TG SET Syllabus PDF Download

The Mathematical Sciences syllabus summary for TG SET 2025 follows the CSIR NET pattern, ensuring that candidates are tested across both theoretical and applied mathematics concepts. Below is the detailed structure of the TG SET Mathematical Sciences syllabus, divided into key units:

Unit 1: Analysis and Linear Algebra
Elementary set theory, finite, countable, and uncountable sets, and the real number system as a complete ordered field.
Sequences, series, convergence tests, Bolzano-Weierstrass theorem, and Heine-Borel theorem.
Continuity, differentiability, and uniform convergence of functions.
Riemann sums, improper integrals, functions of bounded variation, and Lebesgue integral.
Vector spaces, basis, dimension, linear transformations, rank and determinant of matrices, and eigenvalues.
Unit 2: Complex Analysis and Algebra
Algebra of complex numbers, power series, Cauchy-Riemann equations, and contour integration.
Cauchy’s theorem, Laurent series, calculus of residues, and conformal mappings.
Group theory, subgroups, homomorphisms, cyclic groups, and quotient groups.
Rings, ideals, fields, and Galois theory.
Unit 3: Differential Equations, Numerical Analysis, and Mechanics
Existence and uniqueness of solutions to ODEs, Sturm-Liouville problems, and boundary value problems.
Lagrange and Charpit’s methods, Laplace and Wave equations, and separation of variables.
Newton-Raphson method, finite differences, interpolation, and Runge-Kutta methods.
Euler-Lagrange equations and Hamiltonian mechanics.
Unit 4: Probability, Statistics, and Optimization
Random variables, probability distributions, expectation, and moments.
Laws of large numbers and Central Limit Theorem.
Hypothesis testing, estimation, ANOVA, and regression analysis.
Linear programming, simplex method, and Markov chains.
This syllabus ensures that candidates are well-versed in the fundamental and advanced branches of mathematics, preparing them for both academic and analytical challenges in their careers.