MTMDSC101T: Algebra (Credits: 5, Marks: 100)

• Classical Algebra: De-Moivre's theorem, nth roots of unity, exponential and trigonometrical functions, logarithm of complex numbers; Polynomial equations, relation between roots and coefficients, transformation of equations, Cardan's solution of cubic, Ferrari's method for biquadratic; AM ≥ GM ≥ HM inequality
• Number Theory: Equivalence relations, functions, permutations; Well-ordering principle, mathematical induction, division algorithm, GCD, Euclid's lemma, Fundamental Theorem of Arithmetic, congruences, Euler φ function, Euler's theorem, Fermat's theorem
• Matrix Theory: Algebra of matrices, symmetric, skew-symmetric, Hermitian, unitary matrices; Determinants, inverse of matrix, Cramer's rule; Elementary row/column operations, rank of matrix, system of linear equations; Eigenvalues, eigenvectors, Cayley-Hamilton theorem

MTMMIN101T / MTMCOR101T: Algebra (Minor) (Credits: 5, Marks: 100)

• Classical Algebra, Abstract Algebra (groups, subgroups, Lagrange's theorem, rings, integral domains, fields), Linear Algebra (vector spaces, linear transformations, rank, eigenvalues, Cayley-Hamilton theorem)

MTMDSC202T: Calculus (Credits: 5, Marks: 100)

• Limits, Continuity and Differentiability: ε-δ definition, types of discontinuities, successive differentiation, Leibnitz theorem, partial differentiation, Euler's theorem
• Mean Value Theorems: Rolle's theorem, Lagrange's MVT, Cauchy's MVT, Taylor's theorem, Maclaurin's series, indeterminate forms
• Integral Calculus: Integration of rational and irrational functions, reduction formulae, improper integrals, Beta and Gamma functions
• Applications: Tangent and normal, curvature, asymptotes, maxima/minima, tracing of curves, length of plane curves, volume and surface area of solids of revolution

MTMMIN202T / MTMCOR202T: Calculus (Minor) (Credits: 5, Marks: 100)

• Limits, continuity, differentiability, mean value theorems, integral calculus, Beta and Gamma functions, applications of calculus

MTMDSC303T: Analytical Geometry and Vector Analysis (Credits: 5, Marks: 100)

• Analytical Geometry: Translation and rotation of axes, conics, polar equations, tangent and normal; Equations of planes, straight lines in 3D, shortest distance between skew lines; Spheres, cylinders, conicoids, paraboloids, ellipsoid, hyperboloids
• Vector Analysis: Scalar and vector triple products, vector functions, gradient, divergence and curl, line integrals, surface integrals, volume integrals; Green's theorem, Stokes' theorem, Gauss' theorem

MTMMIN303T / MTMCOR303T: Differential Equations (Minor) (Credits: 5, Marks: 100)

• First order ODEs (exact equations, integrating factors), linear ODEs with constant coefficients, method of variation of parameters; First order PDEs (Lagrange's method, Charpit's method), classification of second order PDEs

MTMDSC404T: Ordinary Differential Equations-I and Mechanics-I (Credits: 5, Marks: 100)

• ODE-I: First order equations, exact equations, integrating factors, Picard's existence theorem; Linear ODEs with constant coefficients, method of undetermined coefficients; Plane autonomous systems, critical points, stability, Lotka-Volterra system
• Mechanics-I: Coplanar forces, friction, center of gravity, virtual work; Particle kinematics, conservation laws; Motion in straight line, SHM, projectile motion, central orbits, inverse square law

MTMDSC405T: Real Analysis-I (Credits: 5, Marks: 100)

• Properties of real numbers, countable sets, supremum and infimum, Archimedean property; Open/closed sets, Bolzano-Weierstrass theorem, Heine-Borel theorem; Sequences, convergence, Cauchy sequences; Infinite series, convergence tests (comparison, ratio, root, integral tests); Limits and continuity of functions; Differentiability, Darboux theorem; Monotone functions, functions of bounded variation

MTMDSC406T: Group Theory-I and Number Theory (Credits: 5, Marks: 100)

• Group Theory-I: Groups, subgroups, cyclic groups, permutation groups, cosets, Lagrange's theorem, normal subgroups, quotient groups, homomorphisms, isomorphism theorems
• Number Theory: Division algorithm, Euclidean algorithm, fundamental theorem of arithmetic, linear Diophantine equations; Congruences, Chinese remainder theorem, Fermat's theorem, Wilson's theorem; Number theoretic functions (φ, μ, σ, τ), Möbius inversion; Primitive roots, quadratic residues, Legendre symbol, quadratic reciprocity

MTMDSC407T: Partial Differential Equations & Integral Transforms (Credits: 5, Marks: 100)

• PDEs: Derivation of PDEs, first order PDEs (Lagrange's method, Charpit's method), higher order PDEs with constant coefficients, classification of second order PDEs; Wave equation, Laplace equation, heat equation, separation of variables
• Integral Transforms: Fourier transform, Fourier cosine/sine transforms, convolution theorem; Laplace transform, properties, inverse Laplace transform, applications to ODEs and PDEs; Hankel transform

MTMDSC508T: Real Analysis-II (Credits: 5, Marks: 100)

• Riemann integration, Darboux theorem, integrability of monotone and continuous functions; Pointwise and uniform convergence of sequences of functions, theorems on continuity, derivability and integrability; Fourier series, Bessel's inequality, Parseval's identity; Power series, radius of convergence, Abel's theorem, Weierstrass approximation theorem

MTMDSC509T: Ring Theory and Linear Algebra-I (Credits: 5, Marks: 100)

• Ring Theory: Rings, integral domains, fields, subrings, ideals, factor rings, ring homomorphisms, isomorphism theorems; Maximal and prime ideals; Divisibility in integral domains, UFD, Euclidean domain; Polynomial rings, Eisenstein's irreducibility criterion
• Linear Algebra-I: Vector spaces, subspaces, linear independence, basis, dimension; Inner product spaces, orthogonality, Gram-Schmidt process; Linear transformations, rank-nullity theorem; Linear functionals, dual spaces; Eigenvalues, eigenvectors, Cayley-Hamilton theorem

MTMDSC510M: Numerical Analysis (Theory & Practical) (Credits: 5, Marks: 100)

• Representation of numbers, errors; Root finding: Bisection, Regula-falsi, Newton-Raphson methods; System of linear equations: Gaussian elimination, LU decomposition, Gauss-Jacobi, Gauss-Seidel; Interpolation: Newton's forward/backward, Lagrange's interpolation; Numerical integration: Trapezoidal rule, Simpson's 1/3 rule; Numerical solution of ODEs: Euler's method, Runge-Kutta methods; PDEs: Heat equation by FTCS and Crank-Nicolson methods

MTMDSC511T: Multivariate Calculus and Metric Spaces (Credits: 5, Marks: 100)

• Multivariate Calculus: Functions of several variables, partial differentiation, total differentiability, chain rule, directional derivatives, gradient, extrema, Lagrange multipliers; Double and triple integrals, change of variables; Vector fields, divergence, curl, line integrals, Green's theorem, Stokes' theorem, divergence theorem
• Metric Spaces: Definition and examples, open/closed sets, sequences, Cauchy sequences, completeness; Continuous mappings, uniform continuity; Connectedness, compactness, Heine-Borel property; Contraction mappings, Banach fixed point theorem

MTMDSC612T: Operations Research and Game Theory (Credits: 5, Marks: 100)

• Linear Programming Problem, simplex method, two-phase method, duality; Transportation problem, assignment problem, Hungarian method; Game theory, two-person zero-sum games, graphical method, dominance method

MTMDSC613T: Group Theory-II and Ordinary Differential Equations-II (Credits: 5, Marks: 100)

• Group Theory-II: Direct products, fundamental theorem of finite abelian groups; Group actions, orbit-stabilizer theorem, class equation, Sylow theorems; Composition series, solvable groups
• ODE-II: Power series solutions, ordinary points, regular singular points, Frobenius method; Special functions: Legendre polynomials, Bessel functions; Sturm-Liouville problems, eigenvalues and eigenfunctions, Green's function

MTMDSC614T: Probability & Statistics (Credits: 5, Marks: 100)

• Axiomatic probability, conditional probability, Bayes' theorem; Random variables, distribution functions, expectation, moments; Discrete distributions (Binomial, Poisson), continuous distributions (Normal, Exponential); Joint distributions, correlation, regression; Laws of large numbers, central limit theorem; Sampling distributions, estimation, hypothesis testing, confidence intervals, chi-square test

MTMDSC615T: Complex Analysis (Credits: 5, Marks: 100)

• Complex numbers, Riemann sphere; Analytic functions, Cauchy-Riemann equations, harmonic functions; Complex integration, Cauchy-Goursat theorem, Cauchy's integral formula; Power series, Taylor and Laurent series, singularities; Calculus of residues, Cauchy's residue theorem, evaluation of real integrals; Conformal mappings, Möbius transformations

MTMDSC716T: Topology (Credits: 5, Marks: 100)

• Topological spaces, bases, open/closed sets, closure, interior; Continuous maps, homeomorphisms; Countability axioms, separation axioms (T0-T4), Urysohn's lemma; Connectedness, compactness, product topology

MTMDSC717T: Field Extension & Linear Algebra-II (Credits: 5, Marks: 100)

• Field Extension: Extension fields, algebraic elements, splitting fields, algebraic closure; Finite fields, classification of finite fields; Galois theory (fundamental theorem), solvability by radicals
• Linear Algebra-II: Minimal polynomial, diagonalization, Jordan canonical form; Adjoint of linear operator, normal and self-adjoint operators, spectral theorem; Bilinear forms, quadratic forms, Sylvester's law of inertia

MTMDSC818T: Functional Analysis (Credits: 5, Marks: 100)

• Review of metric spaces, Baire category theorem; Normed linear spaces, Banach spaces; Bounded linear operators, Hahn-Banach theorem; Dual spaces, reflexivity, weak convergence; Uniform boundedness principle, open mapping theorem, closed graph theorem; Inner product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem

MTMDSC819T: Mechanics-II (Credits: 5, Marks: 100)

• System of particles, rigid body dynamics, Euler angles, inertia tensor; Constraints, generalized coordinates, Lagrange's equations; Hamiltonian mechanics, Hamilton's equations; Small oscillations, normal modes; Hamilton's principle, canonical transformations, Hamilton-Jacobi theory

MTMDSC820T: Discrete Mathematics & Differential Geometry (Credits: 5, Marks: 100)

• Discrete Mathematics: Boolean algebra, logic gates, switching circuits; Graph theory, Eulerian and Hamiltonian graphs, trees, spanning trees, matrix representation of graphs
• Differential Geometry: Curves in plane and space, curvature, torsion, Frenet formulae; Surfaces in R³, first and second fundamental forms, Gaussian curvature, geodesics

MTMDSC821M: Data Science (Credits: 5, Marks: 100)

• Python programming review; Statistics for data science, correlation, regression; Binary logistic regression; Clustering and classification (K-means, hierarchical clustering); Big data concepts, missing value imputation; Hands-on practical with Python for EDA, data visualization, and machine learning algorithms

• Sem I: MTMMIN101T / MTMCOR101T - Algebra
• Sem II: MTMMIN202T / MTMCOR202T - Calculus
• Sem III: MTMMIN303T / MTMCOR303T - Differential Equations
• Sem IV: MTMCOR404T - Probability Theory & Mechanics
• Sem V: MTMCOR505T - Linear Programming Problem & Game Theory
• Sem VI: MTMCOR606T - Numerical Methods and Integral Transforms
• Sem VII: MTMSMC701T - Discrete Mathematics

MTMHMD101T / 201T / 301T / MTMGMD401T / 501T / 601T: Basic Mathematics (Credits: 3, Marks: 50)

• Sets, relations, functions; Probability and statistics (mean, median, mode, variance); Matrix and determinants, inverse of matrix, rank, solution of linear equations; Coordinate geometry (2D) - straight lines, circles, parabola, ellipse, hyperbola; Linear Programming Problem - graphical solution

C-Programming Language (Credits: 3, Marks: 50)

• Basics of programming, data types, operators, control statements, arrays, functions, pointers, matrix operations

Programming Language-Python (Credits: 3, Marks: 50)

• Python basics, variables, conditionals, loops, functions, strings, lists, tuples, dictionaries, files, modules; Practical examples including solving equations, matrix operations, plotting functions

MTMRES801T/M: Research Project/Dissertation (Credits: 15, Marks: 300)

Research Project/Dissertation as per UG Regulation