ISI Admission Test 2025 Syllabus PDF - Download Latest ISI Admission Test Syllabus for All Subjects

ISI Admission Test 2025 Syllabus: Download PDF

ISI Admission Test Syllabus 2025: The ISI Admission Test syllabus is specified by the Indian Statistical Institute. To check the syllabus, candidates must visit the official website or use the below link. Once they hit the said link, they will find the list of the offered courses. By clicking on the offered courses, aspirants will get the syllabus for the respective programmes they are interested in joining for UG or PG studies.

Check out the details on this page.

ISI Admission Test 2025 Syllabus PDFs

Here, we have provided the syllabus PDFs for the ISI Admission Test 2025 for the various offered degree courses - 

ISI Admission Test 2025 Syllabus for B.Statistics and B.Mathematics

Find the detailed syllabus for the ISI Admission Test 2025 for Bachelor of Statistics and Bachelor of Mathematics here. Questions for these subjects will be a combination of multiple-choice (test code - UGA) and short-answer (test code - UGB) questions.

Algebra: 

• Sets, 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 2 dimensions with 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 and 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 sequences, monotone sequences, limit of a sequence.
• Functions, one-one functions, 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.

ISI Admission Test 2025 Syllabus for Bachelor of Statistical Data Science Honours

Explore the ISI Admission Test Syllabus for the Bachelor of Statistical Data Science Honours here -

Sets, relations and functions

• Sets and their representations
• Union
• Intersection
• Difference and complement of sets and their algebraic properties
• Power set.

Types of relations and equivalence relations

• Functions as maps, One-one, into and onto functions
• Essential real-valued functions such as polynomials, rational, trigonometric, logarithmic, and exponential functions
• Equations involving polynomials, exponential and logarithmic functions
• Inverse functions
• Transformation of functions
• Composition of functions
• Graphs of simple functions

Complex number system

• Different representations of complex numbers
• Conjugate
• Modulus and argument of a complex number
• Powers of complex numbers
• Roots of unity
• Quadratic equations and their solutions
• Fundamental theorem of algebra. 

Basics of Combinatorics

• Permutation and combination
• Fundamental principles of counting
• Binomial theorem and its applications
• Principle of mathematical induction and its applications

Sequence and Series

• Arithmetic and geometric progressions and their combinations
• Convergence of infinite series
• Sums of integer powers of natural numbers
• Relationship between arithmetic and geometric means

Limits, continuity and differentiability of functions

• Definition of limit
• Continuity and differentiability
• Properties of continuous functions and differentiable functions
• Chain rule of differentiation
• Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite, and implicit functions
• Rolle’s theorem and mean-value theorem and their applications
• Maxima and minima of functions of one variable. 

Trigonometry

• Trigonometric functions and their inverses
• Trigonometric identites and equations
• Applications to measuring heights
• computation of distances and areas

Integral Calculus

• Integrals as limits of sums
• Properties of indefinite integrals
• Fundamental theorem of calculus and its simple applications
• Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions. Integration by substitution and by parts
• Definite integrals, their properties, and applications to determining areas of regions bounded by simple and standard curves

Basics of Differential Equations

• Ordinary differential equations, their order and degree
• First order linear differential equations
• Solving differential equations by methods of separation of variables and substitution
• Solution of homogeneous and first order linear differential equations

Coordinate Geometry

• Cartesian system and locus of a point
• Straight lines and their intersections
• Angles between straight lines and distance between a point and a straight line
• Equation of a circle, its radius and centre
• Equations of conic sections (parabola, ellipse, and hyperbola) in standard forms and in parametric forms
• Tangent and normal at a point on a circle and on conics

Vector Algebra

• Vectors and scalars
• Addition of vectors
• Components of a vector in two dimensions and three dimensional space 
• Scalar (dot) and vector (cross) products
• Scalar and vector triple products
• Simple properties and applications: Directions ratios, and direction cosines
• Angle between two straight lines and skew lines
• Point of intersection of two straight lines and shortest distance between two straight lines.

3-Dimensional Geometry

• Coordinates of points in 3D space
• Angles between straight lines and planes
• Intersection formulas

Matrices and Determinants

• Algebra of matrices
• Types of matrices
• Matrices of order two and three
• Evaluation of determinants
• Adjoint and determinant of a matrix
• Evaluation of the inverse of a nonsingular matrix
• Properties of matrix inverses
• Elementary transformations of a matrix
• Rank of a matrix
• Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Introductory Statistics and Probability

• Measures of centrality and dispersion
• Mean, median, and mode
• Variance and standard deviation for grouped and ungrouped data
• Probability of an event
• Fundamental rules of probability calculation
• Probability distribution
• Binomial distribution
• Bayes theorem.

ISI Admission Test 2025 Syllabus for Master of Statistics (M.Stat)

Find out the main segments and topics as per the ISI Admission Test 2025 syllabus for Master of Statistics (M.Stat) below -

Mathematics

• Arithmetic, Geometric and harmonic progressions, Trigonometry, Two dimensional coordinate geometry: Straight lines, circles, parabolas, ellipses and hyperbolas
• Elementary set theory, Functions and relations, Elementary combinatorics: Permutations and combinations, Binomial and multinomial theorem
• Theory of equations
• Complex numbers and De Moivre’s theorem
• Vector spaces, Determinant, Rank, Trace and inverse of a matrix, System of linear equations, Eigenvalues and eigenvectors of matrices
• Limit and continuity of functions of one variable, Differentiation and integration, Applications of differential calculus, Maxima and minima. 

Statistics and Probability 

• Notions of sample space and probability, Combinatorial probability, Conditional probability and independence, Bayes Theorem, Random variables and expectations, Moments and moment generating functions, Standard univariate discrete and continuous distributions, Distribution of functions of a random variable, Distribution of order statistics, Joint probability distributions. Marginal and conditional probability distributions, Multinomial distribution, Bivariate normal and multivariate normal distributions. 
• Sampling distributions of statistics, Statement and applications of Weak law of large numbers and Central limit theorem. 
• Descriptive statistical measures, Pearson product-moment correlation and Spearman’s rank correlation, Simple and multiple linear regression. 
• Elementary theory of estimation (unbiasedness, minimum variance, sufficiency), Methods of estimation (maximum likelihood method, method of moments), Tests of hypotheses (basic concepts and simple applications of Neyman-Pearson Lemma), Confidence intervals, Inference related to regression.
• Basic experimental designs such as CRD, RBD, LSD and their analyses, ANOVA. Elements of factorial designs, Conventional sampling techniques (SRSWR/SRSWOR) including stratification.

ISI Admission Test 2025 Syllabus for Master of Mathematics (M.Math)

Here is the ISI Admission Test 2025 syllabus for the Master of Mathematics. The test codes for the M.Math programme are PMA and PMB-

Analysis and metric spaces

• Countable and uncountable sets
• Equivalence relations and partitions
• Convergence and divergence of sequences and series
• Cauchy sequence and completeness
• Bolzano–Weierstrass theorem
• Continuity, uniform continuity, differentiability, Taylor expansion
• Sequences and series of functions
• Elements of ordinary differential equations
• Integral calculus of one variable–existence of Riemann integral
• Fundamental theorem of calculus
• Change of variable, improper integrals
• Elementary topological notions for metric spaces: open, closed and compact sets, continuous functions, completeness of metric spaces.

Linear algebra and abstract 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
• Groups, subgroups, quotient groups, homomorphisms, products
• Lagrange’s theorem, Sylow’s theorems
• Rings, ideals, maximal ideals, prime ideals, quotient rings
• Integral domains, Chinese remainder theorem, polynomial rings, fields.

Elementary probability theory

• Combinatorial probability, events, random variables, independence, expectation and variance.

ISI Admission Test 2025 Syllabus for Master of Science in Quantitative Economics (MS in QE)

Students can discover the ISI Admission Test 2025 syllabus for Master of Science in Quantitative Economics (MS in QE)

Syllabus for Mathematics: 

Algebra: 

• Binomial Theorem
• AP, GP, Series
• Permutations and combinations
• Theory of polynomial equations. 

Linear Algebra:

• Vector spaces
• Linear transformations
• Matrix representations and elementary operations
• Systems of linear equations
• Eigenvalues

Calculus:

• Functions
• Limits
• Continuity
• Differentiation of functions of one or more variables,
• Unconstrained Optimization
• Definite and Indefinite Integrals
• Integration by parts and integration by substitution
• Convexity and quasi-convexity
• Constrained optimization of functions of not more than two variables
• Implicit function theorem
• Homogeneous and homothetic functions

Syllabus for Statistics:

• Elementary probability theory
• Measures of central tendency
• Dispersion
• Correlation and regression
• Probability distributions
• Standard distributions: Binomial and Normal

Syllabus for Microeconomics: 

• Theory of consumer behaviour
• Theory of production
• Market structure under perfect competition
• Monopoly
• Price discrimination
• Duopoly with Cournot and Bertrand competition
• Elementary strategic interaction
• Public goods
• Externalities
• General equilibrium
• Welfare economics

Syllabus for Macroeconomics: 

• National income accounting
• Simple Keynesian Model of income determination and the multiplier
• IS-LM Model
• Models of aggregate demand and aggregate supply
• Money
• Banking and Inflation
• Phillips curve
• Elementary open economy macroeconomics
• The Harrod-Domar Model
• The Solow Model.

ISI Admission Test 2025 Syllabus for M.Tech in Computer Science (ISI Test Channel)

We have curated the main components and the topics associated with each according to the ISI Admission Test 2025 syllabus for M.Tech in Computer Science -

Syllabus: PCA

Analytical Reasoning

Elementary Number Theory:

• Divisibility
• Congruence
• Primality

Elementary Algebra:

• Arithmetic
• Geometric and Harmonic Progression
• Inequalities involving Arithmetic
• Geometric and Harmonic Mean
• Binomial Theorem and Multinomial Theorem
• Theory of Polynomials

Linear Algebra:

• Matrices
• Determinant
• Rank and Inverse
• Properties of Symmetric and Idempotent Matrices
• Vectors
• Eigenvalues and Eigenvectors
• Quadratic Forms
• System of linear equations

Euclidean and Coordinate Geometry:

• Straight line
• Circle
• Triangles

Calculus:

• Sequence and their properties
• Series
• Power Series
• Taylor Series
• Maclaurin Series
• Convergence
• Limits
• Continuity
• Differentiation and Integration of Functions
• Rolle’s Theorem and Mean Value of Theorem
• Maxima and Minima

Discrete Mathematics:

• Elementary Set Theory
• Permutations and Combinations
• Functions and Relations
• Recurrences

Basic Graph Theory:

• Paths and Cycles
• Connected Components
• Trees
• Digraphs

Elementary Discrete Probability Theory:

• Combinatorial Probability
• Conditional Probability
• Bayes Theorem

Mathematical Logic:

• Boolean Algebra
• Propositional Logic
• Predicate Logic

Basic Automata Theory:

• Strings
• Languages
• Finite State Automata
• Regular Expressions

Basic Algorithmic Concepts:

• Interpreting Simple Pseudocodes written with Sequential, Conditional, Iterative, and Recursive Constructs

Syllabus: PCB

Suggested CS Paper Syllabus for MTech

Analytical Reasoning

Data Structures:

• Array
• Stack
• Queue
• Linked List
• Binary Tree
• Heap 
• AVL Tree
• B Tree

Discrete Mathematics

• Recurrence Relations
• Generating Functions

Graph Theory:

• Paths and Cycles
• Connected Components
• Trees
• Digraphs

Design and Analysis of Algorithms

• Asymptotic Notation
• Searching
• Sorting
• Selection
• Graph Traversal
• Minimum Spanning Tree

Formal Languages and Automata Theory

• Finite Automata and Regular Expressions
• Pushdown Automata
• Context-free Grammar
• Turing Machine
• Elements of Undecidability

Switching Theory and Logic Design

• Boolean Algebra
• Minimization of Boolean Functions
• Combination and Sequential Circuits - Synthesis and Design

Computer Organization and Architecture

• Number Representation
• Computer Arithmetic
• Memory Organization
• Microprogramming
• Pipelining
• Instruction Level Parallelism

Operating Systems

• Memory Management
• Processor Manegement
• Critical Selection Problem
• Dead locks
• Device Management
• File Systems

Database Management Systems

• Relational Model
• Relational Algebra
• Relational Calculus
• Functional Dependency
• Normalisation (2 NF, 3 NF, BCNF)

Computer Networks

• OSI
• LAN Technology - Bus, Star, Ring/ Star
• MAC Protocols
• WAN Technology
• Packet Switching
• Data Communications - Data Encoding
• Routing
• Flow Control
• Error Detection/ Correction
• Inter Networking
• TCP/IP Networking, including IPv4

Suggested Non-CS Paper Syllabus 

Analytical Reasoning

Discrete Mathematics:

• Permutations and Combinations
• Recurrence Relations

Linear Algebra:

• Algebra of Matrices
• Determinant
• Rank and Inverse of a Matrix
• System of Linear Equations
• Properties of Symmetric and Idempotent Matrices
• Eigenvalues and Eigenvectors

Polynomials:

• Polynomials of a Single Variable
• Binomial/ Multinomial Theorem

Elementary Discrete Probability Theory:

• Combinatorial Probability
• Conditional Probability
• Bayes Theorem
• Discrete Random Variables
• Expectation and Variance of Discrete Random Variables

Graph Theory:

• Graphs
• Adjacency Matrix and Adjacency List representations of Graphs
• Subgraphs
• Connectivity
• Trees and their Properties
• Vertex Colouring
• Planar Graphs

Algorithmic Thinking

• Asymptotic Notations
• Searching
• Sorting
• Selection
• Graph Traversal
• Minimum Spanning Tree

Basic Programming Concepts

Linear Programming

• LP/ ILP formulations of Optimisation Problems

Calculus: 

• Sequence and their Properties
• Series
• Power Series
• Taylor Series
• Maclaurin Series
• Convergence
• Limits
• Continuity
• Differentiation and Integration of Functions
• Maxima and Minima
• Functions of Several Variables

Formal Languages and Automata Theory

• Finite Automata
• Regular Expressions

Elementary Set Theory

Functions and Relations

Elementary Number Theory

• Divisibility
• Congruences
• Primality

ISI Admission Test 2025 Exam Pattern

The ISI Admission Test exam pattern is specified by the conducting body on the official website. It may differ based on the offered programmes. Students are recommended to check the test pattern for the respective courses to be acquainted with the structure, marking scheme, overall marks, duration, etc.

Students can refer to the below link to know more about the exam pattern of the ISI Admission Test 2025-

ISI Admission Test 2025 Best Books

It is important to follow the right set of materials to do well in any examination. To help the candidates excel in their preparation, we have collected the following list of ISI Admission Test 2025 best books based on the inputs by experts course-wise.

ISI Admission Test 2025 Best Books for B.Statistics and B.Mathematics

• Books from the Cengage Series
• Books from the Arihant Series
• Books from the Vinay Kumar Series
• Problem Plus in IIT Mathematics by A Das Gupta
• MCQ by A Das Gupta
• ISI TOMATO Book
• Mathematical Proofs: A Transition to Advanced Mathematics
• Study Materials For ISI Entrance B.Stat/ B.Math for 2025 by Sorav Sir’s Classes
• Test of Mathematics at the 10+2 Level by East West Press
• Excursion in Mathematics
• Problem Solving Strategies by Arthur Engel
• Challenge and Thrill of Pre-College Mathematics" by V. Krishnamurthy
• TMH Comprehensive Mathematics
• Mathematical Circles
• Problem Primer

How To Prepare for ISI Admission Test 2025

The ISI Admission Test 2025 offers admission to several courses like B.Stat, B.Math, M.Stat, M.Math, etc. Some of the basic yet powerful tips on how to prepare for the ISI Admission Test 2025 include -

• Candidates must be aware of the exam syllabus. Depending on the target courses, students are required to take a look and create their study plan. The syllabus is different for each course.
• They must understand the exam pattern for the ISI Admission Test. The questions will be a mix of multiple choice and short answer type questions. Hence, they should practice accordingly. The MCQs will assess the basic conceptual understanding, while the subjective questions will analyse their basic problem-solving abilities.
• Exam-takers must focus on key concepts of Mathematics, Algebra, Geometry, Statistics, Probability, Calculus, etc. They must attempt questions from NCERT-based Class 11 and 12 books.
• They must solve as many past-year questions as possible. The conducting authority releases the last year question papers on their official portal. 
• Students must assess their performances at regular intervals and tweak their strategies to maximise their chances of success.
• To get exposure to the real exam environment, they must take mock tests issued by several coaching institutes.
• Revision is important. They must revise the areas they have covered, most importantly key formulas and theorems