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AL-401 · Introduction to Discrete Structure &Linear Algebra/Official Syllabus

Introduction to Discrete Structure &Linear Algebra (AL-401) - Official Syllabus

1
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
  • Lattice
2
Unit 2

Algebraic structure

  • 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
  • Generating Functions
3
Unit 3

Propositional logic and Graph theory

  • 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
4
Unit 4

Matrices

  • Matrices: Determinant and Trace
  • Cholesky Decomposition
  • Eigen decomposition
  • Singular Value decomposition(SVD)
  • Gradient of a matrix:Useful identities For computing Gradient
5
Unit 5

Test of Hypothesis

  • Test of Hypothesis : Concept and Formulation
  • Type-I and Type-II Errors
  • Time Series Analysis
  • Analysis of Variance (ANOVA)

Reference Books

  • Elements of Discrete Mathematics — C.L. Liu — Tata Mc Graw-Hill Edition
  • Discrete Mathematical Structure with Application CS — Trembley, J.P, Manohar — McGraw Hill
  • Discrete Mathematics and its applications — Kenneth H. Rosen — McGraw Hill
  • Discrete Mathematics — Bisht — Oxford University Press
  • Discrete Mathematics & Graph Theory — Biswal — PHI
  • Mathematics For Machine Learning — Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong
  • Statistical Method — S.P. Gupta
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