CSIR NET Mathematics Sciences syllabus aims to strengthen understanding of mathematical principles and their applications. It emphasizes problem-solving, logical reasoning, and analytical skills across areas such as real analysis, complex analysis, algebra, and statistics. CSIR NET Mathematics preparation is a question many aspirants ask. The key lies in understanding the syllabus thoroughly, covering all important topics like Algebra, Analysis, Mathematical Methods, and Applied Mathematics. Effective preparation involves consistent practice of previous yearsโ papers and mock tests, maintaining conceptual clarity, and managing time efficiently. By following a structured study plan and focusing on both theory and problem-solving, candidates can systematically prepare for the exam and increase their chances of success.
The CSIR NET Mathematics Sciences Syllabus 2026is a high-level academic framework divided into four distinct units. It encompasses core subjects like Real Analysis, Linear Algebra, and Complex Analysis, alongside applied topics such as Differential Equations and Numerical Analysis. Mastery of this syllabus is essential for securing a Junior Research Fellowship (JRF) or Assistant Professorship in Indian universities.
CSIR NET Mathematics Sciences Exam Overviewย
CSIR NET exam is a prestigious national-level examination conducted twice a year by the NTA (National Testing Agency). It covers five subjects: Life Sciences, Physical Sciences, Chemical Sciences, Earth, Atmospheric, Ocean and Planetary Sciences, and Mathematical Sciences. For candidates aspiring to pursue a career as a Junior Research Fellow (JRF) or Assistant Professor in Mathematical Sciences, understanding how to prepare for CSIR NET Mathematics preparation is crucial.
This national-level exam can be effectively cracked with a clear preparation strategy, access to the right study materials, and consistent practice. Candidates must be aware of the best study resources, includingย vedprep online references, and previous yearsโ question papers, and know how to use them efficiently.
CSIR NET Mathematics Sciences Exam Preparation Tips
The CSIR NET Mathematical Sciences exam is one of the most competitive national-level exams, conducted by the NTA to select candidates for the roles of Junior Research Fellow (JRF) and Assistant Professor. The exam is divided into three parts โ Part A, Part B, and Part C, with a total of 120 questions.
Some of the key topics in the CSIR NET Mathematical Sciences syllabus include:
-
- Linear Algebra
- Complex Analysis
- Ordinary Differential Equations (ODEs)
- Partial Differential Equations (PDEs)
- Classical Mechanics
- And other core areas of mathematical sciences
Success in this exam depends not only on understanding the concepts but also on strategic preparation. Here, we share some of the best CSIR NET Mathematical Sciences preparation tips that can help candidates plan their study schedule, strengthen problem-solving skills, and increase their chances of cracking the exam.ย ย
CSIR NET Mathematics Sciences Exam Pattern
Understanding the exam pattern is a critical step in effective preparation. The CSIR NET Mathematical Sciences exam may seem challenging initially, but with proper analysis,ย
| Particulars | Details |
| Duration of examination | 3 hours (180 minutes) |
| Total number of questions | 120 |
| Total marks | 200 |
| Type of questions | Objective Type Questions |
| Negative marking | Part A & B: 25%
Part C: No negative marking |
CSIR NET Mathematics Sciences Syllabus preparation
Before starting preparation, the first and foremost step is to thoroughly go through the CSIR NET Mathematicsย syllabus and exam pattern. Understanding the exam structure, marking scheme, and type of questions helps candidates plan their preparation effectively and know what to expect on the actual exam day.
| Unit | Topics |
| Unit 1 | Analysis, Linear Algebra |
| Unit 2 | Complex Analysis, Algebra, topology |
| Unit 3 | Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), Numerical Analysis, Calculus of Variations, Linear Integral Equations, Classical Mechanics |
| Unit 4 | Descriptive Statistics, Exploratory Data Analysis |
- Part B and Part C focus on conceptual understanding and problem-solving in the above topics.
- Candidates must prioritize core areas like Linear Algebra, ODEs, PDEs, and Classical Mechanics as they are frequently asked in previous papers.
- Reviewing the syllabus before planning your study schedule ensures efficient and targeted preparation.
Also read – Important Topics for CSIR NET Physical Science: Syllabus, Best Books, Revision Strategy, PYQs
CSIR NET Mathematical Science Syllabus Unit-wiseย
The CSIR NET Mathematical Sciences syllabus includes Unit 1, Unit 2, Unit 3 and Unit 4: for complete exam preparation.
CSIR NET Mathematics Sciences Syllabus PDF
Mathematical Sciences Syllabus pdf can be downloaded directly from the link given below or the NTA or CSIR HRDG websites.
| CSIR NET Mathematical Sciences Syllabus PDF | |
| Subjects | Download Link |
| CSIR NET Syllabus Mathematical Sciences | Download PDF |
CSIR NET All Syllabus PDF
The official CSIR NET 2025 syllabus PDF for all subjects (including General Aptitude โ Part A, Life Sciences, Chemical Sciences, Physical Sciences, and Earth Sciences) can be downloaded directly from the link given below or the NTA or CSIR HRDG websites.
|
CSIR NET Syllabus PDF |
|
| Subjects | Download Link |
| CSIR NET Syllabus Life Sciences | Download PDF |
| CSIR NET Syllabus Chemical Sciences | Download PDF |
| CSIR NET Syllabus Physical Sciences | Download PDF |
| CSIR NET Syllabus Earth Sciences | Download PDF |
How to Download CSIR NET Syllabus PDFย
To download the CSIR NET Syllabus PDF:
- Visit the official National Testing Agency (NTA) CSIR NET website: csirnet.nta.ac.in.
- Look for the โSyllabusโ or โInformation Bulletinโ section on the homepage.
- Download the syllabus PDF for your chosen subject (Life Sciences, Physical Sciences, Chemical Sciences, Earth Sciences, or Mathematical Sciences) from the provided links.
- The downloaded PDF will contain the detailed, topic-wise syllabus for Part A (General Aptitude) and Parts B/C (subject-specific).
Also read – CSIR NET Application Form 2026 : Age Limit, Eligibility Criteria, Process, Fee, Exam Dates, Exam Centres
CSIR NET Mathematics Science Syllabus 2025 Unit-wise Topics โโ
Explore the complete CSIR NET Mathematical Science Syllabus 2025 with detailed unit-wise topics, including Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics for effective exam preparation.
Unit 1: Analysis CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Set Theory & Real Numbers | Elementary Set Theory | Basics of sets, operations, relations, Cartesian product |
| Finite, Countable, Uncountable Sets | Classification of sets by cardinality | |
| Real Number System | Complete ordered field; supremum and infimum | |
| Archimedean Property | For any real numbers x,y>0x, y > 0x,y>0, โ nโNn \in \mathbb{N}nโN s.t. nx>ynx > ynx>y | |
| Sequences & Series | Convergence of Sequences | Definition of limit; monotone and bounded sequences |
| limsup & liminf | Upper and lower limits of sequences | |
| Series | Convergence tests, absolute and conditional convergence | |
| Theorems in Analysis | Bolzano-Weierstrass Theorem | Every bounded sequence has a convergent subsequence |
| Heine-Borel Theorem | Closed and bounded subsets of Rn\mathbb{R}^nRn are compact | |
| Continuity & Differentiability | Continuity & Uniform Continuity | Definitions and properties |
| Differentiability | Derivative at a point; linear approximation | |
| Mean Value Theorem | Relates derivative to function increments | |
| Sequences & Series of Functions | Pointwise & Uniform Convergence | Definitions; uniform convergence preserves continuity |
| Integration | Riemann Sums & Riemann Integral | Definition of integral using partitions |
| Improper Integrals | Integrals over infinite intervals or with unbounded integrand | |
| Advanced Function Properties | Monotonic Functions | Increasing, decreasing, and their limits |
| Types of Discontinuity | Removable, jump, essential | |
| Bounded Variation | Functions whose total variation is finite | |
| Lebesgue Measure & Integral | Generalization of length and integral for more functions | |
| Functions of Several Variables | Directional & Partial Derivatives | Rate of change in a direction or along coordinate axes |
| Derivative as Linear Transformation | Total derivative as a linear map approximating function | |
| Inverse & Implicit Function Theorems | Conditions for existence of local inverse or implicit functions | |
| Metric Spaces & Topology | Metric Spaces | Definition, open/closed sets, convergence |
| Compactness & Connectedness | Fundamental topological properties | |
| Normed Linear Spaces & Functional Analysis | Normed Spaces | Vector spaces with norm; convergence and completeness |
| Spaces of Continuous Functions | Examples of normed spaces; sup norm, C[a,b] |
Unit 1: Linear Algebra CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Vector Spaces | Vector Spaces & Subspaces | Definition, examples, closure under addition and scalar multiplication |
| Linear Dependence & Independence | Linear combination of vectors; dependence criteria | |
| Basis & Dimension | Minimal generating set; dimension as number of basis vectors | |
| Algebra of Linear Transformations | Addition, scalar multiplication, composition of linear maps | |
| Matrices & Linear Equations | Algebra of Matrices | Matrix addition, multiplication, transpose, inverse |
| Rank & Determinant | Rank: dimension of row/column space; determinant properties | |
| Linear Equations | Systems of equations; solutions via matrix methods | |
| Eigenvalues & Eigenvectors | Eigenvalues & Eigenvectors | Av=ฮปvAv = \lambda vAv=ฮปv; spectral properties |
| Cayley-Hamilton Theorem | Every square matrix satisfies its characteristic equation | |
| Matrix Representation | Linear Transformations as Matrices | Representation depends on choice of basis |
| Change of Basis | Similarity transformations; coordinate changes | |
| Canonical Forms | Diagonal, triangular, Jordan forms; simplification of matrices | |
| Inner Product Spaces | Inner Product & Orthonormal Basis | Length, angle, orthogonality, Gram-Schmidt process |
| Quadratic Forms | Quadratic Forms | Expression Q(x)=xTAxQ(x) = x^T A xQ(x)=xTAx; symmetric matrices |
| Reduction & Classification | Diagonalization; positive definite, negative definite, indefinite forms |
You can also check – How to prepare for CSIR NET Mathematics preparation : Syllabus,Tips Preparation strategy, Books
Unit 2: Complex Analysis CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Complex Numbers & Functions | Algebra of Complex Numbers | Addition, multiplication, modulus, conjugate, polar form |
| Complex Plane | Representation of complex numbers; Argand diagram | |
| Polynomials & Power Series | Roots of polynomials, radius of convergence, analytic properties | |
| Transcendental Functions | Exponential, logarithmic, trigonometric, hyperbolic functions in complex domain | |
| Analytic Functions | Analyticity | Function differentiable in complex sense; Cauchy-Riemann equations |
| Cauchy-Riemann Equations | Necessary condition for differentiability of complex functions | |
| Complex Integration | Contour Integrals | Line integrals along paths in complex plane |
| Cauchy’s Theorem | Integral over closed contour of analytic function is zero | |
| Cauchy’s Integral Formula | Value of analytic function inside contour in terms of integral over contour | |
| Liouville’s Theorem | Bounded entire functions are constant | |
| Maximum Modulus Principle | Maximum of modulus occurs on boundary of domain | |
| Schwarz Lemma | Bounds analytic functions mapping unit disk to itself | |
| Open Mapping Theorem | Non-constant analytic functions map open sets to open sets | |
| Series Expansion & Residues | Taylor Series | Power series expansion around regular point |
| Laurent Series | Expansion with negative powers around singularity | |
| Calculus of Residues | Residue theorem for evaluating integrals; poles, essential singularities | |
| Conformal Mappings | Conformal Maps | Angle-preserving maps; locally analytic and non-constant |
| Mรถbius Transformations | Linear fractional transformations; preserve circles and angles |
Unit 2: Algebra CSIR NET Mathematical Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Combinatorics | Permutations | Arrangement of nnn objects in order; with/without repetition |
| Combinations | Selection of rrr objects from nnn without order; (nr)=n!r!(nโr)!\binom{n}{r} = \frac{n!}{r!(n-r)!}(rnโ)=r!(nโr)!n!โ | |
| Pigeonhole Principle | If nnn objects in mmm boxes with n>mn>mn>m, at least one box contains >1 object | |
| Inclusion-Exclusion Principle | Counting union of overlapping sets: ( | |
| Derangements | Permutations where no element is in its original position; !n=n!โk=0n(โ1)kk!!n = n!\sum_{k=0}^{n} \frac{(-1)^k}{k!}!n=n!โk=0nโk!(โ1)kโ | |
| Number Theory | Fundamental Theorem of Arithmetic | Every integer >1 can be expressed uniquely as a product of primes |
| Divisibility in Z\mathbb{Z}Z | (a | |
| Congruences | (a \equiv b \ (\text{mod } n) \iff n | |
| Chinese Remainder Theorem | System of congruences with coprime moduli has a unique solution modulo the product | |
| Euler’s ฯ\phiฯ-function | Counts integers โค n coprime to n; ฯ(pk)=pkโpkโ1\phi(p^k) = p^k – p^{k-1}ฯ(pk)=pkโpkโ1 | |
| Primitive Roots | ggg is primitive root modulo n if all numbers coprime to n are powers of ggg | |
| Group Theory | Groups & Subgroups | Definitions, examples, subgroup criteria |
| Normal Subgroups & Quotient Groups | NโGN \triangleleft GNโG; cosets form quotient group G/NG/NG/N | |
| Homomorphisms & Cyclic Groups | Structure-preserving maps; groups generated by single element | |
| Permutation Groups | Groups of bijections under composition | |
| Cayley’s Theorem | Every group is isomorphic to a subgroup of a symmetric group | |
| Class Equations | ( | |
| Sylow Theorems | Existence, conjugacy, and number of subgroups of order pkp^kpk in finite groups | |
| Ring Theory | Rings & Ideals | Set with two operations; ideals closed under addition and multiplication by ring elements |
| Prime & Maximal Ideals | Prime: abโPโ โโนโ โaโPab \in P \implies a \in PabโPโนaโP or bโPb \in PbโP; Maximal: no ideal strictly between MMM and RRR | |
| Quotient Rings | R/IR/IR/I with addition and multiplication modulo I | |
| UFD, PID, Euclidean Domain | Unique factorization, principal ideal generation, division algorithm | |
| Polynomial Rings | Polynomial Rings | Rings of polynomials R[x]R[x]R[x] |
| Irreducibility Criteria | Eisenstein criterion, degree tests | |
| Field Theory & Galois Theory | Fields & Finite Fields | Commutative rings with inverses; GF(pn)GF(p^n)GF(pn) |
| Field Extensions | FโKF \subseteq KFโK, KKK extension of FFF | |
| Galois Theory | Connection between field extensions and group theory; solvability of polynomials |
Unit 2: Topology CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Topology | Basis | Collection of open sets such that every open set can be expressed as a union of them |
| Dense Sets | A subset DDD of XXX is dense if every point of XXX is either in DDD or is a limit point of DDD | |
| Subspace Topology | Topology induced on a subset YโXY \subseteq XYโX from the parent space XXX | |
| Product Topology | Topology on a product of spaces; open sets are products of open sets of component spaces | |
| Separation Axioms | T0, T1, T2 (Hausdorff), T3, T4: conditions that separate points and closed sets | |
| Connectedness | A space is connected if it cannot be represented as the union of two non-empty disjoint open sets | |
| Compactness | Every open cover has a finite subcover; in metric spaces, equivalent to sequential compactness |
Unit 3: Ordinary Differential Equations (ODEs) CSIR NET Mathematical Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| First-Order ODEs | Existence & Uniqueness | Conditions for solutions of initial value problems (IVPs); Picard-Lindelรถf theorem |
| Singular Solutions | Solutions not obtained from general solution; often envelope of family of curves | |
| Systems of First-Order ODEs | Coupled first-order equations; can be written in matrix form | |
| Higher-Order Linear ODEs | Homogeneous Linear ODEs | Solutions of form yโฒโฒ+p(x)yโฒ+q(x)y=0y” + p(x)y’ + q(x)y = 0yโฒโฒ+p(x)yโฒ+q(x)y=0; superposition principle |
| Non-Homogeneous Linear ODEs | General solution = complementary function + particular solution | |
| Variation of Parameters | Method to find particular solution for non-homogeneous ODEs | |
| Boundary Value Problems | Sturm-Liouville Problems | Eigenvalue problems; orthogonal eigenfunctions; arises in physics and engineering |
| Green’s Function | Integral kernel representing solution of linear differential equations with boundary conditions |
Unit 3: Partial Differential Equations (PDEs) CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| First-Order PDEs | Lagrange Method | Solves linear first-order PDEs using characteristic equations |
| Charpit Method | Solves nonlinear first-order PDEs; extends Lagrange method | |
| Cauchy Problem | Determining solution from initial curve or surface data | |
| Second-Order PDEs | Classification | Elliptic, Parabolic, Hyperbolic types based on discriminant of second-order terms |
| Higher-Order PDEs with Constant Coefficients | Solve using characteristic equation; general solution depends on roots | |
| Separation of Variables | Laplace Equation | Solution as product of functions of individual variables; boundary value problems |
| Heat Equation | Diffusion equation; separation leads to Fourier series solutions | |
| Wave Equation | Hyperbolic PDE; solutions via separation or dโAlembert formula |
Also read – CSIR NET Mathematical Science Question Papers 2025 pdf
Unit 3: Integral Equations CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Linear Integral Equations | First Kind | Unknown function appears only under the integral; โซabK(x,t)ฯ(t)dt=f(x)\int_a^b K(x,t) \phi(t) dt = f(x)โซabโK(x,t)ฯ(t)dt=f(x) |
| Second Kind | Unknown function appears inside and outside integral; ฯ(x)โฮปโซabK(x,t)ฯ(t)dt=f(x)\phi(x) – \lambda \int_a^b K(x,t)\phi(t)dt = f(x)ฯ(x)โฮปโซabโK(x,t)ฯ(t)dt=f(x) | |
| Fredholm Type | Limits of integration are fixed | |
| Volterra Type | Upper limit of integration depends on variable; e.g., โซaxK(x,t)ฯ(t)dt\int_a^x K(x,t) \phi(t) dtโซaxโK(x,t)ฯ(t)dt | |
| Solutions with Separable Kernels | Separable Kernels | Kernel K(x,t)=โi=1nfi(x)gi(t)K(x,t) = \sum_{i=1}^n f_i(x) g_i(t)K(x,t)=โi=1nโfiโ(x)giโ(t); reduces integral equation to algebraic system |
| Eigenvalues and Eigenfunctions | Characteristic Numbers & Eigenfunctions | Eigenvalues ฮป\lambdaฮป for which homogeneous equation has non-trivial solution |
| Resolvent Kernel | Resolvent Kernel | Kernel used to express solution of integral equation as series; helps solve Fredholm equations |
Unit 3: Numerical Analysis CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Numerical Solutions of Algebraic Equations | Method of Iteration | Solve x=g(x)x = g(x)x=g(x) iteratively; convergence requires ( |
| Newton-Raphson Method | Iterative formula: xn+1=xnโf(xn)fโฒ(xn)x_{n+1} = x_n – \frac{f(x_n)}{f'(x_n)}xn+1โ=xnโโfโฒ(xnโ)f(xnโ)โ; quadratic convergence | |
| Rate of Convergence | Measures speed of convergence; linear, quadratic, cubic orders | |
| Systems of Linear Algebraic Equations | Gauss Elimination | Direct method; reduces system to upper triangular form, then back substitution |
| Gauss-Seidel Method | Iterative method; updates solution component-wise using latest approximations | |
| Finite Differences | Forward, Backward, Central Differences | Approximates derivatives using differences of function values at discrete points |
| Interpolation | Lagrange Interpolation | Polynomial passing through given points; formula: P(x)=โyiโjโ ixโxjxiโxjP(x) = \sum y_i \prod_{j\neq i} \frac{x-x_j}{x_i-x_j}P(x)=โyiโโj=iโxiโโxjโxโxjโโ |
| Hermite Interpolation | Uses function values and derivatives at given points for approximation | |
| Spline Interpolation | Piecewise polynomials; cubic splines ensure smoothness at data points | |
| Numerical Differentiation & Integration | Numerical Differentiation | Approximate derivative using finite difference formulas |
| Numerical Integration | Approximate definite integrals using Trapezoidal rule, Simpsonโs rules, etc. | |
| Numerical Solutions of ODEs | Picard Method | Successive approximations using integral form of differential equation |
| Euler Method | First-order method: yn+1=yn+hf(xn,yn)y_{n+1} = y_n + h f(x_n, y_n)yn+1โ=ynโ+hf(xnโ,ynโ) | |
| Modified Euler Method | Improved Euler/Heunโs method; second-order accuracy | |
| Runge-Kutta Methods | Higher-order methods (RK2, RK4) for accurate solutions |
Unit 3: Calculus of Variations, CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Functionals & Variations | Variation of a Functional | Small change in a functional; ฮดJ[y]=0\delta J[y] = 0ฮดJ[y]=0 for extremum |
| Euler-Lagrange Equation | Necessary condition for a functional J[y]=โซF(x,y,yโฒ)dxJ[y] = \int F(x, y, y’) dxJ[y]=โซF(x,y,yโฒ)dx to have an extremum: โFโyโddxโFโyโฒ=0\frac{\partial F}{\partial y} – \frac{d}{dx} \frac{\partial F}{\partial y’} = 0โyโFโโdxdโโyโฒโFโ=0 | |
| Necessary & Sufficient Conditions | Conditions to identify maxima, minima, or saddle points of functionals | |
| Variational Methods for BVPs | Ordinary Differential Equations | Solve boundary value problems by minimizing associated functional |
| Partial Differential Equations | Extend variational principles to PDEs; e.g., energy methods, Ritz method |
Unit 3: Classical Mechanics CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Generalized Coordinates | Definition & Examples | Coordinates that uniquely define configuration of system; reduce degrees of freedom |
| Lagrange’s Equations | Formulation | ddtโLโqหiโโLโqi=0\frac{d}{dt} \frac{\partial L}{\partial \dot{q}_i} – \frac{\partial L}{\partial q_i} = 0dtdโโqหโiโโLโโโqiโโLโ=0; Lagrangian L=TโVL = T – VL=TโV |
| Hamiltonian Mechanics | Hamiltonโs Canonical Equations | qหi=โHโpi, pหi=โโHโqi\dot{q}_i = \frac{\partial H}{\partial p_i}, \ \dot{p}_i = -\frac{\partial H}{\partial q_i}qหโiโ=โpiโโHโ, pหโiโ=โโqiโโHโ; phase space formulation |
| Hamiltonโs Principle & Principle of Least Action | Action S=โซLdtS = \int L dtS=โซLdt is stationary for true path; variational approach | |
| Rigid Body Dynamics | Two-Dimensional Motion | Motion in plane; translation + rotation about center of mass |
| Eulerโs Dynamical Equations | Lห+ฯรL=N\dot{\mathbf{L}} + \boldsymbol{\omega} \times \mathbf{L} = \mathbf{N}Lห+ฯรL=N; motion about a fixed axis | |
| Small Oscillations | Theory of Small Oscillations | Linearization near equilibrium; normal modes and frequencies; application to coupled systems |
Unit 4: Statistics CSIR NET Mathematics Sciences Syllabus
| Main Topic | Subtopics / Concepts | Key Points / Notes |
| Descriptive Statistics & EDA | Descriptive Statistics | Measures of central tendency, dispersion, skewness, kurtosis |
| Exploratory Data Analysis | Graphical and numerical methods to summarize data; boxplots, histograms | |
| Probability Theory | Sample Space & Discrete Probability | Basic probability concepts; independent events; Bayes theorem |
| Random Variables & Distribution Functions | Univariate & multivariate; cumulative distribution, probability mass/density functions | |
| Expectation & Moments | Mean, variance, higher moments, covariance | |
| Characteristic Functions | Tool for studying distributions; moment generating properties | |
| Probability Inequalities | Markov, Chebyshev, Jensen inequalities | |
| Modes of Convergence & Limit Theorems | Convergence in probability, almost surely; weak & strong laws of large numbers; Central Limit Theorem (i.i.d.) | |
| Stochastic Processes | Markov Chains | Finite/countable state space; classification of states; n-step transition probabilities; stationary distributions |
| Poisson & Birth-and-Death Processes | Counting processes; transition rates; applications | |
| Standard Distributions & Sampling | Discrete & Continuous Distributions | Binomial, Poisson, Geometric, Uniform, Normal, Exponential, etc. |
| Sampling Distributions & Standard Errors | Distribution of sample mean, variance; asymptotic distributions | |
| Order Statistics | Distribution of min, max, and other order statistics | |
| Estimation & Hypothesis Testing | Methods of Estimation | Method of moments, maximum likelihood; properties of estimators |
| Confidence Intervals | Interval estimation for parameters | |
| Tests of Hypotheses | Most powerful, uniformly most powerful, likelihood ratio tests | |
| Chi-square & Large Sample Tests | Goodness-of-fit tests, asymptotic testing procedures | |
| Nonparametric Tests | Sign test, Wilcoxon tests, rank correlation, independence tests | |
| Elementary Bayesian Inference | Prior, posterior, Bayesian estimation | |
| Regression & ANOVA | Gauss-Markov Models | Estimability, BLUE, linear hypotheses tests, confidence intervals |
| Analysis of Variance & Covariance | Fixed, random, mixed effects models | |
| Regression Models | Simple and multiple linear regression; diagnostics; logistic regression | |
| Multivariate Analysis | Multivariate Normal & Wishart Distributions | Properties, quadratic forms |
| Correlation & Partial Correlation | Inference for parameters, tests | |
| Data Reduction Techniques | Principal Component Analysis, Discriminant Analysis, Cluster Analysis, Canonical Correlation | |
| Sampling Techniques | Sampling Methods | Simple random, stratified, systematic, PPS sampling; ratio & regression methods |
| Design of Experiments | Experimental Designs | Completely randomized, randomized block, Latin-square designs |
| Block Designs | Connectedness, orthogonality, BIBD | |
| Factorial Experiments | 2K2^K2K factorial designs; confounding and construction | |
| Reliability & Life Testing | Hazard Function & Failure Rates | Reliability measures, censoring, life testing |
| Series & Parallel Systems | System reliability analysis | |
| Operations Research & Queuing | Linear Programming Problem | Formulation, simplex method, duality |
| Queuing Models | Steady-state solutions: M/M/1, M/M/1 with limited waiting, M/M/C, M/M/C with limited waiting, M/G/1 | |
| Inventory Models | Elementary inventory control models |
CSIR NET Mathematics Sciences Topic-Wise Weightageย
A highly effective approach to excel in the CSIR NET Mathematical Sciences exam is to concentrate on topics that contribute the most marks. Knowing the weightage of each topic allows you to plan your preparation strategically, optimize your scoring potential, and manage your study time efficiently. By analyzing trends from previous yearsโ question papers, we can create a comprehensive topic-wise weightage guide for the CSIR NET Mathematical Sciences exam.
| Subject Area | Approx. Questions | Estimated Marks | Paper Section | Priority Level |
| Linear Algebra | 7โ9 | 20โ30 | Sections B & C | Very High |
| Real Analysis | 6โ8 | 20โ25 | Sections B & C | Very High |
| Complex Analysis | 5โ6 | 15โ20 | Sections B & C | High |
| Ordinary Differential Equations (ODEs) | 4โ6 | 15โ20 | Sections B & C | High |
| Partial Differential Equations (PDEs) | 4โ5 | 12โ18 | Sections B & C | High |
| Abstract Algebra / Group Theory | 4โ5 | 12โ18 | Sections B & C | High |
| Topology | 3โ4 | 10โ15 | Sections B & C | Moderate |
| Numerical Analysis | 3โ4 | 8โ12 | Sections B & C | Moderate |
| Calculus of Variations | 2โ3 | 5โ10 | Section C | Moderate |
| Classical Mechanics | 2โ3 | 5โ10 | Section C | Moderate |
| Linear Integral Equations | 1โ2 | 3โ5 | Section C | Low |
| Functional Analysis | 1โ2 | 3โ5 | Section C | Low |
| General Aptitude (Part A) | 15 | 30 | Section A | Easy & High Scoring |
Notes / Tips for Preparation:
- Very High Priority: Linear Algebra and Real Analysis are must-prepare topicsโthey appear most frequently.
- High Priority: Complex Analysis, ODEs, PDEs, and Abstract Algebra are consistently tested.
- Moderate Priority: Topics like Topology, Numerical Analysis, Calculus of Variations, and Classical Mechanics can be attempted after focusing on high-priority areas.
- Low Priority: Linear Integral Equations and Functional Analysis appear less often but should not be ignored entirely.
- General Aptitude: Easy to score; prepare thoroughly for quick marks in Section A.
How to Make the Most of the CSIR NET Mathematics Sciences Syllabus
CSIR NET Mathematical Sciences syllabus provides a clear pathway to organize your studies and focus on key concepts efficiently.
- Familiarize Yourself with the Complete Syllabus
Begin by thoroughly going through the CSIR NET Mathematical Sciences syllabus. Break it down into individual topics to quickly identify your strengths and the areas that need more focus. - Give Priority to High-Weightage Topics
Focus on topics that carry more marks in the exam, such as Linear Algebra, Real Analysis, and Complex Analysis. These subjects appear frequently and have a significant impact on your overall score. - Create a Weekly Study Schedule
Plan your preparation week by week, ensuring that all topics of the syllabus are systematically covered. Include time for revision to consolidate learning. - Practice Previous Year Questions by Topic
Solve past CSIR NET papers by linking each question to its corresponding syllabus topic. This approach reinforces your understanding and shows how concepts are tested in the actual exam. - Take Syllabus-Based Mock Tests
Attempt regular mock tests that follow the structure of the syllabus. This practice improves speed, accuracy, and helps you manage exam pressure effectively. - Use Notes, Formula Sheets, and Flashcards
Maintain concise notes, formula sheets, or flashcards for each topic. These tools are extremely useful for quick revisions just before the exam. - Include General Aptitude in Your Routine
Donโt overlook the General Aptitude section. Practicing it weekly can help you gain additional marks with minimal effort, boosting your overall score.
Recommended Books for CSIR NET General Aptitude
A strong foundation in General Aptitude is crucial for scoring well in the CSIR NET examination. Several books are available to help aspirants build concepts, practice problems, and prepare effectively. Here are some highly recommended titles:
| Book Name | Author |
| CSIR UGC NET Paper I | R. Gupta |
| CSIR-UGC-NET General Aptitude: Theory and Practice | Ram Mohan Pandey |
| General Aptitude: Comprehensive Theory & Practice | Kailash Choudhary |
| CSIR NET General Aptitude โ A New Outlook | Christy Varghese |
CSIR NET Chemical Science Previous Year Question Paper,ย
Recommended Books for CSIR NET Mathematics Sciences
To effectively prepare for the CSIR NET Mathematical Sciences exam, having a structured study plan and access to the right books is crucial. Below is a curated list of essential reference books for aspirants:
| Book Name | Author |
| Complex Variables and Applications | Brown & Churchill |
| Integral Equations and Boundary Value Problems | M. D. Raisinghania |
| Foundations of Functional Analysis | S. Ponnusamy |
| Real Analysis | H. L. Royden & P. M. Fitzpatrick |
| CSIR-UGC NET/JRF/SLET Mathematical Sciences (Paper I & II) | Dr. A. Kumar |
| Fundamentals of Statistics | S. C. Gupta |
These books cover all major areas of the syllabus including Real Analysis, Complex Analysis, Functional Analysis, Integral Equations, and Statistics, providing a solid base for both theory and problem-solving practice.
CSIR NET Mathematics Sciences Preparation 3-Monthย Plan
CSIR NET Mathematical Sciences in 3 months with a plan that covers all important topics like Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics.
Month 1: Build Strong Fundamentals
Focus: High-weightage topics & conceptual clarity
| Week | Topics | Activities |
| Week 1 | Linear Algebra | Vector spaces, subspaces, basis, dimension, linear transformations; practice 30โ40 problems |
| Week 2 | Linear Algebra & Real Analysis | Matrices, eigenvalues, Cayley-Hamilton theorem, Inner product spaces; sequences, series, limits |
| Week 3 | Real Analysis | Continuity, differentiability, mean value theorem, uniform convergence, Riemann integration |
| Week 4 | Real Analysis | Improper integrals, functions of several variables, metric & normed spaces, compactness and connectedness |
Weekend Tasks: Solve previous year questions for Linear Algebra & Real Analysis
Month 2: Core Topics + Application
Focus: High & medium-weightage topics
| Week | Topics | Activities |
| Week 5 | Complex Analysis | Algebra of complex numbers, analytic functions, Cauchy-Riemann equations, contour integration |
| Week 6 | Complex Analysis & ODEs | Taylor & Laurent series, residues, Cauchyโs theorem; First-order ODEs, existence/uniqueness, singular solutions |
| Week 7 | ODEs & PDEs | Linear ODEs (homogeneous/non-homogeneous), variation of parameters, Sturm-Liouville problems; First-order PDEs (Lagrange & Charpit), Cauchy problem |
| Week 8 | PDEs & Numerical Analysis | Second-order PDEs classification, separation of variables; Numerical solutions of algebraic equations, Newton-Raphson, Gauss-Seidel, interpolation |
Weekend Tasks: Attempt topic-wise mock tests for Complex Analysis, ODEs, PDEs
Month 3: Revision, Practice & Low-Weight Topics
Focus: Revision, low-weight topics, and mock tests
| Week | Topics | Activities |
| Week 9 | Abstract Algebra | Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic & permutation groups, Sylow theorems |
| Week 10 | Rings & Fields | Rings, ideals, quotient rings, UFD, PID, Euclidean domain; Polynomial rings, irreducibility; Field extensions, Galois theory |
| Week 11 | Calculus of Variations & Classical Mechanics | Euler-Lagrange equation, variational methods; Lagrangeโs & Hamiltonโs equations, rigid body motion, small oscillations |
| Week 12 | Integral Equations, Topology & Final Revision | Fredholm & Volterra equations, resolvent kernel; Basis, dense sets, subspace/product topology, connectedness, compactness; Full syllabus revision + Previous year papers |
|
Related Topicsย |
|
| important topics for csir net Physical Science | important topics for csir net Life Science |
| important topics for csir net Chemistry | important topics for csir net Mathematicsย |
Structural Overview of the CSIR NET Mathematical Sciences Examination
The CSIR NET Mathematics Sciences Syllabus 2026is organized to test candidates through three partsโPart A, Part B, and Part C. Part A focuses on General Aptitude, while Part B and Part C dive deep into the core mathematical disciplines. The syllabus demands a transition from computational proficiency to rigorous logical proofs, making it significantly more advanced than the standard CUET PG Syllabus found in many postgraduate entrance exams.
A key feature of the CSIR NET Mathematics Sciences Syllabus 2026is the credit-based scoring system. Part B consists of single-choice questions, while Part C features multiple-select questions where no partial credit is awarded. This structure forces candidates to have an exhaustive understanding of every theorem and counter-example. While students might use CUET PG Books to brush up on basic algebra, the CSIR NET necessitates specialized advanced texts to cover the depth required for the NET qualification.
Understanding the unit-wise distribution is critical for time management. Unit I covers Analysis and Linear Algebra, which generally carry the highest weightage. Unit II moves into Abstract Algebra and Complex Analysis. Unit III includes Applied Mathematics topics like ODE, PDE, and Calculus of Variations. Finally, Unit IV is dedicated to Statistics. This breadth ensures that the CSIR NET Mathematics Sciences Syllabus 2026remains the gold standard for evaluating research potential in India.
Unit I: Mastery of Analysis and Linear Algebra
Within the CSIR NET Mathematics Sciences Syllabus, Unit I acts as the foundational pillar. Real Analysis involves the study of topology of R, sequences, series, and Riemann integration. Linear Algebra focuses on vector spaces, linear transformations, and canonical forms. These topics are not merely about solving equations; they require proving existence and uniqueness, which is a departure from the more application-heavy CUET PG Exam Pattern.
Candidates often find that the CUET PG Syllabus provides a surface-level introduction to these fields, but the CSIR NET requires delving into Lebesgue measure and metric spaces. Linear Algebra in this syllabus also extends to inner product spaces and bilinear forms. Successful aspirants prioritize these sections because they appear in both Part B and Part C, offering the highest potential for accumulating marks through conceptual clarity.
Proficiency in Unit I is often the deciding factor for ranking. Unlike the CUET PG Exam Pattern, which may rely on speed, the CSIR NET rewards the ability to identify subtle nuances in mathematical statements. For example, understanding the difference between pointwise and uniform convergence is a recurring theme that requires more than just a basic overview of calculus found in standard CUET PG Books.
Unit II: Advanced Algebra and Complex Analysis
Unit II of the CSIR NET Mathematics Sciences Syllabus 2026shifts toward Abstract Algebra and Complex Analysis. This section evaluates a candidate’s grasp of groups, rings, and fields, including advanced concepts like Sylow theorems and Galois theory. Complex Analysis covers the geometry of complex numbers, analytic functions, and the residue theorem. These topics form the bridge between pure mathematics and its various theoretical applications.
For many, the CUET PG Syllabus covers basic group theory, but the CSIR NET extends this to polynomial rings and irreducibility criteria. Complex Analysis requires a deep understanding of Cauchyโs integral formula and the maximum modulus principle. These are high-yield topics where precision is paramount. Using specialized literature instead of general CUET PG Books is highly recommended to master the rigorous proof-based nature of this unit.
The difficulty level in Unit II is characterized by its abstractness. Candidates must be comfortable with visualizing transformations in the complex plane and understanding the structural properties of algebraic systems. While the CUET PG Exam Pattern might focus on direct computations, the CSIR NET often asks about the properties of entire functions or the number of non-isomorphic groups of a certain order, demanding a higher level of intellectual engagement.
Unit III: Applied Mathematics and Differential Equations
The CSIR NET Mathematics Sciences Syllabus 2026dedicates Unit III to Applied Mathematics, covering Ordinary and Partial Differential Equations (ODE & PDE), Numerical Analysis, and the Calculus of Variations. This unit is often a favorite for candidates who prefer algorithmic problem-solving over abstract proofs. It includes the study of Greenโs functions, wave equations, and boundary value problems, which are essential for physical science applications.
While the CUET PG Syllabus includes basic ODE and PDE, the CSIR NET delves into second-order linear equations and the classification of first-order PDEs. Numerical Analysis requires understanding errors, interpolation, and numerical integration methods like Runge-Kutta. This section is highly scoring because the problems are often structured and follow predictable patterns, provided the candidate has practiced extensively with relevant materials.
Calculus of Variations and Linear Integral Equations are also critical components of this unit. These subjects involve finding extremals of functionals and solving Fredholm and Volterra equations. These topics are rarely covered in the CUET PG Exam Pattern, giving candidates who master them a distinct competitive advantage. Success here relies on a balance between theoretical derivations and numerical accuracy.
Unit IV: Probability and Statistics for Mathematics
Unit IV of the CSIR NET Mathematics Sciences Syllabus 2026is specialized for students with a background in Statistics. It covers Descriptive Statistics, Probability Distributions, and Statistical Inference. Topics include Markov chains, sampling distributions, and hypothesis testing. For a mathematics student, this unit offers an alternative path to scoring, especially in Part C where specific statistics problems can be less time-consuming than complex analysis proofs.
The overlap between this unit and the CUET PG Syllabus is minimal for pure math tracks but significant for those appearing in Statistics papers. The CSIR NET version focuses on the mathematical rigor of probability spaces and multivariate analysis. Understanding the properties of the Normal, Binomial, and Poisson distributions is standard, but the syllabus also requires knowledge of Gauss-Markov models and design of experiments.
Aspiring researchers often find that Unit IV requires a different mental framework than the rest of the CSIR NET Mathematics Sciences Syllabus. It is less about absolute certainty and more about likelihood and estimation. Using the right CUET PG Books as a starting point for probability can be helpful, but the advanced inference and regression topics in the NET require focused study of graduate-level statistics texts.
Critical Analysis: Why Traditional Proof-Learning May Fail
A common strategy for the CSIR NET Mathematics Sciences Syllabus 2026is to memorize standard proofs. However, this approach often fails in the contemporary exam environment. The current trend in the CSIR NET Exam Pattern is to present “modified theorems” or specific counter-examples that test the boundaries of a rule. If a student knows the proof of the Mean Value Theorem but cannot apply it to a non-differentiable function, they will likely struggle.
The limitation of many CUET PG Books is that they focus on “solved examples” rather than “conceptual boundaries.” To mitigate this, candidates should practice “mathematical stress-testing.” This involves taking a known theorem and seeing what happens when one of its conditions is removed. For instance, what happens to the Fundamental Theorem of Calculus if the function is not continuous? This analytical depth is what the CSIR NET rewards over rote memorization.
Furthermore, the “breadth-first” approach often leads to superficial knowledge. Given the choice in the CSIR NET Mathematics Sciences Syllabus, it is often more strategic to be an expert in three units than a novice in four. Over-extending into Unit IV without a statistics background, for example, can waste valuable preparation time that could be spent mastering the nuances of Lebesgue integration in Unit I.
Strategic Comparison: CSIR NET vs. CUET PG
Understanding the difference between the CSIR NET Mathematics Sciences Syllabus 2026and the CUET PG Syllabus is vital for career planning. The CUET PG is an entrance test for Master’s programs, focusing on undergraduate-level proficiency. In contrast, the CSIR NET is a qualifying exam for research and teaching, demanding a postgraduate-level grasp of complex systems. The CUET PG Exam Pattern is generally faster-paced with more questions, whereas the CSIR NET is slower and more analytical.
While you can use CUET PG Books for revising basic concepts of Group Theory or Vector Calculus, they will not suffice for the Advanced Topology or Measure Theory sections of the NET. The CUET PG Exam Pattern typically avoids the multiple-select questions (MSQs) that define Part C of the CSIR NET. In MSQs, if three options are correct and you only mark two, you receive zero marks. This lack of partial credit makes the NET significantly more punishing.
For students transitioning from the CUET PG Syllabus level to the CSIR NET, the first step is to upgrade their reading list. Transitioning from “how-to” books to “why” books is essential. This means moving from simple calculation-based exercises to proof-heavy literature that explores the underlying structure of mathematical logic.
Practical Application: The Role of Linear Algebra in Data Science
To see the CSIR NET Mathematics Sciences Syllabus 2026in action, consider the role of Linear Algebra in modern technology. Singular Value Decomposition (SVD) and Eigenvalue problems, which are core parts of the syllabus, are the mathematical engines behind Googleโs Search algorithm and Netflixโs recommendation systems. These are not just abstract concepts; they are tools for dimensionality reduction in massive datasets.
In a research scenario, a mathematician might use the properties of Hilbert spaces (Unit I) to develop new signal processing techniques. Similarly, the study of Differential Equations (Unit III) is the basis for modeling everything from the spread of infectious diseases to the behavior of financial markets. The CSIR NET Mathematics Sciences Syllabus 2026ensures that qualifiers have the mathematical maturity to contribute to these high-impact fields.
By viewing the syllabus through the lens of application, the abstract nature of topics like “Inner Product Spaces” becomes more grounded. Whether you are using CUET PG Books for a refresh or diving into advanced research papers, realizing that these mathematical structures govern our digital world provides extra motivation for the rigorous study required to clear the exam.
Recommended Books for Mathematics Sciences
Selecting the right resources is the most critical part of tackling the CSIR NET Mathematics Sciences Syllabus. For Real Analysis, H.L. Royden or Bartle and Sherbert are highly regarded for their clarity and rigor. Linear Algebra is best studied through Kenneth Hoffman and Ray Kunze, which provides the depth needed for the NET that standard CUET PG Books might lack.
For Unit II, Joseph Gallianโs “Contemporary Abstract Algebra” is excellent for group and ring theory, while Ponnusamyโs “Foundations of Complex Analysis” is a staple for the complex units. Unit III students should look toward S.L. Ross for Differential Equations. While the CUET PG Syllabus might be covered by general guides, the CSIR NET requires these standard reference books to handle the conceptual challenges of Part C.
It is also beneficial to keep a set of CUET PG Books for the General Aptitude section (Part A). Topics like logical reasoning, graphical analysis, and basic percentage calculations are common to both exams. Mastering these “easier” marks using the CUET PG Exam Pattern logic can provide a vital buffer for the more difficult math sections.
Effective Revision Strategies for the Mathematics Syllabus
Finalizing the CSIR NET Mathematics Sciences Syllabus 2026requires a disciplined revision phase. Creating a “Counter-Example Bank” is a highly effective technique. For every major theorem in the syllabus, write down at least two examples where the theorem does not apply because a specific condition is violated. This prepares you specifically for the “multiple-select” challenges of Part C.
Regularly practicing with the CUET PG Exam Pattern in mind for Part A, but switching to deep-thinking mode for Parts B and C, helps in cognitive flexibility. Mock tests should be taken in a single three-hour sitting to build the mental endurance needed for the actual exam. Since the CSIR NET Mathematics Sciences Syllabus 2026is vast, do not attempt to revise everything in the last week; focus on your “High-Yield” topics like Linear Algebra and Real Analysis.
Lastly, ensure you are familiar with the digital interface of the CBT mode. Unlike the paper-based CUET PG Exam Pattern of the past, the current NET requires comfort with on-screen reading and virtual navigation. By integrating these technical habits with a deep understanding of the CSIR NET Mathematics Sciences Syllabus, you position yourself for success in the 2025 examination cycle.
CSIR NET Mathematics Sciences preparation
Prepare for CSIR NET Mathematical Sciences with a complete syllabus covering Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics.
| Priority Level | Topics / Areas | Focus / Tips |
| High Priority | Linear Algebra, Real Analysis, Complex Analysis, ODEs & PDEs, Abstract Algebra | Must be mastered thoroughly; frequent in past papers; focus on concepts, problem-solving, and previous year questions |
| Medium Priority | Numerical Analysis, Topology, Calculus of Variations, Classical Mechanics | Important but less frequent; understand key methods and applications; practice selectively |
| Low Priority | Integral Equations, Functional Analysis | Appear rarely; prepare basics and key formulas; attempt only if time permits |
| General Aptitude | Logical reasoning, quantitative ability, analytical reasoning | Daily 20โ30 min practice; easy scoring area, ensure maximum marks in Part A |
| Revision | Entire Syllabus | Last 7โ10 days should be dedicated to full syllabus revision and mock tests for speed, accuracy, and confidence |
CSIR NET Mathematics Sciences Syllabus FAQs
Who prescribes the CSIR NET syllabus?
The CSIR NET syllabus is prescribed by the Council of Scientific and Industrial Research (CSIR) in India, and the exam is conducted by the National Testing Agency (NTA) following the guidelines set by CSIR.
How are questions distributed in each part of the CSIR NET Mathematical Science exam?
CSIR NET Mathematical Sciences exam consists of two papers. Paper 1 tests general aptitude with 50 questions carrying 35โ50 marks, while Paper 2 is subject-specific with 75 questions worth 100 marks, covering Units 1โ4. The question distribution generally reflects the syllabus weightage: Units 1 and 2 focus on Algebra, Analysis, and Topology; Unit 3 covers ODE, PDE, and Mechanics; and Unit 4 deals with Probability and Statistics. However, the NTA may slightly adjust the weightage each year.
How can exam analysis help me prepare for future CSIR NET Mathematical Science exams?
Analyzing past CSIR NET Mathematical Sciences exams helps candidates identify trends, such as repeated topics and frequently asked concepts. It also aids in time management, showing which sections require more time and attention. By focusing on weak areas, students can prioritize units where mistakes are common, while practicing question patterns improves familiarity with multiple-choice strategies and tricky conceptual problems, ultimately enhancing overall preparation and performance.
What does the CSIR NET Mathematical Science Syllabus cover?
The CSIR NET Mathematical Sciences syllabus covers four main units. Unit 1 focuses on Linear Algebra and Real Analysis, including matrices, determinants, vector spaces, sequences, series, and Riemann integration. Unit 2 includes Algebra, Complex Analysis, and Topology, covering group theory, rings, fields, analytic functions, and topological concepts. Unit 3 deals with Ordinary and Partial Differential Equations, Integral Equations, Calculus of Variations, and Classical Mechanics. Unit 4 covers Probability and Statistics, including probability theory, distributions, correlation, regression, and hypothesis testing.
