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, Well
ordered 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.
- Teacher: Divya p FACULTY