ISI Admission Test 2025 Syllabus: A Comprehensive Guide

The Indian Statistical Institute (ISI) is one of the most prestigious institutes in India, known for its cutting-edge research in statistics, mathematics, computer science, and related fields. Admission to ISI’s various undergraduate and postgraduate courses is highly competitive, and candidates need to clear the ISI Admission Test to secure a seat. To ace this exam, a thorough understanding of the syllabus is crucial.

In this guide, we’ll walk you through the syllabus for the ISI Admission Test 2025 for different programs. We’ll cover the syllabus for key courses such as B.Stat, B.Math, M.Stat, M.Math, and MS in Quantitative Economics, among others.

1. ISI Admission Test Syllabus for B.Stat and B.Math

The Bachelor of Statistics (B.Stat) and Bachelor of Mathematics (B.Math) programs are flagship undergraduate courses at ISI. Both of these programs have a similar entrance test syllabus, which focuses heavily on mathematics.

Exam Structure:

• Objective Type Questions: The test includes multiple-choice questions covering various mathematics topics.
• Subjective Type Questions: These are problems that require detailed written solutions.

Topics Covered in B.Stat and B.Math Entrance Exam:

Algebra:

• Basic Algebra: Simplification, factorization, linear equations, quadratic equations, inequalities.
• Sets, Relations, and Functions: Basic properties of sets, types of functions, inverse functions, binary operations.
• Complex Numbers: Properties, polar representation, De Moivre’s Theorem.
• Polynomials: Roots and coefficients, theorems of algebra, relations between roots and coefficients.
• Sequences and Series: Arithmetic progression (AP), geometric progression (GP), harmonic progression (HP), sum of series, binomial theorem.

Trigonometry:

• Trigonometric Functions: General solutions, identities, properties.
• Inverse Trigonometric Functions: Principal values, properties, and applications.
• Trigonometric Equations and Inequalities: Solutions to various trigonometric equations.
• Applications of Trigonometry: Heights, distances, and angles.

Calculus:

• Limits and Continuity: Basic limits, algebra of limits, continuity, L’Hopital’s Rule.
• Differentiation: Basic differentiation techniques, chain rule, product and quotient rules, implicit differentiation.
• Applications of Derivatives: Tangents and normals, maxima and minima, rate of change.
• Integration: Definite and indefinite integrals, techniques of integration, substitution, partial fractions, integration by parts.
• Applications of Integration: Area under curves, volume of solids of revolution, simple differential equations.

Coordinate Geometry:

• Straight Lines: Slope, intercepts, equations of lines, distance between two points.
• Circles: Equations, tangents, chords, and properties.
• Parabola, Ellipse, and Hyperbola: Equations, properties, tangents, and normals.

Vectors and 3D Geometry:

• Vectors: Magnitude, direction, dot product, cross product.
• Geometry in Three Dimensions: Lines, planes, and spheres, distance between points, angles between lines and planes.

Probability and Statistics:

• Basic Probability: Definition, conditional probability, Bayes’ theorem, random variables, expected value, variance.
• Probability Distributions: Binomial, Poisson, and normal distributions.

2. ISI Admission Test Syllabus for M.Stat and M.Math

The Master of Statistics (M.Stat) and Master of Mathematics (M.Math) programs require a more advanced understanding of mathematical concepts. The exam tests candidates on both undergraduate-level mathematics and basic statistical methods.

Topics Covered in M.Stat and M.Math Entrance Exam:

Real Analysis:

• Sequences and Series: Convergence, divergence, monotonicity, and boundedness.
• Functions of One Variable: Limits, continuity, differentiability, Taylor’s theorem.
• Riemann Integration: Properties of definite integrals, improper integrals, and applications.

Linear Algebra:

• Matrices: Rank, determinants, inverse, eigenvalues, and eigenvectors.
• Vector Spaces: Basis, dimension, linear transformations, and properties.
• Systems of Linear Equations: Solving systems using Gaussian elimination.

Probability Theory:

• Probability Spaces: Events, random variables, probability mass function (PMF), and probability density function (PDF).
• Distributions: Binomial, Poisson, normal, and uniform distributions.
• Expectation and Variance: Definitions, properties, and applications.
• Law of Large Numbers and Central Limit Theorem: Statements and applications.

Statistical Inference:

• Estimation: Methods of moments, maximum likelihood estimation.
• Hypothesis Testing: Neyman-Pearson lemma, types of errors, power of the test.
• Confidence Intervals: Calculation and interpretation.

Multivariable Calculus and Differential Equations:

• Partial Differentiation: Chain rule, gradient, divergence, curl.
• Multiple Integrals: Double and triple integrals, applications in geometry.
• Differential Equations: First and second-order differential equations, homogeneous and non-homogeneous equations.

Algebra and Number Theory:

• Group Theory: Basic definitions, subgroups, Lagrange’s theorem.
• Rings and Fields: Definitions and properties, homomorphisms.
• Elementary Number Theory: Divisibility, prime numbers, congruences, Chinese remainder theorem.

3. ISI Admission Test Syllabus for MS in Quantitative Economics

The MS in Quantitative Economics program focuses on equipping students with rigorous analytical tools in economics and quantitative methods. The entrance exam tests candidates on their knowledge of economics, mathematics, and statistics.

Topics Covered in MS in Quantitative Economics Entrance Exam:

Microeconomics:

• Consumer Theory: Utility functions, indifference curves, budget constraints.
• Production Theory: Production functions, cost minimization, profit maximization.
• Market Structures: Perfect competition, monopoly, oligopoly.

Macroeconomics:

• National Income Accounting: GDP, GNP, NNP.
• IS-LM Model: Interaction between the goods market and the money market.
• Inflation and Unemployment: Phillips curve, theories of inflation, causes of unemployment.

Mathematics for Economics:

• Linear Algebra: Matrices, determinants, systems of equations.
• Calculus: Functions of several variables, optimization, constrained optimization (Lagrange multipliers).

Statistics for Economics:

• Probability: Conditional probability, Bayes’ theorem, random variables, expectation.
• Hypothesis Testing: Parametric and non-parametric tests, confidence intervals.

Conclusion

The ISI Admission Test 2025 syllabus varies depending on the course you are applying for, but a strong foundation in mathematics, statistics, and economics is essential across the board. Understanding the syllabus and focusing on key areas will significantly improve your chances of success. Candidates should thoroughly review all topics, practice extensively, and refer to past year question papers to excel in the exam.