Kerala SET Mathematics Syllabus 2026 PDF Download: Complete Unit-Wise Syllabus & Exam Pattern

Official Kerala SET Mathematics Syllabus 2026 has been prescribed by the LBS Centre for Science and Technology. The syllabus evaluates candidates' understanding of core mathematical concepts, including Real Analysis, Algebra, Topology, Functional Analysis, Differential Equations, Number Theory, and Matrix Theory. Get the Kerala SET Mathematics Syllabus 2026 PDF download, unit-wise topics, exam pattern, and preparation resources to help candidates prepare confidently for the Kerala SET July 2026 examination.

Kerala SET Mathematics Syllabus 2026 Highlights

The Kerala SET Mathematics Syllabus 2026 is designed to assess postgraduate-level knowledge required for Paper 2 (Mathematics) of the Kerala State Eligibility Test. The syllabus consists of six units covering both fundamental and advanced areas of Mathematics, making it essential for candidates to follow the official syllabus throughout their preparation. Before downloading the syllabus, check the important details related to the Kerala SET Mathematics Exam 2026 below.

Kerala SET Mathematics Syllabus 2026 PDF Download

Candidates preparing for the Kerala SET Mathematics Exam 2026 should always study from the official Kerala SET Mathematics Syllabus PDF issued by the LBS Centre for Science and Technology. The syllabus clearly defines every unit and module included in Paper 2 (Mathematics), helping candidates plan their preparation more effectively. 

• Click Here for Kerala SET Mathematics Syllabus 2026 PDF Download
• Click Here for Kerala SET Paper 1 (General Paper) Syllabus PDF Download

Kerala SET Mathematics Syllabus 2026 Unit-Wise

The Kerala SET Mathematics Syllabus 2026 is divided into six major units, covering Sets and Functions, Real and Complex Analysis, Abstract Algebra, Linear Algebra, Matrix Theory, Number Theory, Differential Equations, Topology, and Functional Analysis. Candidates should prepare every unit thoroughly, as questions in Kerala SET Paper 2 (Mathematics) can be asked from any part of the prescribed LBS SET syllabus 2026.

Kerala SET Mathematics Syllabus 2026: Unit 1 – Fundamental Concepts

Module 1. Sets and functions  

General ideas of sets, sets of numbers and operations on sets. Countable and uncountable sets. Properties of relations and functions. Domain, codomain and range of functions. Injective and surjective functions, bijections and inverses. Graphs of polynomials, trigonometric functions and other elementary real valued functions. Composition of functions. Polynomials and polynomial equations - remainder and factor theorems. Relation between roots and coefficients of a polynomial of degree up to three. 

Module 2. Analytic geometry  

Coordinates of points in plane and space. Distance in terms of co-ordinates. Determination of coordinates of points on a line in terms of two points. Slope of a line. Representation of curves in a plane as equations - straight lines, circles and conics. Geometric and algebraic properties of their equations. Direction cosines and direction ratios of a line in space. Coplanar and non-coplanar lines. Equations of lines, planes and spheres in both cartesian and vector forms. 

Module 3. Elementary calculus  

Limits of functions, differentiability, and derivative as slope. Derivatives of polynomial functions, exponential functions and trigonometric functions. Derivatives of sums, products, composite and inverse functions. Increasing and decreasing functions, local extrema, and simple appli-cations. Integration as anti-differentiation, integral as sum. Length of curves, area under curves and volume of solids of revolution using integration. 

Module 4. Probability  

Basic Combinatorics - Pigeonhole principle, permutations and combinations. Random experiment, sample space, events, probability, discrete Probability, conditional probability and independent events. 

Kerala SET Mathematics Syllabus 2026: Unit 2 – Real and Complex Analysis

Module 1. Basic concepts in Real Analysis  

Convergence and limits of sequences and series of real numbers. Geometric and harmonic series. Sequences and series of real functions, point-wise and uniform convergence. The exponential series. Limits, continuity, directional and total derivatives of functions of several variables. 

Module 2. Integration and basic Measure Theory  

Functions of bounded variations. Riemann integrals and Riemann Stieltjes integrals of real valued functions. The concepts of Lebesgue measure and Lebesgue integral of real valued functions. Lebesgue measurable sets, measurable functions and simple functions. 

Module 3. Basic concepts in Complex Analysis  

Basic properties of complex numbers. Absolute value. Polar form of a complex number. De Moivre's theorem and nth roots of unity and nth roots of complex numbers. Properties of complex analytic functionsCauchy Riemann equations, infinite differentiability, Harmonic conjugates. Conformal mappings. Mobius transformations and cross ratio. 

Module 4. Complex Integration  

Power series of functions, Radius of convergence of power series. Zeroes, poles and singularities of functions. Liouville's Theorem. Open Mapping Theorem. Maximum Modulus Theorem. Line integrals of complex valued functions, Cauchys Theorem and Cauchys integral formula for complex functions. Contour integration and residue theorem 

Kerala SET Mathematics Syllabus 2026: Unit 3 – Abstract Algebra

Module 1. Groups  

Groups and subgroups, Groups of permutations. Abelian and non-abelian groups. Cyclic groups. Finite and infinite groups. Normal subgroups and quotients. Homomorphisms and isomorphisms. Homomorphic images and quotients. Lagrange's theorem. Order of an element. Groups of prime order and prime-square order. Direct products and direct sums of groups. Sylow's theorem. 

Module 2. Rings  

Ring of integers and ring of polynomials. Ring of integers modulo n. Finite rings. Commutative and non-commutative rings. Ideals, maximal ideals and prime ideals. Quotient Rings. Homomorphisms and isomorphisms. Homomorphic images and quotients. Zero divisors. Integral domains. Euclidean domains. Units, associates and primes in a ring. Groups of units of rings. 

Module 3. Fields  

Field of rational numbers, real numbers and complex numbers. Integers modulo a prime number. Finite fields. Finite integral domains. Polynomials over fields, reducibility and irreducibility. Algebraic and transcendental extensions of fields. Degree of extension and irreducible polynomial of an element, Splitting fields, groups of automorphisms and fixed fields. 

Kerala SET Mathematics Syllabus 2026: Unit 4 – Linear Algebra and Matrix Theory

Module 1. Matrix Theory  

Algebra of matrices - Types of matrices, nilpotent matrices, invertible matrices. Determinants of square matrices. Echelon matrices and rank of a matrix. Systems of linear equations and solutions and matrix methods for checking consistency. 

Module 2. Vector spaces  

Vector spaces over an arbitrary field, real numbers and complex numbers. Linear independence and dependence. Basis and dimension. subspaces and quotients. Direct sums of vector spaces. Geometry of points, lines and planes in R2 and R3 in terms of subspaces. 

Module 3. Linear Transformation  

Linear maps. Differentiation and integration as linear maps Range, null space and dimensional relations. Invertible transformations. Representation of linear maps between finite dimensional vector spaces as matrices and vice-versa. Dependence of matrix of a linear trans- formation on the basis and relation with change of basis. Linear functional and dual basis. Linear functionals on R2. Eigenvalues and eigenvectors. Minimal polynomial, characteristic polynomial and Cayley Hamilton theorem, Diagonalization. 

Kerala SET Mathematics Syllabus 2026: Unit 5 – Number Theory and Differential Equations

Module 1. Number theory  

Principle of Mathematical Induction. Prime factorization. Properties of divisibility. Coprime numbers. G C D and L C M of numbers. Euler's totient function and its multiplicative property. Congruences. Chinese remainder theorem. Fermat's little theorem. Wilson's theorem. 

Module 2. Ordinary Differential Equations  

Order and degree of differential equations. Formation of di er-ential equations and different types of differential equations of first order. Representation of family of curves by differential equations. Orthogonal trajectories. Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, Method of variation of parameters, Wronskian. Power series solutions of differential equations. Bessel and Legendre polynomials. 

Module 3. Partial Differential Equations  

Solution of the equation of the form Pdx+Qdy+Rdz=0. Charpits and Jacobis method for solving first order PDEs, Classification of higher order PDEs (parabolic, elliptic and hyperbolic types). General solution of higher order PDEs with constant coefficients. Method of separation of variables. Wave equation, Heat equation and Laplace equation. 

Kerala SET Mathematics Syllabus 2026: Unit 6 – Topology and Functional Analysis

Module 1. Metric Topology  

Metric spaces. Discrete metric. Euclidean metric on Rn and Cn. Supremum metric on the set of real valued functions and complex valued functions on a closed interval. Limit points and convergence of sequences in a metric space. Cauchy sequences. Complete metric spaces. Completion of a metric space. Cantor's intersection theorem and Baires category theorem. Compact subsets and connected subsets of R and C. Heine-Borel theorem for Rn 

Module 2. General Topology  

Topological spaces, open sets and closed sets. Usual topology on R and C. Base and subbase for a topology. Closure, interior and boundary of subsets. Compactness and connectedness. Convergence of sequences in a topological space. Non-uniqueness of limits. Hausdor Spaces and separation axioms. Continuity of functions between topological spaces. Preservation of compactness and connectedness under continuous functions. Homeomorphisms. Product topology. 

Module 3. Normed linear spaces  

Norm on linear spaces. Euclidean norm on Rn and Cn. Finite and infinite dimensional p spaces. Lp spaces. Closed and non-closed linear subspaces. Closure and interior of linear subspaces. Continuous linear maps between normed linear spaces. Bounded operators and operator norm. Banach spaces. Open mapping theorem and closed graph theorem. 

Module 4. Inner product spaces  

Inner products. Examples of norms arising from inner products and not arising from any inner product. Parallelogram law. Orthogonality in inner product spaces. Orthonormal bases. Fourier Expansion. Bessel's inequality. Hilbert spaces. Parsevals identity. Continuous linear maps between Hilbert spaces. Projection map, Riesz representation theorem. 

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Kerala SET Mathematics Exam Pattern 2026

Understanding the Kerala SET Mathematics Exam Pattern 2026 is equally important as covering the LBS SET syllabus. The examination is conducted in offline (OMR-based) mode and consists of two objective-type papers. Every correct answer carries one mark, and there is no negative marking, allowing candidates to attempt all questions confidently.

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Frequently Asked Questions for Kerala SET 2026

Where can I download the Kerala SET Mathematics Syllabus 2026 PDF?

Candidates can download the official Kerala SET Mathematics Syllabus 2026 PDF from the LBS Centre for Science and Technology. The official PDF download link is provided in this article for easy access.

How many units are included in the Kerala SET Mathematics Syllabus 2026?

The Kerala SET Mathematics Syllabus 2026 consists of six major units, covering topics such as Real Analysis, Complex Analysis, Abstract Algebra, Linear Algebra, Matrix Theory, Number Theory, Differential Equations, Topology, and Functional Analysis.

Is the Kerala SET Mathematics syllabus 2026 based on the postgraduate curriculum?

Yes. The Kerala SET Mathematics syllabus 2026 follows the postgraduate (Master's degree) curriculum and tests candidates on both theoretical concepts and problem-solving abilities.

What is the Kerala SET Mathematics exam pattern 2026?

The Kerala SET Mathematics examination consists of Paper 1 (General Paper) and Paper 2 (Mathematics). Both papers contain 120 objective-type questions carrying one mark each, and there is no negative marking.

What are the most important topics for Kerala SET Mathematics preparation?

Candidates should focus on Real Analysis, Abstract Algebra, Linear Algebra, Matrix Theory, Number Theory, Differential Equations, Complex Analysis, Topology, and Functional Analysis, while ensuring they complete the entire official syllabus.