MSET (Maharashtra SET)
- 8
- Years
- 10
- Papers
- 1568
- Questions
Eligibility for Assistant Professor posts in Maharashtra and Goa. The Mathematical Sciences Paper II booklet has a common Section I, then a Mathematics section (II) and a Statistics section (III); each candidate answers Section I plus one of the other two.
Exam pattern
- Paper I: teaching and research aptitude (common to all subjects)
- Paper II: Mathematical Sciences — Section I, then Section II (Mathematics) or Section III (Statistics)
- Objective, multiple choice with four options
The most recent paper solved here, MSET June 2025, ran to 180 questions: 20 in Section I, 80 in Section II (mathematics) and 80 in Section III (statistics).
Conducted by Savitribai Phule Pune University. Patterns change from year to year, so confirm the current one at setexam.unipune.ac.in.
Topic analysis
How many questions each syllabus topic and subtopic was worth, year by year, across the 10 solved MSET papers (1568 questions). Sittings of the same year are counted together.
| Topic · subtopic | 2025 | 2024 | 2023 | 2021 | 2020 | 2019 | 2018 | 2017 | Total |
|---|---|---|---|---|---|---|---|---|---|
| Random Variables and Distribution Functions, Expectation and Moments | 17 | 17 | 22 | 16 | 20 | 16 | 10 | 11 | 129 |
| Random variables and distribution functions (univariate and multivariate) | 10 | 6 | 8 | 5 | 8 | 6 | 5 | 3 | 51 |
| Expectation and moments | 3 | 7 | 7 | 8 | 7 | 7 | 3 | 5 | 47 |
| Independent random variables, marginal and conditional distributions | 4 | 4 | 7 | 3 | 5 | 3 | 2 | 3 | 31 |
| Methods of Estimation, Properties of Estimators | 8 | 5 | 8 | 7 | 5 | 7 | 10 | 9 | 59 |
| Properties of estimators | 8 | 5 | 7 | 6 | 5 | 7 | 8 | 8 | 54 |
| Methods of estimation | · | · | 1 | 1 | · | · | 2 | 1 | 5 |
| Linear Programming Problem, Simplex Method, Duality | 3 | 3 | 3 | 6 | 10 | 9 | 9 | 7 | 50 |
| Linear programming problem | 2 | 1 | 1 | 2 | 5 | 5 | 6 | 4 | 26 |
| Duality | 1 | 1 | 2 | 2 | 4 | 4 | 2 | 2 | 18 |
| Simplex methods | · | 1 | · | 2 | 1 | · | 1 | 1 | 6 |
| Continuity, Uniform Continuity, Differentiability, Mean Value Theorem | 2 | 7 | 5 | 4 | 7 | 5 | 6 | 7 | 43 |
| Differentiability, mean value theorem | 1 | 6 | 4 | 2 | 6 | 5 | 5 | 3 | 32 |
| Continuity, uniform continuity | 1 | 1 | 1 | 2 | 1 | · | 1 | 4 | 11 |
| Groups, Subgroups, Sylow Theorems, Cayley's Theorem | 5 | 5 | 5 | 6 | 4 | 5 | 5 | 7 | 42 |
| Groups, subgroups, normal subgroups, quotient groups, homomorphisms | 4 | 2 | 2 | 3 | 1 | 3 | 3 | 1 | 19 |
| Cyclic groups, permutation groups, Cayley's theorem | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 5 | 16 |
| Class equations, Sylow theorems | · | 2 | 1 | 1 | 1 | · | 1 | 1 | 7 |
| Sequences and Series | 3 | 9 | 6 | 4 | 4 | 5 | 4 | 2 | 37 |
| Sequences and series of functions, uniform convergence | 1 | 6 | 3 | 1 | 2 | 2 | 1 | 1 | 17 |
| Sequences and series, convergence, limsup, liminf | 2 | 2 | 2 | 3 | 2 | 3 | 2 | 1 | 17 |
| Bolzano Weierstrass theorem, Heine Borel theorem | · | 1 | 1 | · | · | · | 1 | · | 3 |
| Metric Spaces, Compactness, Connectedness, Normed Linear Spaces | 5 | 2 | 7 | 3 | 5 | 5 | 5 | 4 | 36 |
| Metric spaces, compactness, connectedness | 3 | 1 | 3 | 1 | 2 | 3 | 2 | 1 | 16 |
| Normed linear Spaces | · | · | 2 | 1 | 2 | · | 3 | 3 | 11 |
| Spaces of continuous functions as examples | 2 | 1 | 2 | 1 | 1 | 2 | · | · | 9 |
| Monotonic Functions, Bounded Variation, Lebesgue Measure & Integral | 3 | 7 | 5 | 4 | 10 | 6 | 35 | ||
| Lebesgue measure, Lebesgue integral | · | 2 | · | 4 | 5 | 3 | 8 | 6 | 28 |
| Functions of bounded variation | · | 1 | · | 3 | · | · | 1 | · | 5 |
| Monotonic functions, types of discontinuity | · | · | · | · | · | 1 | 1 | · | 2 |
| Tests of Hypotheses: MP and UMP Tests, Likelihood Ratio Tests | 3 | 3 | 2 | 2 | 5 | 3 | 8 | 7 | 33 |
| Likelihood ratio tests | 2 | 3 | 1 | 2 | 4 | 3 | 7 | 4 | 26 |
| Tests of hypotheses: most powerful and uniformly most powerful tests | 1 | · | 1 | · | 1 | · | 1 | 3 | 7 |
| Multivariate Normal Distribution, Wishart Distribution, Quadratic Forms | 2 | 2 | 3 | 5 | 4 | 6 | 5 | 6 | 33 |
| Multivariate normal distribution | 1 | 2 | 1 | 3 | 3 | 5 | 2 | 3 | 20 |
| Wishart distribution and their properties | 1 | · | 1 | 2 | · | · | 3 | 2 | 9 |
| Distribution of quadratic forms | · | · | 1 | · | 1 | 1 | · | 1 | 4 |
| Standard Discrete and Continuous Univariate Distributions | 2 | 3 | 4 | 5 | 4 | 3 | 6 | 5 | 32 |
| Standard continuous univariate distributions | 2 | 2 | 3 | 3 | 3 | 1 | 3 | 3 | 20 |
| Standard discrete univariate distributions | · | 1 | 1 | 2 | 1 | 2 | 3 | 2 | 12 |
| Algebra of Complex Numbers, Power Series, Transcendental Functions | 5 | 2 | 5 | 4 | 5 | 2 | 5 | 3 | 31 |
| Algebra of complex numbers, the complex plane | 3 | 1 | 2 | 1 | 3 | · | 4 | 1 | 15 |
| Polynomials, power series | 1 | 1 | 2 | 1 | 2 | · | 1 | 1 | 9 |
| Transcendental functions such as exponential, trigonometric and hyperbolic functions | 1 | · | 1 | 2 | · | 2 | · | 1 | 7 |
| Simple and Multiple Linear Regression, Logistic Regression | 4 | 4 | 4 | 3 | 3 | 3 | 5 | 5 | 31 |
| Simple and multiple linear regression | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 14 |
| Logistic regression | 1 | 1 | 2 | · | 1 | · | 2 | 2 | 9 |
| Elementary regression diagnostics | 2 | 1 | · | 1 | · | 2 | 1 | 1 | 8 |
| Algebra of Matrices, Rank, Determinant, Linear Equations | 4 | 8 | 3 | 2 | 3 | 3 | 3 | 4 | 30 |
| Rank and determinant of matrices | 2 | 5 | 2 | · | 3 | 2 | 2 | 2 | 18 |
| Algebra of matrices | 1 | 2 | 1 | 1 | · | · | 1 | 1 | 7 |
| Linear equations | 1 | 1 | · | 1 | · | 1 | · | 1 | 5 |
| Variation of a Functional, Euler-Lagrange Equation, Conditions for Extrema | 6 | 3 | 3 | 4 | 3 | 2 | 2 | 3 | 26 |
| Variation of a functional, Euler-Lagrange equation | 3 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 14 |
| Necessary and sufficient conditions for extrema | 3 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 12 |
| Characteristic Functions, Probability Inequalities | 3 | 1 | 2 | 5 | 3 | 2 | 4 | 5 | 25 |
| Characteristic functions | 2 | 1 | 1 | 2 | 2 | 1 | 2 | 4 | 15 |
| Probability inequalities (Tchebyshef, Markov, Jensen) | 1 | · | 1 | 3 | 1 | 1 | 2 | 1 | 10 |
| Markov Chains: Classification of States, Stationary Distribution | 4 | 4 | 5 | 3 | 2 | 2 | 2 | 3 | 25 |
| Classification of states | 3 | 1 | 4 | · | 1 | · | · | 1 | 10 |
| Stationary distribution | 1 | · | 1 | 2 | · | 2 | 2 | · | 8 |
| Markov chains with finite and countable state space | · | 2 | · | 1 | 1 | · | · | 2 | 6 |
| Limiting behaviour of n-step transition probabilities | · | 1 | · | · | · | · | · | · | 1 |
| Rings, Ideals, UFD, PID, Euclidean Domain | 2 | 2 | 3 | 2 | 4 | 2 | 6 | 3 | 24 |
| Rings, ideals, prime and maximal ideals, quotient rings | 1 | 1 | · | 2 | 3 | · | 5 | 1 | 13 |
| Unique factorization domain, principal ideal domain, Euclidean domain | 1 | 1 | 3 | · | 1 | 2 | 1 | 2 | 11 |
| Fredholm and Volterra Type, Separable Kernels, Resolvent Kernel | 6 | 3 | 2 | 2 | 3 | 2 | 3 | 3 | 24 |
| Linear integral equation of the first and second kind of Fredholm and Volterra type | 3 | 1 | · | 1 | 1 | 2 | 2 | 2 | 12 |
| Solutions with separable kernels | 1 | 2 | 2 | · | 1 | · | 1 | · | 7 |
| Characteristic numbers and eigenfunctions, resolvent kernel | 2 | · | · | 1 | 1 | · | · | 1 | 5 |
| Simple Random, Stratified and Systematic Sampling | 3 | 2 | 3 | 4 | 4 | 2 | 3 | 3 | 24 |
| Systematic sampling | 1 | 2 | 2 | 1 | 3 | · | 1 | 1 | 11 |
| Stratified sampling | 1 | · | 1 | 1 | 1 | 2 | · | 1 | 7 |
| Simple random sampling | 1 | · | · | 2 | · | · | 2 | 1 | 6 |
| Vector Spaces, Subspaces, Linear Dependence, Basis, Dimension | 3 | 4 | 3 | 6 | 5 | 2 | 1 | 24 | |
| Basis, dimension | · | 2 | 1 | 3 | 4 | 4 | 1 | 1 | 16 |
| Vector spaces, subspaces, linear dependence | · | 1 | 3 | · | 2 | 1 | 1 | · | 8 |
| Taylor Series, Laurent Series, Calculus of Residues | 2 | 4 | 3 | 1 | 3 | 2 | 5 | 3 | 23 |
| Calculus of residues | 2 | 3 | 2 | 1 | 3 | 2 | 4 | 2 | 19 |
| Taylor series, Laurent series | · | 1 | 1 | · | · | · | 1 | 1 | 4 |
| General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's Function | 2 | 2 | 5 | 4 | 2 | 2 | 4 | 2 | 23 |
| General theory of homogenous and non-homogeneous linear ODEs | 2 | · | 4 | 2 | 2 | · | 2 | 1 | 13 |
| Sturm-Liouville boundary value problem, Green's function | · | 1 | · | 1 | · | 2 | 1 | · | 5 |
| Variation of parameters | · | 1 | 1 | 1 | · | · | 1 | 1 | 5 |
| Lagrange and Charpit Methods, Cauchy Problem for First Order PDEs | 6 | 3 | 4 | 1 | 1 | 3 | 5 | 23 | |
| Cauchy problem for first order PDEs | 6 | · | 3 | · | · | 1 | 1 | 1 | 12 |
| Lagrange and Charpit methods for solving first order PDEs | · | 3 | 1 | 1 | · | · | 2 | 4 | 11 |
| Finite Differences, Lagrange/Hermite/Spline Interpolation | 4 | 3 | 5 | 2 | 2 | 1 | 3 | 3 | 23 |
| Finite differences | 3 | 2 | 4 | · | 2 | 1 | 2 | 1 | 15 |
| Lagrange, Hermite and spline interpolation | 1 | 1 | 1 | 2 | · | · | 1 | 2 | 8 |
| Separation Axioms, Connectedness and Compactness | 5 | 5 | 1 | 1 | 2 | 1 | 3 | 3 | 21 |
| Connectedness and compactness | 4 | 5 | · | 1 | 2 | 1 | 2 | 2 | 17 |
| Separation axioms | 1 | · | 1 | · | · | · | 1 | 1 | 4 |
| Existence & Uniqueness, Singular Solutions, Systems of First Order ODEs | 5 | 3 | 3 | 2 | 3 | 2 | 3 | 21 | |
| Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations | 3 | 3 | 3 | 2 | · | 3 | 2 | 2 | 18 |
| System of first order ODEs | 1 | · | · | · | · | · | · | 1 | 2 |
| Singular solutions of first order ODEs | 1 | · | · | · | · | · | · | · | 1 |
| Modes of Convergence, Laws of Large Numbers, Central Limit Theorem | 2 | 4 | 3 | 1 | 2 | 3 | 3 | 3 | 21 |
| Weak and strong laws of large numbers | 1 | 3 | 1 | · | 1 | 1 | 1 | 2 | 10 |
| Central Limit theorems (i.i.d. case) | · | 1 | 1 | 1 | 1 | 1 | 1 | · | 6 |
| Modes of convergence | 1 | · | 1 | · | · | 1 | 1 | 1 | 5 |
| Elementary Set Theory, Real Number System, Supremum, Infimum | 3 | 2 | 5 | 5 | 4 | 19 | |||
| Elementary set theory, finite, countable and uncountable sets | 2 | 2 | 5 | 5 | · | 2 | · | · | 16 |
| Real number system as a complete ordered field | 1 | · | · | · | · | 1 | · | · | 2 |
| Archimedean property, supremum, infimum | · | · | · | · | · | 1 | · | · | 1 |
| Generalized Coordinates, Lagrange's Equations | 4 | 4 | 2 | 2 | 2 | 2 | 3 | 19 | |
| Generalized coordinates, Lagrange's equations | 4 | 4 | 2 | 2 | · | 2 | 2 | 3 | 19 |
| Connectedness and Orthogonality of Block Designs, BIBD | 4 | 3 | 1 | 2 | 3 | 2 | 2 | 2 | 19 |
| BIBD | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 11 |
| Connectedness and orthogonality of block designs | 1 | 2 | · | 1 | 2 | 1 | · | 1 | 8 |
| Permutations, Combinations, Pigeon-Hole Principle, Inclusion-Exclusion | 1 | 6 | 2 | 2 | 3 | 1 | 2 | 1 | 18 |
| Permutations, combinations | 1 | 4 | 2 | 2 | 1 | 1 | 1 | 1 | 13 |
| Pigeon-hole principle, inclusion-exclusion principle, derangements | · | 2 | · | · | 2 | · | 1 | · | 5 |
| Fields, Finite Fields, Field Extensions, Galois Theory | 3 | 2 | 2 | 2 | 2 | 4 | 2 | 17 | |
| Fields, finite fields, field extensions | 2 | 2 | 2 | 2 | · | 1 | 3 | 2 | 14 |
| Galois Theory | 1 | · | · | · | · | 1 | 1 | · | 3 |
| Fundamental Theorem of Arithmetic, Congruences, Chinese Remainder Theorem | 2 | 1 | 2 | 1 | 4 | 3 | 4 | 17 | |
| Congruences, Chinese Remainder Theorem | · | · | 1 | 2 | · | 3 | 2 | 1 | 9 |
| Fundamental theorem of arithmetic, divisibility in Z | 1 | · | · | · | 1 | 1 | · | 2 | 5 |
| Euler's phi-function, primitive roots | 1 | · | · | · | · | · | 1 | 1 | 3 |
| Basis, Dense Sets, Subspace and Product Topology | 3 | 2 | 5 | 3 | 1 | 1 | 2 | 17 | |
| Subspace and product topology | 3 | 1 | 3 | · | · | 1 | 1 | 2 | 11 |
| Basis, dense sets | · | 1 | 2 | · | 3 | · | · | · | 6 |
| Sample Space, Discrete Probability, Independent Events, Bayes Theorem | 5 | 1 | 3 | 3 | 2 | 3 | 17 | ||
| Sample space, discrete probability | · | 1 | · | 2 | · | · | 1 | 3 | 7 |
| Independent events | 1 | · | · | 1 | · | 3 | 1 | · | 6 |
| Bayes theorem | 4 | · | · | · | · | · | · | · | 4 |
| Algebra of Linear Transformations | 1 | 3 | 4 | 3 | 1 | 3 | 1 | 16 | |
| Algebra of linear transformations | 1 | 3 | 4 | · | 3 | 1 | 3 | 1 | 16 |
| Sampling Distributions, Standard Errors, Asymptotic Distributions | 1 | 1 | 3 | 3 | 5 | 3 | 16 | ||
| Asymptotic distributions | 1 | · | · | 1 | 3 | 2 | 3 | 2 | 12 |
| Sampling distributions | · | · | · | · | · | 1 | 1 | · | 2 |
| Standard errors | · | · | · | · | · | · | 1 | 1 | 2 |
| Functions of Several Variables, Inverse & Implicit Function Theorems | 1 | 1 | 3 | 5 | 5 | 15 | |||
| Functions of several variables, directional derivative, partial derivative | 1 | · | · | · | · | · | 3 | 2 | 6 |
| Derivative as a linear transformation | · | · | · | 1 | · | · | 2 | 2 | 5 |
| Inverse and implicit function theorems | · | · | 1 | 2 | · | · | · | 1 | 4 |
| Steady-State Solutions of Markovian Queuing Models (M/M/1, M/M/C, M/G/1) | 2 | 1 | 2 | 3 | 2 | 2 | 2 | 14 | |
| M/M/1 | 2 | 1 | 1 | 2 | 1 | 1 | · | 2 | 10 |
| M/M/C | · | · | 1 | · | 1 | 1 | · | · | 3 |
| M/G/1 | · | · | · | 1 | · | · | · | · | 1 |
| Gauss-Markov Models, Estimability, Best Linear Unbiased Estimators | 1 | 1 | 1 | 1 | 3 | 3 | 4 | 14 | |
| Best linear unbiased estimators | · | 1 | · | · | · | 1 | 1 | 4 | 7 |
| Estimability of parameters | · | · | 1 | 1 | 1 | 2 | 1 | · | 6 |
| Gauss-Markov models | · | · | · | · | · | · | 1 | · | 1 |
| Elementary Queuing and Inventory Models | 1 | 1 | 4 | 3 | 3 | 2 | 14 | ||
| Elementary inventory models | · | 1 | · | 1 | 2 | 2 | 1 | 2 | 9 |
| Elementary queuing models | · | · | · | · | 2 | 1 | 2 | · | 5 |
| Liouville's Theorem, Maximum Modulus Principle, Open Mapping Theorem | 3 | 1 | 2 | 1 | 1 | 2 | 3 | 13 | |
| Liouville's theorem | 2 | · | 1 | 1 | · | 1 | 1 | · | 6 |
| Open mapping theorem | · | 1 | · | · | · | · | 1 | 2 | 4 |
| Maximum modulus principle, Schwarz lemma | 1 | · | 1 | · | · | · | · | 1 | 3 |
| Elementary Bayesian Inference | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 1 | 13 |
| Elementary Bayesian inference | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 1 | 13 |
| Completely Randomized, Randomized Block and Latin-Square Designs | 1 | 2 | 1 | 2 | 2 | 2 | 3 | 13 | |
| Latin-square designs | 1 | · | · | 1 | · | 1 | · | 2 | 5 |
| Completely randomized designs | · | 2 | 1 | · | · | 1 | · | · | 4 |
| Randomized block designs | · | · | · | 1 | 2 | · | · | 1 | 4 |
| 2^K Factorial Experiments: Confounding and Construction | 1 | 2 | 2 | 1 | 2 | 4 | 1 | 13 | |
| 2K factorial experiments: confounding | · | · | 1 | 2 | 1 | 2 | 4 | 1 | 11 |
| 2K factorial experiments: construction | · | 1 | 1 | · | · | · | · | · | 2 |
| Hazard Function and Failure Rates, Censoring and Life Testing | 2 | 2 | 3 | 2 | 2 | 1 | 12 | ||
| Hazard function and failure rates | 1 | 1 | 3 | · | 2 | 2 | 1 | · | 10 |
| Censoring and life testing | 1 | 1 | · | · | · | · | · | · | 2 |
| Separation of Variables (Laplace, Heat and Wave Equations) | 3 | 1 | 3 | 2 | 2 | 1 | 12 | ||
| Method of separation of variables for Laplace, Heat and Wave equations | · | 3 | 1 | 3 | 2 | 2 | 1 | · | 12 |
| Inner Product Spaces, Orthonormal Basis | 1 | 1 | 1 | 2 | 3 | 4 | 12 | ||
| Inner product spaces, orthonormal basis | · | · | 1 | 1 | 1 | 2 | 3 | 4 | 12 |
| Potential Flow, Streamlines, Doublets | 4 | 4 | 4 | 12 | |||||
| Potential flow, streamlines, sources, sinks and doublets | · | · | · | 4 | 4 | 4 | · | · | 12 |
| Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem | 2 | 1 | 1 | 2 | 5 | 11 | |||
| Cayley-Hamilton theorem | · | 1 | · | · | 1 | · | 1 | 3 | 6 |
| Eigenvalues and eigenvectors | 2 | · | · | · | · | · | 1 | 2 | 5 |
| Conformal Mappings, Mobius Transformations | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 11 |
| Conformal mappings, Mobius transformations | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 11 |
| Motion of Rigid Bodies, Euler's Dynamical Equations, Small Oscillations | 1 | 2 | 2 | 1 | 2 | 1 | 1 | 1 | 11 |
| Euler's dynamical equations for the motion of a rigid body about an axis | 1 | 1 | 2 | · | 1 | 1 | 1 | 1 | 8 |
| Two-dimensional motion of rigid bodies | · | 1 | · | 1 | 1 | · | · | · | 3 |
| Poisson and Birth-and-Death Processes | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 11 | |
| Poisson process | 1 | 1 | · | 2 | 2 | 2 | · | 1 | 9 |
| Birth-and-death processes | · | 1 | · | · | · | · | 1 | · | 2 |
| Analysis of Discrete Data and Chi-Square Test of Goodness of Fit | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 11 | |
| Chi-square test of goodness of fit | 1 | 2 | 1 | 2 | 1 | 2 | 2 | · | 11 |
| Life Tables, Mortality Rate | 1 | 3 | 2 | 2 | 1 | 2 | 11 | ||
| Life tables, mortality and fertility rates | 1 | · | · | 3 | 2 | 2 | 1 | 2 | 11 |
| Curves and Surfaces, Curvature | 3 | 1 | 1 | 3 | 3 | 11 | |||
| Curves and surfaces, curvature and torsion | · | · | · | 3 | 1 | 1 | 3 | 3 | 11 |
| Classification of Second Order PDEs | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 10 | |
| Classification of second order PDEs | 2 | 2 | 1 | · | 1 | 1 | 1 | 1 | 9 |
| General solution of higher order PDEs with constant coefficients | · | · | · | · | · | · | · | 1 | 1 |
| Analysis of Variance and Covariance, Fixed/Random/Mixed Effects | 2 | 3 | 1 | 1 | 1 | 2 | 10 | ||
| Analysis of variance and covariance | 2 | 2 | 1 | 1 | · | · | 1 | · | 7 |
| Fixed, random and mixed effects models | · | 1 | · | · | 1 | · | 1 | · | 3 |
| Matrix Representation, Change of Basis, Canonical and Jordan Forms | 1 | 1 | 1 | 3 | 3 | 9 | |||
| Jordan forms | 1 | · | 1 | 1 | · | · | 1 | 2 | 6 |
| Matrix representation of linear transformations | · | · | · | · | · | · | 2 | 1 | 3 |
| Hamilton's Canonical Equations, Hamilton's Principle | 2 | 3 | 1 | 1 | 1 | 1 | 9 | ||
| Hamilton's canonical equations | 2 | · | 3 | 1 | 1 | 1 | 1 | · | 9 |
| Confidence Intervals | 1 | 2 | 2 | 2 | 2 | 9 | |||
| Confidence intervals | 1 | · | · | 2 | 2 | 2 | · | 2 | 9 |
| Ratio and Regression Methods | 1 | 1 | 1 | 2 | 2 | 2 | 9 | ||
| Ratio and regression methods | · | 1 | 1 | 1 | · | 2 | 2 | 2 | 9 |
| Time Series Models | 1 | 1 | 4 | 3 | 9 | ||||
| Autoregressive, moving average and ARIMA models | · | · | · | 1 | · | · | 2 | 1 | 4 |
| Stationarity, autocorrelation and partial autocorrelation | · | · | · | · | · | · | 1 | 2 | 3 |
| Forecasting from a fitted model | · | · | · | · | 1 | · | 1 | · | 2 |
| Descriptive Statistics, Exploratory Data Analysis | 3 | 1 | 1 | 1 | 1 | 1 | 8 | ||
| Descriptive statistics | 3 | · | 1 | 1 | · | 1 | · | · | 6 |
| Exploratory data analysis | · | 1 | · | · | 1 | · | · | · | 2 |
| Nonparametric Tests, Rank Correlation, Test for Independence | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 8 | |
| Simple nonparametric tests for one and two sample problems | 1 | 1 | · | 1 | · | 1 | 1 | 1 | 6 |
| Rank correlation and test for independence | · | · | · | · | 1 | 1 | · | · | 2 |
| Transportation and Assignment Problems | 1 | 2 | 1 | 2 | 1 | 1 | 8 | ||
| Transportation problem: feasibility, basic feasible solutions and optimality | · | · | · | 1 | 1 | 1 | 1 | 1 | 5 |
| Assignment problem | · | 1 | · | 1 | · | 1 | · | · | 3 |
| Laplace Transform | 1 | 2 | 1 | 2 | 2 | 8 | |||
| Laplace transform | · | · | · | 1 | 2 | 1 | 2 | 2 | 8 |
| Analytic Functions, Cauchy-Riemann Equations | 1 | 1 | 1 | 1 | 1 | 2 | 7 | ||
| Analytic functions, Cauchy-Riemann equations | 1 | 1 | 1 | 1 | 1 | · | · | 2 | 7 |
| Contour Integral, Cauchy's Theorem, Cauchy's Integral Formula | 1 | 2 | 2 | 2 | 7 | ||||
| Cauchy's integral formula | 1 | 1 | · | · | · | · | 1 | 2 | 5 |
| Contour integral, Cauchy's theorem | · | 1 | · | · | · | · | 1 | · | 2 |
| Probability Proportional to Size Sampling | 1 | 1 | 1 | 2 | 2 | 7 | |||
| Probability proportional to size sampling | 1 | · | 1 | · | · | 1 | 2 | 2 | 7 |
| Distribution of Order Statistics and Range | 1 | 2 | 1 | 3 | 7 | ||||
| Distribution of range | · | · | · | · | 1 | · | 1 | 2 | 4 |
| Distribution of order statistics | · | 1 | · | · | 1 | · | · | 1 | 3 |
| Graphs, Trees, Connectivity | 3 | 2 | 1 | 1 | 7 | ||||
| Graphs, trees, connectivity and colouring | · | · | · | 3 | 2 | 1 | · | 1 | 7 |
| Polynomial Rings and Irreducibility Criteria | 2 | 1 | 1 | 2 | 6 | ||||
| Polynomial rings and irreducibility criteria | 2 | 1 | · | 1 | · | · | · | 2 | 6 |
| Data Reduction: PCA, Discriminant, Cluster Analysis | 1 | 2 | 1 | 1 | 1 | 6 | |||
| Principle component analysis | 1 | 1 | · | · | · | · | · | 1 | 3 |
| Canonical correlation | · | · | · | · | · | · | 1 | · | 1 |
| Cluster analysis | · | 1 | · | · | · | · | · | · | 1 |
| Discriminant analysis | · | · | 1 | · | · | · | · | · | 1 |
| Riemann Sums and Riemann Integral, Improper Integrals | 1 | 1 | 2 | 1 | 1 | 6 | |||
| Riemann sums and Riemann integral | · | · | · | 1 | · | 2 | · | 1 | 4 |
| Improper Integrals | · | · | 1 | · | · | · | 1 | · | 2 |
| Fourier Transform | 1 | 2 | 1 | 1 | 1 | 6 | |||
| Fourier transform | · | · | · | 1 | 2 | 1 | 1 | 1 | 6 |
| Martingales | 1 | 1 | 1 | 1 | 2 | 6 | |||
| Martingales, stopping times and martingale convergence | · | · | · | 1 | 1 | 1 | 1 | 2 | 6 |
| Quadratic Forms, Reduction and Classification | 2 | 1 | 1 | 1 | 5 | ||||
| Quadratic forms, reduction and classification of quadratic forms | 2 | · | 1 | · | · | 1 | · | 1 | 5 |
| Partial and Multiple Correlation Coefficients | 1 | 1 | 1 | 1 | 1 | 5 | |||
| Partial and multiple correlation coefficients and related tests | · | 1 | 1 | 1 | · | 1 | 1 | · | 5 |
| Dynamic and Integer Programming | 1 | 2 | 1 | 1 | 5 | ||||
| Dynamic programming and Bellman's principle of optimality | · | · | · | 1 | 2 | 1 | · | · | 4 |
| Integer programming and branch and bound | · | · | · | · | · | · | · | 1 | 1 |
| Lattice Theory (Distributive/Modular/Boolean Lattices) | 3 | 1 | 1 | 5 | |||||
| Lattices and Boolean algebras | · | · | · | · | · | 3 | 1 | 1 | 5 |
| Numerical Differentiation and Integration | 2 | 1 | 1 | 4 | |||||
| Numerical differentiation and integration | 2 | · | · | · | 1 | · | 1 | · | 4 |
| Sequencing and Project Scheduling | 1 | 1 | 1 | 1 | 4 | ||||
| Sequencing jobs on machines (Johnson's rule) | · | · | · | · | 1 | · | 1 | 1 | 3 |
| Project scheduling: CPM and PERT | · | · | · | 1 | · | · | · | · | 1 |
| Series and Parallel Systems | 1 | 1 | 1 | 3 | |||||
| Series and parallel systems | · | 1 | · | · | · | · | 1 | 1 | 3 |
| Game Theory | 1 | 1 | 1 | 3 | |||||
| Two-person zero-sum games, saddle points and mixed strategies | · | · | · | 1 | · | · | 1 | 1 | 3 |
| Acceptance Sampling | 2 | 1 | 3 | ||||||
| Sampling inspection plans, average outgoing quality and rectifying inspection | · | · | · | 2 | · | · | · | 1 | 3 |
| Control Charts | 1 | 1 | 1 | 3 | |||||
| Average run length and chart performance | · | · | · | · | · | · | 1 | 1 | 2 |
| Control charts for variables and attributes | · | · | · | · | 1 | · | · | · | 1 |
| Variational Methods for Boundary Value Problems | 1 | 1 | 2 | ||||||
| Variational methods for boundary value problems in ordinary and partial differential equations | · | 1 | · | · | · | · | 1 | · | 2 |
| Numerical Solutions of Algebraic Equations, Newton-Raphson, Rate of Convergence | 1 | 1 | 2 | ||||||
| Method of iteration and Newton-Raphson method | · | · | 1 | · | · | 1 | · | · | 2 |
| Replacement Models | 1 | 1 | 2 | ||||||
| Individual and group replacement policies | · | · | · | 1 | · | 1 | · | · | 2 |
| Solution of Linear Systems: Gauss Elimination and Gauss-Seidel | 1 | 1 | |||||||
| Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods | · | 1 | · | · | · | · | · | · | 1 |
| Numerical Solutions of ODEs (Picard, Euler, Runge-Kutta) | 1 | 1 | |||||||
| Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods | · | · | · | · | · | · | · | 1 | 1 |
| Response Surface Designs | 1 | 1 | |||||||
| Response surface designs and rotatability | · | · | · | · | · | · | · | 1 | 1 |
| All topics | 180 | 180 | 180 | 190 | 190 | 190 | 229 | 229 | 1568 |
Syllabus
From the Savitribai Phule Pune University Mathematical Sciences (subject code 30) syllabus. The MSET Mathematical Sciences syllabus follows the CSIR-UGC NET syllabus. Paper II Units 1-3 are mathematics and Unit 4 is statistics. The board prints Unit 4 as one paragraph, so the topic headings below group the syllabus's own clauses. Always check it against the current notification.
Unit 1
Analysis
- Elementary Set Theory, Real Number System, Supremum, InfimumElementary set theory, finite, countable and uncountable sets · Real number system as a complete ordered field · Archimedean property, supremum, infimum
- Sequences and SeriesSequences and series, convergence, limsup, liminf · Bolzano Weierstrass theorem, Heine Borel theorem · Sequences and series of functions, uniform convergence
- Continuity, Uniform Continuity, Differentiability, Mean Value TheoremContinuity, uniform continuity · Differentiability, mean value theorem
- Riemann Sums and Riemann Integral, Improper IntegralsRiemann sums and Riemann integral · Improper Integrals
- Monotonic Functions, Bounded Variation, Lebesgue Measure & IntegralMonotonic functions, types of discontinuity · Functions of bounded variation · Lebesgue measure, Lebesgue integral
- Functions of Several Variables, Inverse & Implicit Function TheoremsFunctions of several variables, directional derivative, partial derivative · Derivative as a linear transformation · Inverse and implicit function theorems
- Metric Spaces, Compactness, Connectedness, Normed Linear SpacesMetric spaces, compactness, connectedness · Normed linear Spaces · Spaces of continuous functions as examples
Linear Algebra
- Vector Spaces, Subspaces, Linear Dependence, Basis, DimensionVector spaces, subspaces, linear dependence · Basis, dimension
- Algebra of Linear TransformationsAlgebra of linear transformations
- Algebra of Matrices, Rank, Determinant, Linear EquationsAlgebra of matrices · Rank and determinant of matrices · Linear equations
- Eigenvalues and Eigenvectors, Cayley-Hamilton TheoremEigenvalues and eigenvectors · Cayley-Hamilton theorem
- Matrix Representation, Change of Basis, Canonical and Jordan FormsMatrix representation of linear transformations · Change of basis, canonical forms, diagonal forms, triangular forms · Jordan forms
- Inner Product Spaces, Orthonormal BasisInner product spaces, orthonormal basis
- Quadratic Forms, Reduction and ClassificationQuadratic forms, reduction and classification of quadratic forms
Unit 2
Complex Analysis
- Algebra of Complex Numbers, Power Series, Transcendental FunctionsAlgebra of complex numbers, the complex plane · Polynomials, power series · Transcendental functions such as exponential, trigonometric and hyperbolic functions
- Analytic Functions, Cauchy-Riemann EquationsAnalytic functions, Cauchy-Riemann equations
- Contour Integral, Cauchy's Theorem, Cauchy's Integral FormulaContour integral, Cauchy's theorem · Cauchy's integral formula
- Liouville's Theorem, Maximum Modulus Principle, Open Mapping TheoremLiouville's theorem · Maximum modulus principle, Schwarz lemma · Open mapping theorem
- Taylor Series, Laurent Series, Calculus of ResiduesTaylor series, Laurent series · Calculus of residues
- Conformal Mappings, Mobius TransformationsConformal mappings, Mobius transformations
Algebra
- Permutations, Combinations, Pigeon-Hole Principle, Inclusion-ExclusionPermutations, combinations · Pigeon-hole principle, inclusion-exclusion principle, derangements
- Fundamental Theorem of Arithmetic, Congruences, Chinese Remainder TheoremFundamental theorem of arithmetic, divisibility in Z · Congruences, Chinese Remainder Theorem · Euler's phi-function, primitive roots
- Groups, Subgroups, Sylow Theorems, Cayley's TheoremGroups, subgroups, normal subgroups, quotient groups, homomorphisms · Cyclic groups, permutation groups, Cayley's theorem · Class equations, Sylow theorems
- Rings, Ideals, UFD, PID, Euclidean DomainRings, ideals, prime and maximal ideals, quotient rings · Unique factorization domain, principal ideal domain, Euclidean domain
- Polynomial Rings and Irreducibility CriteriaPolynomial rings and irreducibility criteria
- Fields, Finite Fields, Field Extensions, Galois TheoryFields, finite fields, field extensions · Galois Theory
- Lattice Theory (Distributive/Modular/Boolean Lattices) asked, not named in the syllabusLattices and Boolean algebras
Topology
- Basis, Dense Sets, Subspace and Product TopologyBasis, dense sets · Subspace and product topology
- Separation Axioms, Connectedness and CompactnessSeparation axioms · Connectedness and compactness
Unit 3
Ordinary Differential Equations
- Existence & Uniqueness, Singular Solutions, Systems of First Order ODEsExistence and uniqueness of solutions of initial value problems for first order ordinary differential equations · Singular solutions of first order ODEs · System of first order ODEs
- General Theory of Linear ODEs, Variation of Parameters, Sturm-Liouville, Green's FunctionGeneral theory of homogenous and non-homogeneous linear ODEs · Variation of parameters · Sturm-Liouville boundary value problem, Green's function
Partial Differential Equations
- Lagrange and Charpit Methods, Cauchy Problem for First Order PDEsLagrange and Charpit methods for solving first order PDEs · Cauchy problem for first order PDEs
- Classification of Second Order PDEsClassification of second order PDEs · General solution of higher order PDEs with constant coefficients
- Separation of Variables (Laplace, Heat and Wave Equations)Method of separation of variables for Laplace, Heat and Wave equations
Numerical Analysis
- Numerical Solutions of Algebraic Equations, Newton-Raphson, Rate of ConvergenceNumerical solutions of algebraic equations · Method of iteration and Newton-Raphson method · Rate of convergence
- Solution of Linear Systems: Gauss Elimination and Gauss-SeidelSolution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods
- Finite Differences, Lagrange/Hermite/Spline InterpolationFinite differences · Lagrange, Hermite and spline interpolation
- Numerical Differentiation and IntegrationNumerical differentiation and integration
- Numerical Solutions of ODEs (Picard, Euler, Runge-Kutta)Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods
Calculus of Variations
- Variation of a Functional, Euler-Lagrange Equation, Conditions for ExtremaVariation of a functional, Euler-Lagrange equation · Necessary and sufficient conditions for extrema
- Variational Methods for Boundary Value ProblemsVariational methods for boundary value problems in ordinary and partial differential equations
Linear Integral Equations
- Fredholm and Volterra Type, Separable Kernels, Resolvent KernelLinear integral equation of the first and second kind of Fredholm and Volterra type · Solutions with separable kernels · Characteristic numbers and eigenfunctions, resolvent kernel
Classical Mechanics
- Generalized Coordinates, Lagrange's EquationsGeneralized coordinates, Lagrange's equations
- Hamilton's Canonical Equations, Hamilton's PrincipleHamilton's canonical equations · Hamilton's principle and principle of least action
- Motion of Rigid Bodies, Euler's Dynamical Equations, Small OscillationsTwo-dimensional motion of rigid bodies · Euler's dynamical equations for the motion of a rigid body about an axis · Theory of small oscillations
Integral Transforms
- Laplace Transform asked, not named in the syllabusLaplace transform
- Fourier Transform asked, not named in the syllabusFourier transform
Fluid Dynamics
- Potential Flow, Streamlines, Doublets asked, not named in the syllabusPotential flow, streamlines, sources, sinks and doublets
Differential Geometry
- Curves and Surfaces, Curvature asked, not named in the syllabusCurves and surfaces, curvature and torsion
Graph Theory
- Graphs, Trees, Connectivity asked, not named in the syllabusGraphs, trees, connectivity and colouring
Unit 4
Descriptive Statistics
- Descriptive Statistics, Exploratory Data AnalysisDescriptive statistics · Exploratory data analysis
Probability
- Sample Space, Discrete Probability, Independent Events, Bayes TheoremSample space, discrete probability · Independent events · Bayes theorem
- Random Variables and Distribution Functions, Expectation and MomentsRandom variables and distribution functions (univariate and multivariate) · Expectation and moments · Independent random variables, marginal and conditional distributions
- Characteristic Functions, Probability InequalitiesCharacteristic functions · Probability inequalities (Tchebyshef, Markov, Jensen)
- Modes of Convergence, Laws of Large Numbers, Central Limit TheoremModes of convergence · Weak and strong laws of large numbers · Central Limit theorems (i.i.d. case)
Stochastic Processes
- Markov Chains: Classification of States, Stationary DistributionMarkov chains with finite and countable state space · Classification of states · Limiting behaviour of n-step transition probabilities · Stationary distribution
- Poisson and Birth-and-Death ProcessesPoisson process · Birth-and-death processes
- Martingales asked, not named in the syllabusMartingales, stopping times and martingale convergence
Distribution Theory
- Standard Discrete and Continuous Univariate DistributionsStandard discrete univariate distributions · Standard continuous univariate distributions
- Sampling Distributions, Standard Errors, Asymptotic DistributionsSampling distributions · Standard errors · Asymptotic distributions
- Distribution of Order Statistics and RangeDistribution of order statistics · Distribution of range
Statistical Inference
- Methods of Estimation, Properties of EstimatorsMethods of estimation · Properties of estimators
- Confidence IntervalsConfidence intervals
- Tests of Hypotheses: MP and UMP Tests, Likelihood Ratio TestsTests of hypotheses: most powerful and uniformly most powerful tests · Likelihood ratio tests
- Analysis of Discrete Data and Chi-Square Test of Goodness of FitAnalysis of discrete data · Chi-square test of goodness of fit
- Large Sample TestsLarge sample tests
- Nonparametric Tests, Rank Correlation, Test for IndependenceSimple nonparametric tests for one and two sample problems · Rank correlation and test for independence
- Elementary Bayesian InferenceElementary Bayesian inference
Linear Models & Regression
- Gauss-Markov Models, Estimability, Best Linear Unbiased EstimatorsGauss-Markov models · Estimability of parameters · Best linear unbiased estimators · Confidence intervals and tests for linear hypotheses
- Analysis of Variance and Covariance, Fixed/Random/Mixed EffectsAnalysis of variance and covariance · Fixed, random and mixed effects models
- Simple and Multiple Linear Regression, Logistic RegressionSimple and multiple linear regression · Elementary regression diagnostics · Logistic regression
Multivariate Analysis
- Multivariate Normal Distribution, Wishart Distribution, Quadratic FormsMultivariate normal distribution · Wishart distribution and their properties · Distribution of quadratic forms
- Partial and Multiple Correlation CoefficientsInference for parameters · Partial and multiple correlation coefficients and related tests
- Data Reduction: PCA, Discriminant, Cluster AnalysisPrinciple component analysis · Discriminant analysis · Cluster analysis · Canonical correlation
Sampling Theory
- Simple Random, Stratified and Systematic SamplingSimple random sampling · Stratified sampling · Systematic sampling
- Probability Proportional to Size SamplingProbability proportional to size sampling
- Ratio and Regression MethodsRatio and regression methods
Design of Experiments
- Completely Randomized, Randomized Block and Latin-Square DesignsCompletely randomized designs · Randomized block designs · Latin-square designs
- Connectedness and Orthogonality of Block Designs, BIBDConnectedness and orthogonality of block designs · BIBD
- 2^K Factorial Experiments: Confounding and Construction2K factorial experiments: confounding · 2K factorial experiments: construction
- Response Surface Designs asked, not named in the syllabusResponse surface designs and rotatability
Survival Analysis
- Hazard Function and Failure Rates, Censoring and Life TestingHazard function and failure rates · Censoring and life testing
- Series and Parallel SystemsSeries and parallel systems
Operations Research
- Linear Programming Problem, Simplex Method, DualityLinear programming problem · Simplex methods · Duality
- Elementary Queuing and Inventory ModelsElementary queuing models · Elementary inventory models
- Steady-State Solutions of Markovian Queuing Models (M/M/1, M/M/C, M/G/1)M/M/1 · M/M/1 with limited waiting space · M/M/C · M/M/C with limited waiting space · M/G/1
- Transportation and Assignment Problems asked, not named in the syllabusTransportation problem: feasibility, basic feasible solutions and optimality · Assignment problem
- Sequencing and Project Scheduling asked, not named in the syllabusSequencing jobs on machines (Johnson's rule) · Project scheduling: CPM and PERT
- Replacement Models asked, not named in the syllabusIndividual and group replacement policies
- Dynamic and Integer Programming asked, not named in the syllabusDynamic programming and Bellman's principle of optimality · Integer programming and branch and bound
- Game Theory asked, not named in the syllabusTwo-person zero-sum games, saddle points and mixed strategies
Demography / Vital Statistics
- Life Tables, Mortality Rate asked, not named in the syllabusLife tables, mortality and fertility rates
Index Numbers & Time Series
- Time Series Models asked, not named in the syllabusStationarity, autocorrelation and partial autocorrelation · Autoregressive, moving average and ARIMA models · Forecasting from a fitted model
Statistical Quality Control
- Control Charts asked, not named in the syllabusControl charts for variables and attributes · Average run length and chart performance
- Acceptance Sampling asked, not named in the syllabusSampling inspection plans, average outgoing quality and rectifying inspection