AICTE Model Curriculum — which book covers which course

4 credits (3L : 1T : 0P) · MT — Basic Science / Mathematics · Semester 1

• Calculus — evolutes & involutes, definite & improper integrals, Beta & Gamma functions, surface areas & volumes of revolution, Rolle’s / Mean-Value / Taylor’s & Maclaurin theorems, L’Hospital’s rule, maxima & minima
• Sequences & Series — convergence, power series, Taylor’s series, Fourier series (half-range sine & cosine), Parseval’s theorem
• Multivariable Calculus (differentiation) — limits, continuity & partial derivatives, directional & total derivatives, tangent plane & normal, maxima–minima & saddle points, Lagrange multipliers, gradient, curl & divergence
• Matrices — rank & rank-nullity, systems of linear equations, symmetric / skew-symmetric / orthogonal matrices, determinants, eigenvalues & eigenvectors, diagonalization, Cayley–Hamilton theorem, orthogonal transformation

Engineering Mathematics-I

Covers: The calculus, sequences-&-series and matrices strands in full — Rolle/MVT/Taylor & Maclaurin, Beta & Gamma functions, maxima–minima, power & Fourier series, partial differentiation with Lagrange multipliers, and the complete matrix-algebra module (rank, eigenvalues, diagonalization, Cayley–Hamilton).

Engineering Mathematics-II

Covers: The vector-calculus operators this course lists — gradient, divergence and curl.

4 credits (3L : 1T : 0P) · BS — Basic Science · Semester 2

• Complex Analysis — analytic functions, Cauchy–Riemann equations, harmonic functions, Taylor / Maclaurin / Laurent series, zeros & poles, residue theorems
• Difference Equations & Chaos — recursion & iteration, first- & second-order difference equations, generating functions, logistic equation / logistic map
• Transfer Functions & Dynamical Systems — first- & second-order differential equations, systems of ODEs, Laplace transforms, transfer & impulse functions, frequency response
• Game Theory — strategic games, Nash equilibrium, mixed strategy, auctions

Engineering Mathematics-II

Covers: The complex-analysis module in full (analytic functions, Cauchy–Riemann, Taylor/Laurent series, residues) and the differential-equations foundation the dynamical-systems module builds on.

Engineering Mathematics-III

Covers: Transform calculus — the Laplace-transform machinery used for transfer functions and solving the differential equations in this course.

3 credits (3L : 0T : 0P) · BS — Basic Science

• Probability — probability spaces, conditional probability, Bayes’ theorem, random variables & distribution functions, joint distributions & independence, expectation, Chebyshev’s inequality
• Special Distributions — binomial, hypergeometric, Poisson, exponential, uniform and normal distributions
• Sampling & Limit Theorems — random sampling, sample mean & variance, weak law of large numbers, central limit theorem
• Statistical Inference — parameter estimation, maximum likelihood, confidence intervals, testing of hypotheses, goodness of fit, non-parametric tests, correlation analysis

Probability & Statistics for Data Science

Covers: The whole course — probability theory & Bayes, the theoretical distributions (binomial, Poisson, normal…), correlation & regression, and hypothesis testing — written specifically for the data-science context.

Introduction to Probability & Statistics

Covers: A parallel, example-first path through the same syllabus: basic & continuous probability, bivariate distributions, sampling and applied statistics including small-sample tests.

4 credits (3L : 0T : 2P) · PC — Professional Core

• Statistical foundations — probability & statistics review, statistical measures & tests
• Regression & inference — linear & polynomial regression, hypothesis testing
• Resampling — resampling techniques & bootstrapping
• Computing lab — statistical analysis in R, Python and MATLAB; contemporary statistical packages

Probability & Statistics for Data Science

Covers: The statistical theory this course is built on — measures & tests, linear & polynomial regression, hypothesis testing and the distributions behind resampling.

4 credits (3L : 1T : 0P) · BS — Basic Science · Semester 1

• Linear Algebra — vector spaces, subspaces, basis & dimension, linear transformations & their matrices, linear functionals & adjoints, canonical forms, bilinear & symmetric/skew-symmetric forms
• Calculus — continuity & differentiability of single-variable functions, Rolle’s & Lagrange’s mean-value theorems, double & triple integrals, change of variables
• Vector Calculus — line integrals, Green’s theorem, path independence, surface integrals, Stokes’ theorem, Gauss divergence theorem
• Differential Equations — first-order linear & Bernoulli equations, exact equations & integrating factors, higher-order linear ODEs with constant coefficients
• Multivariate Calculus — definite integrals as limits of sums, area / volume / surface area, improper integrals, functions of several variables, mixed partials, local maxima–minima, Lagrange multipliers

Engineering Mathematics-I

Covers: The calculus, multivariate-calculus and vector-spaces modules — single- & multi-variable calculus, double/triple integrals, functions of several variables with Lagrange multipliers, and vector spaces with linear transformations.

Engineering Mathematics-II

Covers: The differential-equations and vector-calculus modules in full — first-order & higher-order ODEs, exact equations, plus line/surface integrals with Green’s, Stokes’ and the Gauss divergence theorem.

Introduction to Discrete Structure & Linear Algebra

Covers: The linear-algebra module from the AI angle — vector spaces, basis & dimension and linear transformations, the same foundation ML builds on.

4 credits (3L : 1T : 0P) · BS — Basic Science · Semester 2

• Sequences & Series — limits of sequences, monotone & Cauchy sequences, tests for convergence & divergence, integral test, alternating series & Leibnitz test
• Functional Series — pointwise & uniform convergence, power series, Fourier series
• Mathematical Foundations — statements & quantifiers, operations on sets & functions, relations, proofs
• Number System — countability, transcendental numbers & Liouville’s number, construction of the reals via Cauchy sequences, Fermat’s little theorem & Miller–Rabin primality, Wilson’s & primitive-root theorems
• Probability — sample spaces & events, conditional probability, random variables & distribution functions, moments, Chebyshev inequality, special distributions, law of large numbers

Engineering Mathematics-I

Covers: The sequences-&-series and functional-series modules — convergence tests, power series and Fourier series.

Introduction to Discrete Structure & Linear Algebra

Covers: The mathematical-foundations module — sets, relations, functions and proof technique.

Introduction to Probability & Statistics

Covers: The probability module — sample spaces, random variables, moments and the special distributions with the law of large numbers.

3 credits (3L : 1T : 0P) · PC — Professional Core

• Mathematical Reasoning — propositions, negation/conjunction/disjunction, implication & equivalence, truth tables, predicates & quantifiers, rules of inference, methods of proof, resolution principle
• Set Theory — inductive definition & proof by induction, Peano postulates, relations & their properties, equivalence relations & partitions, partial orderings & posets
• Combinatorics & Functions — elementary combinatorics & counting, recurrence relations, generating functions, injections/surjections & composition, pigeonhole principle
• Graph Theory — Euler & Hamiltonian graphs, trees & tree traversals, spanning trees, representation of relations by graphs
• Algebraic Structures & Discrete Probability — groups, semigroups & monoids, rings, fields, vector spaces & lattices, discrete random variables

Discrete Structure

Covers: The complete course, module for module — set theory, algebraic structures, logic, graph theory and combinatorics & lattices. The closest single-book match to this syllabus.

Introduction to Discrete Structure & Linear Algebra

Covers: The same discrete-structures core from an AI perspective — set theory & relations, algebraic structures, and logic & graph theory.