BPSC Mathematics Syllabus 2026: Section-wise Topics

Topics

Syllabus

Linear Algebra

Vector spaces, subspaces, basis and dimension, linear dependence and independence, linear transformations, rank and nullity, matrices, determinants, eigenvalues, eigenvectors, Cayley-Hamilton theorem, canonical forms, quadratic forms, Hermitian and skew-Hermitian matrices, orthogonal transformations, and simultaneous reduction of quadratic forms.

Calculus

Real number system, limits, continuity, differentiability, Mean Value Theorems, Taylor's theorem, maxima and minima, curve tracing, asymptotes, functions of several variables, partial differentiation, Jacobians, multiple integrals, Beta and Gamma functions, areas, volumes, and centre of gravity.

Analytical Geometry of Two and Three Dimensions

Straight lines, planes, Cartesian and polar coordinates, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid, curves in space, curvature, torsion, envelopes, evolutes, and Frenet's formula.

Differential Equations

Ordinary differential equations of first and higher order, exact and linear differential equations, equations with constant coefficients, complementary function, particular integral, simultaneous differential equations, and methods of solving differential equations.

Vector Analysis, Tensor Analysis, Statics, Dynamics and Hydrostatics

Vector algebra, scalar and vector products, gradient, divergence, curl, line and surface integrals, tensors, equilibrium of particles, virtual work, motion under gravity, simple harmonic motion, projectile motion, central orbits, Kepler's laws, work and energy, hydrostatic pressure, equilibrium of fluids, buoyancy, floating bodies, and pressure on submerged surfaces.

Topics

Syllabus

Abstract Algebra

Groups, subgroups, cyclic groups, permutation groups, homomorphism and isomorphism of groups, quotient groups, normal subgroups, Cayley's theorem, Sylow theorems, rings, ideals, integral domains, principal ideal domains, unique factorisation domains, Euclidean domains, polynomial rings, field extensions, finite fields, and related algebraic concepts.

Real Analysis

Metric spaces, open and closed sets, compactness, connectedness, sequences and series, convergence, continuity, uniform continuity, differentiation, Riemann integration, improper integrals, functions of several variables, infinite series, and convergence tests.

Complex Analysis

Complex functions, analytic functions, Cauchy's theorem, Cauchy's integral formula, Taylor and Laurent series, singularities, residues, contour integration, conformal mapping, and applications of the residue theorem.

Partial Differential Equations

Formation of partial differential equations, complete, singular and general integrals, first-order partial differential equations, Charpit's method, linear partial differential equations with constant coefficients, and standard solution methods.

Mechanics

Generalised coordinates, constraints, virtual work, D'Alembert's principle, Lagrange's equations of motion, Hamilton's equations, moment of inertia, motion of rigid bodies, and oscillatory motion.

Hydrodynamics

Equation of continuity, equation of motion, streamlines, velocity potential, stream function, irrotational motion, two-dimensional flow, sources and sinks, circulation, and fluid motion.

Numerical Analysis

Numerical solutions of algebraic and transcendental equations, interpolation, finite differences, numerical differentiation, numerical integration, spline interpolation, Euler's method, Runge-Kutta methods, predictor-corrector methods, and numerical solutions of ordinary differential equations.

Probability and Statistics

Probability theory, random variables, probability distributions, mathematical expectation, variance, sampling distributions, correlation, regression, estimation, hypothesis testing, Chi-square test, Student's t-test, F-test, analysis of variance, and statistical inference.

Operational Research

Linear programming, simplex method, duality, transportation and assignment problems, game theory, inventory models, queueing theory, replacement models, dynamic programming, network analysis, sequencing, and decision-making techniques.