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Set Theory, Relation & Function
Set theory, Venn diagrams, set identities, relations, composition of relations, equivalence relations, partial ordering, POSET, Hasse diagrams and lattices.
Complete unit-wise study material for AL401 Introduction to Discrete Structure & Linear Algebra for RGPV Artificial Intelligence and Machine Learning IV Semester students.
Study all five units covering set theory, algebraic structures, propositional logic, graph theory, matrices, linear algebra and statistical hypothesis testing.
Set theory, Venn diagrams, set identities, relations, composition of relations, equivalence relations, partial ordering, POSET, Hasse diagrams and lattices.
Semigroup, monoid, groups, Abelian groups, group properties, cyclic groups, normal subgroups, rings, fields, recurrence relations and generating functions.
Propositions, first-order logic, truth tables, tautologies, contradictions, predicates, normal forms, quantifiers, graphs, paths, cycles, shortest paths and graph coloring.
Determinant, trace, Cholesky decomposition, eigen decomposition, Singular Value Decomposition (SVD), matrix gradients and useful identities for gradient computation.
Concept and formulation of hypothesis tests, Type-I and Type-II errors, time series analysis and Analysis of Variance (ANOVA).
Complete unit-wise syllabus for RGPV Artificial Intelligence and Machine Learning IV Semester.
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.
Definition, Properties and 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.
Propositional logic: Proposition, First order Logic, Basic logical operation, Truth tables, Tautologies and Contradiction, algebra of proposition, logical implication, logical equivalence, predicates, Normal Forms and Quantifiers.
Graph theory: Introduction and basic terminology of graph, types of graph, Path, Cycles, Shortest path in weighted graph and graph colorings.
Determinant and Trace, Cholesky Decomposition, Eigen decomposition, Singular Value decomposition (SVD), Gradient of a matrix and useful identities for computing Gradient.
Concept and Formulation, Type-I and Type-II Errors, Time Series Analysis and Analysis of Variance (ANOVA).
AL401 Introduction to Discrete Structure & Linear Algebra provides students with mathematical foundations used in computer science, artificial intelligence and machine learning.
Students can access all five units of AL401 in one place and prepare according to the RGPV syllabus using unit-wise handwritten notes.
Select any unit and start your Discrete Structure & Linear Algebra preparation.
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