Introduction to Discrete Structure & Linear Algebra
The complete RGPV syllabus for Introduction to Discrete Structure & Linear Algebra (AL401 / CD401), the fourth-semester mathematics course for B.Tech CSE — Artificial Intelligence & Machine Learning and Data Science, under the AICTE Flexible Curricula. Five units spanning set theory and algebraic structures, propositional logic and graph theory, and the linear-algebra tools (eigen decomposition, SVD) that underpin machine learning.
Introduction to Discrete Structure & Linear Algebra
by Dr. D.C. Agarwal & Dr. Pradeep K. Joshi · ₹400 — covers this full RGPV syllabus.
Course contents — unit by unit
Unit 1 · Set Theory, Relations, Functions & Theorem-Proving Techniques
Set theory — definition of sets, Venn diagrams, proofs of general identities on sets. Relations — definition, types, composition, equivalence relation, partial-ordering relation, POSET, Hasse diagram and lattice.
Unit 2 · Algebraic Structures
Definition, properties and types — semigroup, monoid, groups, abelian group, properties of groups, cyclic group, normal subgroup; rings and fields (definition and standard results). Introduction to recurrence relations and generating functions.
Unit 3 · Propositional Logic & Graph Theory
Propositional logic — proposition, first-order logic, basic logical operations, truth tables, tautologies and contradiction, algebra of propositions, logical implication and equivalence, predicates, normal forms, quantifiers. Graph theory — basic terminology, types of graphs, paths, cycles, shortest path in weighted graphs, graph colouring.
Unit 4 · Matrices & Linear Algebra
Determinant and trace, Cholesky decomposition, eigen decomposition, Singular Value Decomposition (SVD), gradient of a matrix and useful identities for computing gradients.
Unit 5 · Test of Hypothesis
Concept and formulation, Type-I and Type-II errors, time-series analysis, Analysis of Variance (ANOVA).