Minor Semester III Academic Level 200-299 Credit :4 TOTAL mark: 100 External (70) + Internal (30) Per week Total Hours: 4 Course Summary This course comprises four main modules: Lattice, Boolean Algebra, System of Equations, and Eigenvalue and Eigenvectors. Module I introduce concepts like ordered sets and lattices, while Module II explores Boolean Algebra and its applications. Module III covers linear systems of equations, including Gauss elimination and determinants. Finally, Module IV delves into Eigenvalue and Eigenvectors, offering insights into matrix properties and applications. Course Outcome CO1: Analyse Lattices and Boolean Algebra . CO2: Apply Matrix Operations and Linear Systems . CO3: Investigate Eigenvalue and Eigenvector Problems. Textbook 1. Theory and Problems of Discrete mathematics (3/e), Seymour Lipschutz, Marc Lipson, Schaum's Outline Series. 2. Advanced Engineering Mathematics (10/e), Erwin Kreyzsig, Wiley India. MODULE I Lattice (Text 1) 1 14.2 Ordered set 2 14.3 Hasse diagrams of partially ordered sets 3 14.5 Supremum and Infimum 4 14.8 Lattices 5 14.9 Bounded lattices, 14.10 Distributive lattices 6 14.11 Complements, Complemented lattices MODULEII Boolean Algebra (Text 1) 7 15.2 Basic definitions 8 15.3 Duality 9 15.4 Basic theorems 10 15.5 Boolean algebra as lattices 11 15.8 Sum and Product form for Boolean algebras 12 15.8 Sum and Product form for Boolean algebras Complete Sum and Product forms MODULE lII System of Equations (Text 2) 13 7.1 Matrices, Vectors: Addition and Scalar Multiplication 14 7.2 Matrix Multiplication (Example 13 is optional) 15 7.3 Linear System of Equations- Gauss Elimination 16 7.4 Linear Independence- Rank of a matrix- Vector Space (Proof Theorem 3 is optional) 17 7.5 Solutions of Linear Systems- Existence, Uniqueness (Proof of Theorem 1, Theorem 2 and Theorem 4 are optional) MODULE IV Eigen Value and Eigen Vectors (Text 2) 18 7.6 Second and Third Order Determinants- up to and including Example 1 19 7.6 Second and Third Order Determinants- Third order determinants 20 7.7 Determinants- Theorem 2, Theorem 3 and Theorem 4 are optional) 21 7.8 Inverse of a Matrix- Gauss- Jordan Elimination (Proof Theorem 1, Theorem 2, Theorem 3 and Theorem 4 are optional) 22 8.1 The Matrix Eigenvalue Problem- Determining Eigenvalues and Eigenvectors (Proof of Theorem 1 and Theorem 2 are optional) V Open Ended Module Relation on a set, Equivalence relation and partition, Isomorphic ordered sets, Wellordered sets, Representation theorem of Boolean algebra, Logic gates, Symmetric, Skew-symmetric and Orthogonal matrices, Linear Transformation. References: 1. Howard Anton & Chris Rorres, Elementary Linear Algebra: Application (11/e) : Wiley 2. Ron Larson,Edwards, David C Falvo : Elementary Linear Algebra (6/e), Houghton Mi_in Harcourt Publishing Company (2009) 3. Thomas Koshy - Discrete Mathematics with Applications-Academic Press (2003) 4. George Gratzer, Lattice theory: First concepts and distributive lattices. Courier Corporation (2009) Note: 1) Optional topics are exempted for end semester examination. 2) Proofs of all the results are also exempted for the end semester exam.
Students are introduced to the concepts, procedures, and resources of software project management in this course. Project scheduling, budgeting, quality assurance, risk management, and teamwork are among the subjects covered. The goal of the course is to equip students with the skills necessary for efficient project management in software development settings.
MODULES 1) FUNDAMENTALS OF TESTING. 2) DISTRIBUTION THEORY. 3) TESTS OF HYPOTHESIS. 4) ANALYSIS OF VARIANCE. 5) PRACTICUM.
The objectives of this course are to make the student understand programming language, programming, concepts of Loops, reading a set of Data, stepwise refinement, Functions, Control structure, Arrays, Structures, Unions, and Pointers. After completion of this course the student is expected to analyze the real life problem and write a program in ‘C’ language to solve the problem. The main emphasis of the course will be on problem solving aspect i.e. developing proper algorithms.
Course Number: 20Contact Hours per Week: 4TNumber of Credits: 4Number of Contact Hours: 64 Hrs.Course Evaluation: Internal – 20 Marks + External – 80 Marks Objective • To understand internals of Microprocessor.• To learn architecture of 8085 Microprocessor• To learn instruction set of 8085 Microprocessor• To learn how to program a Microprocessor Prerequisites • Basic knowledge of Computer
Objective • To learn the basics of Computer Graphics. Prerequisites • Basic knowledge in Mathematics and Computer fundamentals.
BCS4B05 – Database Management System and RDBMS Contact Hours per Week: 7 (3T + 4L) Number of Credits: 3 Number of Contact Hours: 112 Hrs. Course Evaluation: Internal – 15 Marks + External – 60 Marks Objective• To learn the basic principles of database and database design• To learn the basics of RDBMS• To learn the concepts of database manipulation SQL• To study PL/SQL language By the end of the course, students will be able to: Understand Database Concepts: Grasp the fundamental principles of databases, including their structure, function, and importance in modern applications. Design Databases: Develop and design a well-structured database using principles of database design and normalization. Implement RDBMS: Demonstrate a solid understanding of Relational Database Management Systems (RDBMS) and how they are used to manage data efficiently. Manipulate Data with SQL: Apply SQL for database manipulation, including querying, updating, and managing databases. Employ PL/SQL: Utilize PL/SQL to create and manage complex database applications with stored procedures, functions, and triggers. Analyze and Optimize Queries: Analyze query performance and optimize SQL queries for better efficiency. Secure Databases: Understand and implement basic database security measures to protect data from unauthorized access and breaches. Troubleshoot Database Issues: Identify, analyze, and resolve common database-related issues. Collaborate on Database Projects: Work effectively in teams to design, implement, and manage databases as part of larger software development projects.
Credit:4 Lectureper week:3 Practicalper week:2 Course Outcomes (CO): CO1 Differentiate basic data structures (arrays, linked lists, stacks, queues) based on their characteristics,operations, and real-world applications. CO2 Perform basic operations (e.g., )insertion, deletion, search) on fundamental data structures using a chosen programming language. CO3 Identify the properties and applications of advanced data structures (trees,graphs). CO4 investigate the properties of various searching and sorting Techniques CO5 Demonstrate critical thinking and problem-solving skills by applying data structures and algorithms to address complex computational challenges. CO6 Implement and analyse different data structure algorithms(to solve practical problems Detailed Syllabus:ModuleUnit Content Hrs(45+30)Marks(70)I Introduction to Data Structures and Basic Algorithms 1 Overview of Data Structures: Data type Vs. Data structure, ADT,Definition of Data structure, Data structure Classification – Linear, Non- Linear (Array, Linked List, Stack, Queue, Tree, Graph) Introduction to Arrays: Definition, Types (1 Dimensional, 2Dimensional, Multi-Dimensional, Sparse matrix), Different Array Operations with Algorithm (insertion, deletion, traversal Structures and Self-referential structures Introduction to Linked list: Definition, Types (Single linked list,Doublelinked list, Circular linked list- concept only). Singly Linked List Operations with Algorithm (insertion, deletion,traversal) 2 Introduction to Stack: Definition, stack operations with Algorithm, Applications: recursion, infix to postfix - example and Algorithm Implementation of Stack: using array (overflow & underflow) and Linkedlist (with algorithm) Introduction to Queue: Definition, queue operations with Algorithm, Types: Double ended queue (Input Restricted and Output restricted), Circular queue, Applications Implementation of Queue: using array and Linked list (withalgorithm)I 3 Non- Linear Data Structures Introduction to Trees: Basic terminology, Types(Binary tree- complete,full, skewed etc., Expression Tree) Properties of Binary tree, Applications. Binary tree representations- using array and linked list 2 Operations on Binary tree- Insertion, Deletion, Traversal- inorder, preorder, postorder - (concepts with examples) Algorithm of non-recursive Binary tree traversal Introduction to Graph: Definition, Basic terminology, Types (Directed,Undirected, Weighted). Graph representation –Adjacency list and Adjacency Matrix, Applications. 4 Sorting and Searching : Introduction to Sorting: Definition, Classification (Internal, External) Internal Sorting Algorithms: Selection sort- Selection sort algorithm, Exchange sort- Bubble sort algorithm External Sorting Algorithms: Merge sort- Demonstrate with example.(NoAlgorithm needed) Advanced sorting Algorithm-: Quick sort- Demonstrate with example. Introduction to Searching: Linear search and Binary search(Algorithm needed) with example. Hashing: Hash Tables, Hash Functions, Different Hash Functions –Division method, Multiplication method, Mid square method, Folding Method, Collision and Collision resolution Techniques: Open hashing- Chaining, Closed hashing- Probing5 5 Hands-on Programming in Data Structures: Practical Implement the following: 1. Basic Operations in a single linked list (Menu driven) 2. Sort the elements in given singly linked list 3. Stack using array. 4. Stack using Linked list 5. Queue using Array 6. Queue using Linked list 7. Sorting algorithms- Selection, Bubble Sort 8. Searching Algorithms- Linear and Binary search
