RSSB Teaching Associate Mathematics syllabus

1Differential and Integral Calculus

• Partial Differentiation, Euler’s Theorem for homogeneous functions, Total Differentiation, Maxima and Minima of two and three variables, Lagrange’s Multipliers Method, Curvature, Asymptotes, Envelopes and Evolutes, Singular Points. Rectification, Multiple Integral, volume and surface of revolution of curves. Beta and Gamma functions.

2Two Dimensional Coordinate Geometry (Cartesian and Polar coordinates)

• Polar equation of conics. Polar equation of tangent, normal, asymptotes and chord of contact. Auxiliary and Director circle. Second degree equation of General Conic. Centre, Asymptotes, eccentricity, foci, directrix axes and latus rectum of a conic, Co-ordinate of center, equation of conic referred to center as origin, lengths and position of axes of a standard conic.

3Three Dimensional Coordinate Geometry

• Straight Line, Sphere, Cylinder, Cone and their properties (Rectangular Coordinates only), Central Conicoids and their properties (Referred to principal axes only).

4Vector Calculus

• Differentiation of Vectors, Del operator, Gradient, divergent, Curl and directional derivative, their identities and related theorems. Integration of Vectors, line, Surface and Volume integration of vectors. Gauss Divergence, Stokes and Green theorem.

5Ordinary Differential Equations

• First order non-linear differential equation, singular solutions and extraneous Loci, Second order linear differential equation with constant and variable coefficients. Simultaneous and Total Differential Equations.

6Partial Differential Equations

• Linear and Non-linear Partial differential equation of first order. Linear Partial Differential Equations of Second Order. Solution of Partial Differential Equations by Lagrange's, Charpit's and Monge’s Method.

7Mechanics

• Equilibrium of coplanar forces, Moments, Friction, Catenary. Simple harmonic motion, Rectilinear motion under variable laws, Motion in resisting medium. Projectile.

8Abstract Algebra

• Groups– Normal Sub-groups, Quotient groups, Homomorphism, Isomorphism of groups. Classification of finite groups. Cauchy's Theorem for finite abelian groups, Permutation groups, Solvable groups and their properties. Rings, Morphism, Principal Ideal domain, Euclidean Rings, Polynomial Rings, Irreducibility criteria, Fields, Finite fields, Field extensions. Integral domain.

9Linear Algebra

• Vector Spaces, Linear dependence and independence, Bases, Dimensions, Linear transformations, Matrix representation of Linear transformations, Change of bases. Inner product spaces, Orthonormal basis, Quadratic forms, reduction and classification of quadratic forms. Algebra of Matrices, Eigenvalues and Eigenvectors, Cayley-Hamilton theorem. Canonical, Diagonal, Triangular and Jordan forms, Rank of Matrix.

10Complex Analysis

• Analytic Functions, Cauchy's Theorem, Cauchy's Integral Formulae, Power Series, Laurent’s Series, Singularities, Theory of Residues, Complex Transformations, Contour Integration.

11Special Functions

• Hypergeometric, Confluent Hypergeometric Functions and their properties. Bessel, Legendre Function/Polynomial of first kind and their properties. Hermite, Laguerre Polynomials and their properties.

12Integral Transforms

• Laplace, Inverse Laplace transform and their properties. Fourier transform, Inverse Fourier transform and their properties, Hankel, Mellin transform and their properties.

13Differential and Integral Equations

• Classification of Second Order Partial Differential Equations, Green’s Functions, Sturm-Liouville Boundary Value Problems, Cauchy’s Problems and Characteristics. Calculus of variation- Variation of a functional, Euler-Lagrange's equation, Necessary and sufficient condition for extrema, Variational method for Boundary Value Problems in ordinary and partial differential equations. Integral Equations of first and second kind of Fredholm and Volterra type, solution by successive substitutions and successive approximations.

14Metric spaces and Topology

• Metric spaces, compactness, Connectedness, Topological spaces, closed sets, closure, Dense set, Neighbourhood. Interior, exterior and boundary points, Accumulation points and derived sets. Bases and sub-bases. First and Second Countable spaces, Separable spaces, Separation axioms, compactness, continuous functions and compact sets, connected spaces.

15Differential Geometry

• Curves in space (Osculating, Normal and rectifying planes, Serret-Frenet formulae, curvature, torsion, circle of curvature and sphere of curvature), Envelopes, curves on surfaces.

16Tensors

• Covariant, Contravariant and Mixed tensors, Invariants and algebraic properties of tensors. Contraction of tensors, Quotient Law of tensors. Fundamental and Associated tensors, Christoffel symbols, Covariant differentiation of tensors.

17Mechanics

• D’Alembert’s Principle, Moment and Product of inertia, Motion in two-dimensions. Lagrange’s equations of Motion, Euler’s Equations of Motion, Motion of a top.

18Numerical Analysis

• Interpolation, Difference schemes, Lagrange's interpolation, Numerical differentiation and integration. Numerical solution by Bisection, Secant, Regula-Falsi and Newton’s Methods, Roots of polynomial. Linear Equation – Direct Methods (Jacobi, Gauss and Seidel Method).

19Operations Research

• Simplex methods, Duality, Degeneracy, Revised Simplex Method, Integer Programming Problems, Assignment and Transportation Problems, Game Theory– Two person zero sum game, Inventories- Single item deterministic inventory models with finite replacement, simple probabilistic models.

20Mathematical Statistics

• Probability, Conditional Probability, Addition and Multiplication theorems of probability, Baye’s Theorem, Expectations, Moment Generating Function, Probability Distributions: Binomial, Poisson, Uniform and Normal, Correlation and Regression, Line of Regressions.

Paper-I — common to every subject

1History, Art, Culture, Literature and Heritage of Rajasthan

• Ancient Civilizations of Rajasthan with special Reference to Mesolithic (Late Stone Age) sites in Rajasthan i.e. Nimbahera, Bagor and Mandia.
• Major dynasties of Rajasthan and its rulers through the Ages and their cultural achievements (1000-1800 A.D.).
• Political resistance of Rajput rulers against Muslim Power. Special reference to Rattan Singh, Hammir, Kanhad dev and Maldev, Chandrasen and Pratap.
• (i) Bhakti Movement and Sufism in Medieval Rajasthan, Special reference to Mira, Dadu and Khawaja Moin-ud-din Chishty. Saints: Special emphasis to be paid to teachings of Ramdevji, Gogaji, Tejaji, Pabuji, Mallinath, Dhanna, Pipa, Haridas, Raidas, Jasnath and other Sects.
• (ii) Folk gods and goddesses.
• Political Awakening and Freedom Movement in Rajasthan: 1857, Peasant and Tribal Movements, Prajamandal Movements, Contribution of Women in Social and Political awakening.
• (i) Folk Culture: Fairs and Festivals, Different Schools of Painting, Folk Tales and Gathas, Folk Songs, Folk Dances, Folk Music and Instruments.
• (ii) Dress and Ornaments, Handicrafts.
• Rajasthani Language: Origin and Development.
• Main Dialects and Region.
• Rajasthani Scripts: Mudia and Devnagari.
• (a) Rajasthani Literature: Its Evolution.
• (i) Early Period
• (ii) Pre-Medieval Period
• (iii) Post- Medieval Period
• (iv) Modern Period.
• (b) Famous Writers and their Works.
• Tourism and Rajasthan: Heritage, Tourism Policy and Vision.

2Geography of Rajasthan

• Physiographic regions, Rivers and lakes.
• Climate, Natural Vegetation, Soil, Minerals and Energy Resources – Renewable and Non-renewable.
• Population – Characteristics, Livestock, Biodiversity and its conservation.
• Production and Distribution of Major crops, Major Irrigation Projects, Major Industries.
• Drought and Famines, Desertification, Environmental Problems, Disaster Management and Pandemics.

3Political and Administrative System of Rajasthan

• Governor, Chief Minister and Council of Ministers.
• State Legislative Assembly, High Court and Judicial System of Rajasthan.
• Rajasthan Public Service Commission, State Election Commission, State Finance Commission, State Human Rights Commission, State Commission for Women, State Information Commission, Lokayukta and Auditor General.
• Chief Secretary, Government Secretariat, Chief Minister’s Office (CMO), Divisional Commissioner, District Administration, Institutions of Panchayati Raj and Urban Local- Self Government.
• Government Policies and Right based Citizenship: Right to Information, Guaranteed Delivery of Public Services, Citizen's Charters, Social Audit, Jan Soochna Portal, Rajasthan Sampark Portal etc.

4Economy of Rajasthan

• Characteristics of state economy.
• Occupational distribution.
• Compositional trend of state domestic product.
• Major Sectoral Issues.
• (i) Agricultural Sector: Characteristics of agricultural sector in Rajasthan. Major rabi and kharif crops with special reference to oil seeds and spices. Irrigated area and trends, Problems of migrant workers and their rehabilitation. Agricultural credit.
• (ii) Livestock: Trends in livestock population. Milk production in Rajasthan.
• (iii) Industrial Outlook: Major industries of Rajasthan. Constraints to development of industries. MSMEs in Rajasthan. Roles and problem of small industries. Industrial sickness. Major state public sector enterprises. SEZ in Rajasthan. Role of RIICO and RFC. Agro-processing policy (2020).
• (iv) Service Sector: Primary education, Development in recent years. Health programmes of state government. Mid-day meal programme. Indira Rasoi Yojana.
• (v) Infrastructure Development: Progress in national highways, state highways and village roads. Power: Progress in power generation. Recent progress in solar power projects.
• (vi) Handicrafts of Rajasthan.
• (vii) Major items of exports from Rajasthan.
• (viii) Latest major welfare schemes of state government with special reference to economically and socially backward classes, disabled people, old aged people. Steps taken for women empowerment and child development.
• (ix) Regional economic inequalities in Rajasthan.

5Contemporary Events

• Major Contemporary Events and Issues of Rajasthan.
• Persons and Places in News.
• Sports and Games.

Official syllabus from RSSB Advertisement 06/2026 (Teaching Associate), verbatim. Paper-I (General Studies of Rajasthan) is common to all subjects.