For Dec 2025 NET exam, 2,38,451 students registered, of which 43,446 students registered for Mathematics science paper. 

I won’t say it's a very tough exam, but if you systematically plan and follow it religiously a student can qualify and secure a good rank.

Few things that every student should understand are detailed syllabus, exam pattern, and focus areas. Below is a comprehensive guide covering the syllabus, important topics, exam pattern, and preparation strategies.

CSIR NET Mathematics Dec 2025: Exam Pattern

The exam is a single paper with Multiple Choice Questions (MCQs) divided into three parts:

• Part A: 20 questions (answer any 15), covering General Science, Quantitative Reasoning & Analysis, and Research Aptitude. Each question carries 2 marks; total 30 marks.

• Part B: 40 questions (answer any 25), covering core syllabus topics. Each question carries 3 marks; total 75 marks.

• Part C: 60 questions (answer any 20), higher-order analytical questions testing scientific concepts and their applications. Each question carries 4.75 marks; total 95 marks.

Total marks: 200

Negative marking: Part A (0.5 marks), Part B (0.75 marks), no negative marking in Part C.

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Detailed Syllabus for CSIR NET Mathematics Dec 2025

The syllabus is broadly divided into four units covering core mathematical disciplines:

Unit 1: Analysis and Linear Algebra

• Elementary set theory, finite, countable and uncountable sets

• Real number system, Archimedean property, supremum and infimum

• Sequences and series, convergence, limsup, liminf

• Bolzano-Weierstrass theorem, Heine-Borel theorem

• Continuity, uniform continuity, differentiability, mean value theorem

• Sequences and series of functions, uniform convergence

• Riemann sums, Riemann integral, improper integrals

• Monotonic functions, types of discontinuity, functions of bounded variation

• Lebesgue measure and integral

• Functions of several variables, directional and partial derivatives, inverse and implicit function theorems

• Metric spaces, compactness, connectedness

• Normed linear spaces, spaces of continuous functions

• Vector spaces, subspaces, linear dependence, basis, dimension

• Algebra of linear transformations, matrix algebra, rank, determinants

• Eigenvalues, eigenvectors, Cayley-Hamilton theorem

• Canonical forms: diagonal, triangular, Jordan forms

• Inner product spaces, orthonormal basis

• Quadratic forms, reduction and classification

Unit 2: Complex Analysis, Algebra, and Topology

• Algebra of complex numbers, complex plane

• Polynomials, power series, transcendental functions (exponential, trigonometric, hyperbolic)

• Analytic functions, Cauchy-Riemann equations

• Contour integrals, Cauchy’s theorem and integral formula, Liouville’s theorem

• Maximum modulus principle, Schwarz lemma, open mapping theorem

• Taylor and Laurent series, calculus of residues

• Conformal mappings, Möbius transformations

• Permutations, combinations, pigeonhole principle, inclusion-exclusion principle, derangements

• Fundamental theorem of arithmetic, divisibility, congruences, Chinese remainder theorem, Euler’s phi function, primitive roots

• Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems

• Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain

• Polynomial rings, irreducibility criteria

• Fields, finite fields, field extensions, Galois theory

• Topology: basis, dense sets, subspace and product topology, separation axioms, connectedness, compactness

Unit 3: Differential Equations, Calculus of Variations, and Integral Equations

• Ordinary differential equations (ODEs): existence and uniqueness of solutions, singular solutions, systems of first-order ODEs

• Linear ODEs: homogeneous and non-homogeneous, variation of parameters, Sturm-Liouville problems, Green’s function

• Partial differential equations (PDEs): Lagrange and Charpit methods, Cauchy problem, classification of second-order PDEs

• General solutions of higher-order PDEs with constant coefficients

• Separation of variables method for Laplace, Heat, and Wave equations

• Calculus of variations: variation of a functional, Euler-Lagrange equation, necessary and sufficient conditions for extrema

• Variational methods for boundary value problems

• Linear integral equations of Fredholm and Volterra types, solutions with separable kernels

Unit 4: Statistics and Experimental Design (Optional but useful)

• Descriptive statistics, exploratory data analysis

• Gauss-Markov models, estimability of parameters, best linear unbiased estimators

• Confidence intervals, tests for linear hypotheses

• Analysis of variance and covariance

• Completely randomized designs, randomized block designs, Latin-square designs

• Connectedness and orthogonality of block designs, Balanced Incomplete Block Designs (BIBD)

• 2^K factorial experiments: confounding and construction

Key Topics to Focus On

Based on the syllabus and exam trends, prioritize these topics:

• Real Analysis: Sequences and series, continuity, differentiability, integration, uniform convergence

• Linear Algebra: Vector spaces, linear transformations, eigenvalues, canonical forms

• Complex Analysis: Analytic functions, contour integration, residue theorem

• Ordinary and Partial Differential Equations: Solution methods, classification, boundary value problems

• Abstract Algebra: Groups, rings, fields, Galois theory basics

• Numerical Analysis: Numerical solutions of algebraic and differential equations, interpolation, numerical integration

• Topology: Basic concepts like compactness and connectedness

• Calculus of Variations and Integral Equations: Euler-Lagrange equations, Fredholm and Volterra equations

Preparation Strategy for NET Maths 2025

• Understand the syllabus thoroughly: Download and review the official syllabus PDF to cover all topics systematically

• Create a study timetable: Divide the syllabus into manageable daily/weekly sections, balancing theory and problem-solving

• Focus on concepts and problem-solving: Master fundamental concepts and practice a variety of problems, especially from previous years’ question papers.

• Practice MCQs: Since the exam is MCQ-based, practice multiple-choice questions regularly to improve speed and accuracy.

• Revise regularly: Make concise notes for quick revision of formulas, theorems, and important results.

• Solve previous papers and mock tests: This helps in understanding the exam pattern, difficulty level, and time management

• Focus on Part C topics: These are analytical and application-based questions that carry the highest marks; practice higher-order problems in ODEs, PDEs, and advanced algebra.

• Use standard reference books: Refer to recommended textbooks and coaching material for in-depth study and clarity.

• Join a test Series - Take a test series in reputed coaching institute like DIPS Academy, DIPS Academy is a reputed organization headed by Dubey Sir, a reputed Mathematician 

• Go through PYQ 

By following this detailed syllabus and preparation plan, candidates can maximize their chances of success in the CSIR NET Mathematics exam 2025.

If you need a regular guide, you can join DIPS Academy, next batch for Dec 2025 will start in 10th July 2025. DIPS has helped 40,000+ student clear Maths Competitive Exam CSIR NET, JAM, UPSc.

Reference: https://csirhrdg.res.in/