable Polynomial: Representation using arrays, Polynomial as array of
structure, Polynomial addition, Polynomial multiplication. Sparse Matrix: Sparse matrix
representation using array, Sparse matrix addition, Transpose of sparse matrix- Simple and Fast
Transpose, Time and Space tradeoff.
#Exemplar/Case Studies Study use of sparse matrix in Social Networks and Maps. Study how Economists use polynomials to model economic growth patterns, how medical researchers use them to describe the behaviour of Covid-19 virus.

Mapping of Course Outcomes for Unit II CO1, CO2, CO3

Unit III Searching and Sorting 
Searching: Search Techniques-Sequential Search/Linear Search, Variant of Sequential Search- Sentinel
Search, Binary Search, Fibonacci Search, and Indexed Sequential Search.
Sorting: Types of Sorting-Internal and External Sorting, General Sort Concepts-Sort Order, Stability,
Efficiency, and Number of Passes, Comparison Based Sorting Methods-Bubble Sort, Insertion Sort,
Selection Sort, Quick Sort, Shell Sort, Non-comparison Based Sorting Methods-Radix Sort, Counting
Sort, and Bucket Sort, Comparison of All Sorting Methods and their complexities.
#Exemplar/Case Studies Use of Fibonacci search in non-uniform access memory storage and in Optimization of Unimodal Functions. Timsort as a hybrid stable sorting algorithm

Mapping of Course Outcomes for Unit III CO1, CO3, CO4

Unit IV Linked List 
Introduction to Static and Dynamic Memory Allocation, Linked List: Introduction, of Linked Lists,
Realization of linked list using dynamic memory management, operations, Linked List as ADT, Types
of Linked List: singly linked, linear and Circular Linked Lists, Doubly Linked List, Doubly Circular Linked
List, Primitive Operations on Linked List-Create, Traverse, Search, Insert, Delete, Sort, Concatenate.
Polynomial Manipulations-Polynomial addition. Generalized Linked List (GLL) concept, Representation
of Polynomial using GLL.
#Exemplar/Case Studies Garbage Collection
Mapping of Course Outcomes for Unit IV CO1, CO2, CO5

Unit V Stack 
Basic concept, stack Abstract Data Type, Representation of Stacks Using Sequential Organization,
stack operations, Multiple Stacks, Applications of Stack- Expression Evaluation and Conversion, Polish
notation and expression conversion, Need for prefix and postfix expressions, Postfix expression
evaluation, Linked Stack and Operations. Recursion- concept, variants of recursion- direct, indirect,
tail and tree, Backtracking algorithmic strategy, use of stack in backtracking.
#Exemplar/Case Studies Android- multiple tasks/multiple activities and back-stack, Tower of Hanoi, 4 Queens problem.

Mapping of Course Outcomes for Unit V CO1, CO2, CO5, CO6

Unit VI Queue
Basic concept, Queue as Abstract Data Type, Representation of Queue using Sequential organization,
Queue Operations, Circular Queue and its advantages, Multi-queues, Linked Queue and Operations.
Deque-Basic concept, types (Input restricted and Output restricted), Priority Queue- Basic concept,
types(Ascending and Descending).
#Exemplar/Case Studies Priority queue in bandwidth management
Mapping of Course Outcomes for Unit VI CO1, CO2, CO5, CO6

Learning Resources

Text Books:
1. Horowitz and Sahani―Fundamentals of Data Structures in C++, University Press, ISBN 10:
0716782928 ISBN 13: 9780716782926.
2. Michael T. Goodrich, Roberto Tamassia, Michael H. Goldwasser, Data Structures and
Algorithms in Python, Wiley Publication, ISBN: 978-1-118-29027-9
Reference Books:
1. Brassard & Bratley ―Fundamentals of Algorithmic Prentice Hall India/Pearson Education, ISBN
13-9788120311312.
2. Allen Downey, Jeffery Elkner, Chris Meyers-How to think like a Computer Scientist: Learning
with Python, Dreamtech Press, ISBN:9789351198147.
3. R. Gillberg, B. Forouzn ―Data Structures: A Pseudo code approach with C, Cenage Learning,
ISBN: 9788131503140.
4. M. Weiss―Data Structures and Algorithm Analysis in C++, 2nd edition, Pearson Education,
2002, ISBN-81-7808-670-0.

210244: Computer Graphics

Credit 03

Unit I Graphics Primitives and Scan Conversion Algorithms 
Introduction, graphics primitives - pixel, resolution, aspect ratio, frame buffer. Display devices,
applications of computergraphics.
Introduction to OpenGL - OpenGL architecture, primitives and attributes, simple modelling and
rendering of two- and three-dimensional geometric objects, GLUT, interaction, events and call-backs
picking.(Simple Interaction with the Mouse and Keyboard)
Scan conversion: Line drawing algorithms: Digital Differential Analyzer (DDA), Bresenham. Circle
drawing algorithms: DDA, Bresenham, and Midpoint.
#Exemplar/Case Studies Study about OpenGL Architecture Review Board (ARB)
Mapping of Course Outcomes for Unit I CO1

Unit II Polygon, Windowing and Clipping 
Polygons: Introduction to polygon, types: convex, concave and complex. Inside test.
Polygon Filling: flood fill, seed fill, scan line fill.
Windowing and clipping: viewing transformations, 2-D clipping: Cohen – Sutherland algorithm line
Clipping algorithm, Sutherland Hodgeman Polygon clipping algorithm,Weiler Atherton Polygon
Clipping algorithm.
#Exemplar/Case Studies
Mapping of Course Outcomes for Unit II CO2

Unit III 2D, 3D Transformations and Projections 
2-D transformations: introduction, homogeneous coordinates, 2-D transformations - Translation,
scaling, rotation and shear, rotation about an arbitrary point.
3-D transformations: introduction, 3-D transformations - Translation, scaling, rotation and shear,
rotation about an arbitrary axis.
Projections : Parallel (Oblique: Cavalier, Cabinet and orthographic: isometric, diametric, trimetric)
and Perspective ( Vanishing Points – 1 point, 2 point and 3 point)
#Exemplar/Case Studies Study use of transformations and projections in education and training softwares.

Mapping of Course Outcomes for Unit III CO3

Unit IV Light, Colour, Shading and Hidden Surfaces 
Colour models: Properties of Light, CIE chromaticity Diagram, RGB, HSV, CMY.
Illumination Models: Ambient Light, Diffuse reflection, Specular Reflection, and the Phong model,
Combined diffuse and Specular reflections with multiple light sources, warn model,
Shading Algorithms: Halftone, Gauraud and Phong Shading.
Hidden Surfaces Introduction, Back face detection and removal, Algorithms: Depth buffer (z), Depth
sorts (Painter), Area subdivision (Warnock)
#Exemplar/Case Studies Study any popular graphics designing software
Mapping of Course Outcomes for Unit IV CO4

Unit V Curves and Fractals 
Curves: Introduction, Interpolation and Approximation, Blending function, B-Spline curve, Bezier
curve,
Fractals: Introduction, Classification, Fractal generation: snowflake, Triadic curve, Hilbert curve,
Applications.
#Exemplar/Case Studies Case study on measuring the length of coastline using fractals
Mapping of Course Outcomes for Unit V CO5

Unit VI Introduction to Animation and Gaming 
Segment: Introduction, Segment table, Segment creation, closing, deleting and renaming, Visibility.
Animation: Introduction, Conventional and computer based animation, Design of animation
sequences, Animation languages, Key- frame, Morphing, Motion specification.
Gaming: Introduction, Gaming platform (NVIDIA, i8060), Advances in Gaming.
#Exemplar/Case Studies Study of any open source tool s. a. Unity/Maya/Blender
Mapping of Course Outcomes for Unit VI CO5

Text Books:
1. S. Harrington-Computer Graphics‖, 2nd Edition, McGraw-Hill Publications, 1987, ISBN 0 – 07 –
100472 – 6.
2. Donald D. Hearn and Baker- Computer Graphics with OpenGL, 4th Edition, ISBN-13:
9780136053583.
1. D. Rogers-Procedural Elements for Computer Graphics, 2nd Edition, Tata McGraw-Hill
Publication, 2001, ISBN 0 – 07 – 047371 – 4.
Reference Books:
1. J. Foley, V. Dam, S. Feiner, J. Hughes, ―Computer Graphics Principles and Practice‖, 2nd
Edition, Pearson Education, 2003, ISBN 81 – 7808 – 038 – 9.
2. D. Rogers, J. Adams, ―Mathematical Elements for Computer Graphics‖, 2nd Edition, Tata
McGrawHill Publication, 2002, ISBN 0 – 07 – 048677 – 8.

210245: Digital Electronics and Logic Design

Credit 03

Unit I Minimization Technique
Logic Design Minimization Technique -: Minimization of Boolean function using K-map(up to 4
variables) and Quine Mc-Clusky Method, Representation of signed number- sign magnitude
representation ,1’s complement and 2’s complement form (red marked can be removed), Sum of
product and Product of sum form, Minimization of SOP and POS using K-map.
#Exemplar/Case Studies Digital locks using logic gates
Mapping of Course Outcomes for Unit I CO1

Unit II Combinational Logic Design
Code converter -: BCD, Excess-3, Gray code, Binary Code. Half- Adder, Full Adder, Half Subtractor, Full
Subtractor, Binary Adder (IC 7483), BCD adder, Look ahead carry generator, Multiplexers (MUX):
MUX (IC 74153, 74151), Cascading multiplexers, Demultiplexers (DEMUX)- Decoder (IC 74138, IC
74154), Implementation of SOP and POS using MUX, DMUX, Comparators (2 bit), Parity generators
and Checker.
#Exemplar/Case Studies Combinational Logic Design of BCD to 7-segment display Controller
Mapping of Course Outcomes for Unit II CO1, CO2

Unit III Sequential Logic Design
Flip-Flop: SR, JK,D,T; Preset &Clear, Master Slave JK Flip Flops, Truth Tables and Excitation tables,
Conversion from one type to another type of Flop Flop. Registers: SISO, SIPO, PISO, PIPO, Shift
Registers, Bidirectional Shift Register, Ring Counter , Universal Shift Register Counters: Asynchronous
Counter, Synchronous Counter, BCD Counter, Johnson Counter, Modulus of the counter ( IC
7490),Synchronous Sequential Circuit Design :Models- Moore and Mealy, State diagram and State
Table ,Design Procedure, Sequence Generator and detector.
#Exemplar/Case Studies Electronic Voting Machine (EVM)
Mapping of Course Outcomes for Unit III CO2,CO3

Unit IV Algorithmic State Machines and Programmable Logic Devices
Algorithmic State Machines: Finite State Machines (FSM) and ASM, ASM charts, notations,
construction of ASM chart and realization for sequential circuits.
PLDS:PLD, ROM as PLD, Programmable Logic Array (PLA), Programmable Array Logic (PAL), Designing
combinational circuits using PLDs.
#Exemplar/Case Studies Wave form generator using MUX controller method
Mapping of Course Outcomes for Unit IV CO2, CO3, CO4

Unit V Logic Families 
Classification of logic families: Unipolar and Bipolar Logic Families, Characteristics of Digital ICs:
Fan-in, Fan-out, Current and voltage parameters, Noise immunity, Propagation Delay, Power
Dissipation, Figure of Merits, Operating Temperature Range, power supply requirements.
Transistor-Transistor Logic: Operation of TTL NAND Gate (Two input ), TTL with active pull up, TTL
with open collector output, Wired AND Connection, Tristate TTL Devices, TTL characteristics.
CMOS: CMOS Inverter, CMOS characteristics, CMOS configurations- Wired Logic, Open drain outputs.
#Exemplar/Case Studies To study the various basic gate design using TTL/CMOS logic family
Mapping of Course Outcomes for Unit V CO3

Unit VI Introduction to Computer Architecture
Introduction to Ideal Microprocessor – Data Bus, Address Bus, Control Bus. Microprocessor based
Systems – Basic Operation, Microprocessor operation, Block Diagram of Microprocessor. Functional
Units of Microprocessor – ALU using IC 74181, Basic Arithmetic operations using ALU IC 74181, 4-bit
Multiplier circuit using ALU and shift registers. Memory Organization and Operations, digital circuit
using decoder and registers for memory operations.
#Exemplar/Case Studies Microprocessor based system in Communication/Instrumentation Control

Mapping of Course Outcomes for Unit VI CO2, CO3, CO6

Learning Resources

Text Books:
1. Modern Digital Electronics by R.P.Jain, 4th Edition, ISBN 978-0-07-06691-16 Tata McGraw Hill
2. Digital Logic and Computer Design by Moris Mano, Pearson , ISBN 978-93-325-4252-5
Reference Books:
1. John Yarbrough, ―Digital Logic applications and Design, Cengage Learning, ISBN – 13: 978-81-
315-0058-3
2. D. Leach, Malvino, Saha, ―Digital Principles and Applications‖, Tata McGraw Hill, ISBN –
13:978-0-07-014170-4.
3. Anil Maini, ―Digital Electronics: Principles and Integrated Circuits‖, Wiley India Ltd, ISBN:978-
81-265-1466-3.
4. Norman B & Bradley, ―Digital Logic Design Principles, Wiley India Ltd, ISBN:978-81-265-1258-