ISI Admission Test

• Algebra

  13 topics

  • Sets, operations on sets
  • Prime numbers, factorization of integers and divisibility
  • Rational and irrational numbers
  • Permutations and combinations, basic probability
  • Principle of mathematical induction
  • Recurrence relation
  • 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

  7 topics

  • 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

  5 topics

  • Measures of angles
  • Trigonometric and inverse trigonometric functions
  • Trigonometric identities including addition formulae, solutions of trigonometric equations
  • Properties of triangles
  • Heights and distances

• Calculus

  10 topics

  • Sequences - bounded sequences, monotone sequences, limit of a sequence
  • Functions, one-one functions, 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

• Mathematics

  15 topics

  • 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

  27 topics

  • 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

• Analysis

  12 topics

  • 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
  • Differentiation of functions from R to Rn
  • Partial and directional derivatives, Jacobians
  • Sequences and series of functions, Weierstrass approximation theorem
  • Elements of ordinary differential equations, linear differential equations
  • Integral calculus of one variable-existence of Riemann integral
  • Fundamental theorem of calculus, change of variable, improper integrals

• Metric spaces

  3 topics

  • Open, closed and compact sets
  • Continuous functions
  • Completeness, connectedness and path connectedness

• Linear algebra

  6 topics

  • Vector spaces, subspaces, basis, dimension, direct sum
  • Matrices, systems of linear equations, determinants
  • Linear transformations and their representation as matrices
  • Dual space of a vector space; transpose of a linear transformation
  • Eigenvalues and eigenvectors, diagonalization, triangular forms
  • Inner product spaces; adjoint of a linear transformation

• Abstract algebra

  4 topics

  • 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

• Algebra

  6 topics

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

• Linear Algebra

  5 topics

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

• Calculus

  12 topics

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

• Statistics

  11 topics

  • Elementary probability theory
  • Measures of central tendency
  • Dispersion
  • Correlation and regression
  • Discrete and continuous probability distributions
  • Standard distributions: Binomial, Geometric, Normal, Poisson and Chi-square
  • Conditional probability
  • Bayes' Theorem
  • Sampling
  • Estimation
  • Hypothesis testing

• Microeconomics

  11 topics

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

• Macroeconomics

  9 topics

  • 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

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

• Elementary Number Theory

  3 topics

  • Divisibility
  • Congruence
  • Primality

• Elementary Algebra

  4 topics

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

• Linear Algebra

  8 topics

  • Matrices
  • Determinants
  • Rank and Inverse
  • Properties of Symmetric and Idempotent Matrices
  • Vectors
  • Eigenvalues and Eigenvectors
  • Quadratic Forms
  • System of Linear Equations

• Euclidean and Coordinate Geometry

  3 topics

  • Straight Lines
  • Circle
  • Triangles

• Calculus

  10 topics

  • Sequences and their Properties
  • Series
  • Power Series
  • Taylor Series and Maclaurin Series
  • Convergence
  • Limits
  • Continuity
  • Differentiation and Integration of Functions
  • Rolle's Theorem and Mean Value Theorem
  • Maxima and Minima

• Discrete Mathematics

  4 topics

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

• Basic Graph Theory

  4 topics

  • Paths and Cycles
  • Connected Components
  • Trees
  • Digraphs

• Elementary Discrete Probability Theory

  3 topics

  • Combinatorial Probability
  • Conditional Probability
  • Bayes Theorem

• Mathematical Logic

  3 topics

  • Boolean Algebra
  • Propositional Logic
  • Predicate Logic

• Basic Automata Theory

  4 topics

  • Strings
  • Languages
  • Finite State Automata
  • Regular Expressions

• Basic Algorithmic Concepts

  1 topics

  • Interpreting Simple Pseudocodes Written with Sequential, Conditional, Iterative, Recursive Constructs

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

• Design and Analysis of Algorithms

  6 topics

  • Asymptotic Notation
  • Searching
  • Sorting
  • Graph Traversal
  • Minimum Spanning Tree
  • Shortest Path Algorithms

• Data Structures

  8 topics

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

• Graph Theory

  9 topics

  • Graphs
  • Adjacency Matrix and Adjacency List representation of Graphs
  • Subgraphs
  • Paths and Cycles
  • Trees and their Properties
  • Connectivity
  • Digraphs
  • Vertex Colouring
  • Planar Graphs

• Formal Languages and Automata Theory

  6 topics

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

• Switching Theory and Logic Design

  12 topics

  • Boolean expressions and their minimization
  • Techniques such as Karnaugh Maps and Quine-McCluskey Method
  • Adders (Half and Full)
  • Subtractors
  • Encoders and Decoders
  • Multiplexers and Demultiplexers
  • Read-Only Memory (ROM)
  • Flip-Flops (SR, JK, D, T)
  • Counters (Asynchronous and Synchronous)
  • Registers (Shift Registers and Storage Registers)
  • Design and Synthesis of Finite-State Machines (FSM)
  • Practical implementation of various digital circuits

• Computer Organization and Architecture

  6 topics

  • Number Representation
  • Computer Arithmetic
  • Memory Organization
  • I/O Organization
  • Processor Organization
  • Pipelining

• Operating Systems

  6 topics

  • Memory Management
  • Processor Management
  • Critical Section Problem
  • Deadlocks
  • Device Management
  • File Systems

• Database Management Systems

  5 topics

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

• Computer Networks

  5 topics

  • OSI
  • LAN Technology - Bus / Tree, Ring, Star
  • MAC Protocols
  • WAN Technology - Circuit Switching, Packet Switching
  • Data Communications - Data Encoding/Decoding, Flow Control, Error Detection/Correction

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

Topics pending official syllabus normalization.

• Design and Analysis of Algorithms

  6 topics

  • Asymptotic Notation
  • Searching
  • Sorting
  • Graph Traversal
  • Minimum Spanning Tree
  • Shortest Path Algorithms

• Linear Algebra

  5 topics

  • System of Linear Equations
  • Determinant, Rank and Inverse of a Matrix
  • Vector Space and Linear Transformation
  • Eigenvalues and Eigenvectors of Matrices
  • Properties of Symmetric and Idempotent Matrices

• Polynomials

  1 topics

  • Polynomials of a Single Variable and Multiple Variables

• Discrete Probability Theory

  4 topics

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

• Graphs

  8 topics

  • Adjacency Matrix and Adjacency List representation of Graphs
  • Subgraphs
  • Paths and Cycles
  • Trees and their Properties
  • Connectivity
  • Digraphs
  • Vertex Colouring
  • Planar Graphs

• Calculus

  9 topics

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

• Formal Languages and Automata Theory

  6 topics

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

• Elementary Circuit Theory

  5 topics

  • Node and Mesh Analysis
  • Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL)
  • Superposition Theorem
  • Thevenin's and Norton's Theorems
  • Maximum Power Transfer Theorem

• Switching Theory and Logic Design

  12 topics

  • Boolean expressions and their minimization
  • Techniques such as Karnaugh Maps and Quine-McCluskey Method
  • Adders (Half and Full)
  • Subtractors
  • Encoders and Decoders
  • Multiplexers and Demultiplexers
  • Read-Only Memory (ROM)
  • Flip-Flops (SR, JK, D, T)
  • Counters (Asynchronous and Synchronous)
  • Registers (Shift Registers and Storage Registers)
  • Design and Synthesis of Finite-State Machines (FSM)
  • Practical implementation of various digital circuits

• Mechanics

  5 topics

  • Gravitation
  • Moments of Inertia and applications
  • Particle Dynamics and Laws of Motion
  • Elasticity and Friction
  • Strength of Materials and their mechanical properties

• Thermodynamics

  3 topics

  • Laws of Thermodynamics (First, Second, and Third Laws)
  • Heat Engines, Efficiency, and Carnot Cycle
  • Applications of Thermodynamic Principles in Engineering