Introduction to Discrete Structure &Linear Algebra (IDSLA)
AL-401-
Unit 1Set Theory, Relation, Function, Theorem Proving Techniques
Definition of sets · Venn diagram · General identities on sets · Definition of relation · Types of relation · Composition of relations · Equivalence relation · Partial ordering relation · Poset · Hasse diagram · Lattice
-
Unit 2Algebraic Structure
Definition and properties of semigroup · Monoid · Group · Abelian group · Properties of groups · Cyclic group · Normal subgroup · Ring · Fields · Standard results for rings and fields · Introduction to recurrence relations · Generating functions
-
Unit 3Propositional Logic and Graph Theory
Proposition · First‑order logic · Basic logical operations · Truth tables · Tautologies and contradictions · Algebra of propositions · Logical implication · Logical equivalence · Predicates · Normal forms · Quantifiers · Graph theory: basic terminology · Types of graphs · Path · Cycles · Shortest path in weighted graphs · Graph colourings
-
Unit 4Matrices and Decompositions
Determinant · Trace · Cholesky decomposition · Eigen decomposition · Singular value decomposition (SVD) · Gradient of a matrix · Useful identities for computing gradient
-
Unit 5Statistical Methods
Test of hypothesis: concept and formulation · Type‑I and Type‑II errors · Time series analysis · Analysis of variance (ANOVA)