ISI Admission Test Syllabus 2026: BStat, BMath, MStat, MMath

Subject

Topics Covered

Algebra

Sets and operations on sets; prime numbers; factorization of integers and divisibility; rational and irrational numbers; permutations and combinations; basic probability; Binomial Theorem; logarithms; polynomials — Remainder Theorem, theory of quadratic equations and expressions, relations between roots and coefficients; arithmetic and geometric progressions; inequalities involving arithmetic, geometric, and harmonic means; complex numbers; matrices and determinants.

Geometry

Plane geometry: geometry of two dimensions using Cartesian and polar coordinates; equation of a line, angle between two lines, distance from a point to a line; concept of a locus; area of a triangle; equations of circle, parabola, ellipse, and hyperbola; equations of their tangents and normals; mensuration.

Trigonometry

Measures of angles; trigonometric and inverse trigonometric functions; trigonometric identities including addition formulae; solutions of trigonometric equations; properties of triangles; heights and distances.

Calculus

Sequences — bounded and monotone sequences, limit of a sequence; functions — one-one and onto functions; limits and continuity; derivatives and methods of differentiation; slope of a curve, tangents and normals; maxima and minima; using calculus to sketch graphs of functions; methods of integration — definite and indefinite integrals; evaluation of area using integrals; homogeneous differential equations of first order and first degree.

Unit

Topics

Subtopics / Areas Covered

1. Analysis and Metric Spaces

Set Theory & Relations

Countable and uncountable sets; Equivalence relations and partitions

Sequences and Series

Convergence and divergence of sequences and series; Cauchy sequences and completeness; Bolzano–Weierstrass theorem

Calculus of Functions

Continuity, uniform continuity, differentiability, Taylor expansion; Sequences and series of functions

Differential Equations

Elements of ordinary differential equations

Integral Calculus

Integral calculus of one variable; existence of Riemann integral; Fundamental theorem of calculus; change of variable; improper integrals

Metric Spaces & Topology

Elementary topological notions for metric spaces: open, closed, and compact sets; continuous functions; completeness of metric spaces

2. Linear Algebra and Abstract Algebra

Linear Algebra

Vector spaces, subspaces, basis, dimension, direct sum; Matrices, systems of linear equations, determinants; Diagonalization, triangular forms; Inner product spaces; Linear transformations and their representation as matrices

Group Theory

Groups, subgroups, quotient groups, homomorphisms, direct products; Lagrange’s theorem; Sylow’s theorems

Ring and Field Theory

Rings, ideals, maximal ideals, prime ideals, quotient rings; Integral domains; Chinese remainder theorem; Polynomial rings; Fields

3. Elementary Probability Theory

Probability Basics

Combinatorial probability; events; random variables; independence; expectation and variance

Unit

Topics

Subtopics / Areas Covered

Mathematics

Progressions

Arithmetic, geometric, and harmonic progressions

Trigonometry

Basic trigonometric functions and identities

Two-Dimensional Coordinate Geometry

Straight lines, circles, parabolas, ellipses, and hyperbolas

Elementary Set Theory

Concepts of sets, subsets, union, intersection, complement

Functions and Relations

Types of functions, domain, range, inverse functions

Elementary Combinatorics

Permutations and combinations, Binomial theorem, Multinomial theorem

Theory of Equations

Roots and coefficients, relations between roots, symmetric functions

Complex Numbers

De Moivre’s theorem, powers and roots of complex numbers

Vector Spaces and Matrices

Determinant, rank, trace, inverse of a matrix, system of linear equations, eigenvalues and eigenvectors

Calculus

Limit and continuity of functions of one variable, differentiation and integration, applications of differential calculus (maxima and minima)

Statistics and Probability

Probability Concepts

Sample space, probability, combinatorial probability, conditional probability, independence, Bayes’ theorem

Random Variables and Expectations

Moments, moment generating functions, univariate discrete and continuous distributions, distribution of functions of a random variable, order statistics

Joint Distributions

Joint, marginal, and conditional probability distributions, multinomial distribution, bivariate and multivariate normal distributions

Sampling and Theorems

Sampling distributions of statistics, Weak Law of Large Numbers, Central Limit Theorem

Descriptive Statistics

Descriptive measures, Pearson correlation, Spearman rank correlation

Regression Analysis

Simple and multiple linear regression

Statistical Inference

Theory of estimation (unbiasedness, minimum variance, sufficiency), methods of estimation (maximum likelihood, method of moments), tests of hypotheses (Neyman-Pearson Lemma), confidence intervals, inference related to regression

Design of Experiments

Completely Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (LSD), ANOVA, elements of factorial designs

Sampling Techniques

Simple Random Sampling (SRSWR/SRSWOR), stratified sampling

ISI Admission Test 2026 for Undergraduate Entrance Test 

Section

Number of Questions

Marks and Weightage

Section 1: Undergraduate Aptitude Test (A) - UGA (Objective Questions)

30 Questions

Marks = 4 marks per question

Weightage = 1 for each question

Section 2: Undergraduate Aptitude Test (B) - UGB (Subjective Questions)

8 Questions

Marks = 10 marks per question

Weightage = 3 for each question

Section 3: Interview

10 Questions (approx.)

Marks = 20 marks per question

Weightage = 6 for each question

Total Marks

480

ISI Admission Test 2026 for Postgraduate Entrance Test 

Sections

Number of Questions

Marks and Weightage

Section 1: Objective Questions

30 Questions

Marks = 4 marks per question

Weightage = 1 for each question

Section 2: Subjective Questions

8 Questions

Marks = 10 marks per question

Weightage = 3 for each question

Section 3: Interview

10 Questions (approx.)

Marks = 20 marks per question

Weightage = 6 for each question

Total Marks

480