- Teacher: Divya p FACULTY
Skill Level: Beginner
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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.
INTRODUCING LSRW PATTERNS TO COMMERCA AND MANAGEMENT STUDENTS
UNDERSTANDING THE IMPORTANCE OF BUSINESS DECSIONS