Syllabus - Introduction to Discrete Structure &Linear Algebra (AL401)

CSE-Artificial Intelligence and Machine Learning/ Artificial Intelligence and Machine Learning

Introduction to Discrete Structure &Linear Algebra (AL401)

IV-Semester

Unit 1

Set Theory, Relation, Function, Theorem Proving Techniques

Set theory: definition of sets, Venn Diagram, proofs of some general identities on set,Relation: Definition, Types of relation ,Composition of relation ,Equivalence relation, Partial ordering relation,POSET,Hasse diagram and Lattice .

Unit 2

Algebraic structure

Definition, Properties, types: Semi Group, Monoid, Groups, Abelian Group, Properties of group, cyclic group, Normal subgroup, Ring and Fields: definition and standard result, Introduction to Recurrence Relation and Generating Functions.

Unit 3

Propositional logic

Proposition, First order Logic, Basic logical operation, Truth tables, Tautologies and Contradiction, algebra of proposition, logical implication, logical equivalence ,predicates, Normal Forms, Quantifiers

Graph theory

Introduction and basic terminology of graph, types of graph, Path, Cycles, Shortest path in weighted graph, graph colorings.

Unit 4

Matrices

Determinant and Trace,Cholesky Decomposition, Eigen decomposition,Singular Value decomposition(SVD),Gradient of a matrix:Useful identities For computing Gradient.

Unit 5

Test of Hypothesis

Concept and Formulation ,Type-I and Type-II Errors,Time Series Analysis ,Analysis of Variance (ANOVA).

Practicals

Reference Books

  • C.L.Liu, “Elements of Discrete Mathematics” Tata Mc Graw-Hill Edition.

  • Trembley, J.P & Manohar; “Discrete Mathematical Structure with Application CS”, McGraw Hill.

  • Kenneth H. Rosen, “Discrete Mathematics and its applications”, McGraw Hill.

  • Bisht, “Discrete Mathematics”,Oxford University Press

  • Biswal,”Discrete Mathematics & Graph Theory”, PHI

  • Mathematics For Machine Learning-Marc Peter Deisenroth,A. Aldo Faisal,Cheng soon ong

  • Statistical Method- S.P. Gupta