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 ISI Syllabus 2021
ISI Syllabus 2021  Check ISI Syllabus, Exam Dates , Application Form, Eligibility, Exam Pattern Here
J Nandhini  Updated: Mar 15, 2021, 18:49 IST
ISI Syllabus 2021 @ www.isical.ac.in
New Update on 15032021: Indian Statistical Institute (ISI), Kolkata will be releasing the exam pattern and syllabus for ISI admission test 2021 on the official website. ISI Syllabus is provided here which can be checked by the concerned candidates who are preparing for the ISI Exam 2021 which will be held on 18th July 2021 for admission in courses – B. Stat (Hons.), B. Maths (Hons.), M. Math, M. Tech (CS), MS (QMS), MS (QE). Candidates are advised to scroll down the page to know all the necessary details regarding ISI Syllabus 2021.
For better training, candidates taking the ISI admission test in 2021 can review the exam pattern and syllabus. Candidates will be able to decide the total number of questions, type of questions, number of sections, and marking scheme by using the ISI exam pattern 2021, while the syllabus will assist them in ensuring that they have covered all topics. ISI Syllabus 2021 for the entrance exam has been framed in a systematic manner to help the students seeking admission. All aspirants need to understand the ISI Syllabus 2021 and question paper pattern to some extent. Candidates should prepare well for the ISI exam 2021 to score good marks.
Check Here  ISI Syllabus 2021
ISI Syllabus 2021 Overview
ISI Syllabus 2021 of MMA for M.Tech CS, CrS, QROR
Analytical Reasoning 

Algebra 
Arithmetic, geometric and harmonic progression. Continued fractions. Elementary combinatorics: Permutations and combinations, Binomial theorem. Theory of equations. Inequalities. Complex numbers and De Moivre’s theorem. Elementary set theory. Functions and relations. Elementary number theory: Divisibility, Congruences, Primality. Algebra of matrices. Determinant, rank and inverse of a matrix. Solutions of linear equations. Eigenvalues and eigenvectors of matrices. Simple properties of a group. 
Coordinate Geometry 
Straight lines, circles, parabolas, ellipses and hyperbolas 
Calculus 
Sequences and series: Power series, Taylor and Maclaurin series. Limits and continuity of functions of one variable. Differentiation and integration of functions of one variable with applications. Definite integrals. Maxima and minima. Functions of several variables  limits, continuity, differentiability. Double integrals and their applications. Ordinary linear differential equations. 
Elementary discrete probability theory 
Combinatorial probability, Conditional probability, Bayes theorem. Binomial and Poisson distributions. 
ISI Syllabus 2021 of PCB for M.Tech CS & CrS
Group A 

S.No. 
Topics 

1 
Analytical Reasoning 

2 
Elementary Euclidean geometry and trigonometry 

3 
Elements of set theory, Functions and relations, Permutations and combinations, Principle of inclusion and exclusion, Pigeonhole principle 

4 
Theory of equations, Inequalities 

5 
Elementary number theory, divisibility, congruences, primality 

6 
Determinants, matrices, solutions of linear equations, vector spaces, linear independence, dimension, rank and inverse 

7 
Limits, continuity, sequences and series, differentiation and integration with applications, maximaminima 

8 
Combinatorial probability, Conditional probability, Discrete random variables and expectation, Binomial distribution 

Group B Mathematics 

1 
Linear algebra 
vector spaces and linear transformations, direct sum, matrices and systems of linear equations, characteristic roots and characteristic vectors, Cayley Hamilton theorem, diagonalization and triangular forms, quadratic forms. 
2 
Abstract algebra 
Groups: subgroups, products, cosets, Lagranges theorem, group homomorphism, normal subgroups and quotient groups, permutation groups, Sylow theorems. Rings and integral domains: subrings, ring homomorphism, ideals and quotient rings, prime and maximal ideals, products, Chinese remainder theorem, prime and irreducible elements, principal ideal domain, unique factorization domains. Polynomial rings: division algorithm, roots of polynomials. Fields: characteristic of a field, field extensions, finite fields. 
3 
Calculus and real analysis 
Real numbers, limits, continuity, uniform continuity of functions, differentiability of functions of one or more variables and applications, convergence of sequences and series; indefinite integral, fundamental theorem of Calculus, Riemann integration, improper integrals, double and multiple integrals and applications, sequences and series of functions, uniform convergence, solutions of ordinary differential equations. 
4 
Graph Theory 
Connectedness, trees, vertex coloring, planar graphs, Eulerian graphs, Hamiltonian graphs, digraphs and tournaments. 
5 
Combinatorics 
Counting principles, Ramsey theory, binomial coefficients, recurrence relations, divideandconquer recurrences, recurrences involving convolution and their use in counting, Fibonacci numbers, generating functions, solving recurrence relations using generating functions 
Statistics 

1 
Notions of sample space and probability, combinatorial probability, conditional probability, Bayes’ theorem and independence 

2 
Random variable and expectation, moments, standard univariate discrete and continuous distributions, sampling distribution of statistics based on normal samples, central limit theorem, approximation of binomial to normal, Poisson law 

3 
Multinomial, bivariate normal and multivariate normal distributions. 

4 
Descriptive statistical measures, productmoment correlation, partial and multiple correlation. 

5 
Regression – simple and multiple. 

6 
Elementary theory and methods of estimation – unbiasedness, minimum variance, sufficiency, maximum likelihood method, method of moments, least squares methods. 

7 
Tests of hypotheses – basic concepts and simple applications of NeymanPearson lemma, confidence intervals. 

8 
Tests of regression, elements of nonparametric inference, contingency tables and Chisquare, ANOVA, basic designs (CRD/RBD/LSD) and their analyses, elements of factorial designs. 

9 
Conventional sampling techniques, ratio and regression methods of estimation. 

Physics 

1 
Classical mechanics 
Lagrangian and Hamiltonian formulation, symmetries and conservation laws, motion in central field of force, planetary motion, simple harmonic motion  damped, undamped and forced, special theory of relativity 
2 
Electrodynamics 
electrostatics, magnetostatics, electromagnetic induction, self and mutual inductance, capacitance, Maxwell’s equation in free space. 
3 
Nonrelativistic quantum mechanics 
Planck’s law, photoelectric effect, Compton effect, waveparticle duality, Heisenberg’s uncertainty principle, Schrodinger equation and applications. 
4 
Thermodynamics and statistical Physics 
laws of thermodynamics and their consequences, thermodynamic potentials and Maxwell’s relations, chemical potential, phase equilibrium, phase space, microstates and macrostates, partition function, free energy, classical statistics. 
5 
Atomic and molecular physics 
quantum states of an electron in an atom, Hydrogen atom spectrum, electron spin, spinorbit coupling, fine structure, Zeeman effect. 
6 
Condensed matter physics 
crystal classes, 2D and 3D lattice, reciprocal lattice, bonding, diffraction and structure factor, point defects and dislocations, lattice vibration, free electron theory, electron motion in periodic potential, energy bands in metals, insulators and semiconductors 
7 
Basic nuclear physics 
nuclear properties, nuclear forces, nuclear structures, nuclear reactions, radioactive nuclear decay 
8 
Electronics 
semiconductor physics; diodes  clipping, clamping, rectification; Zener regulated power supply, bipolar junction transistor  CC, CB, and CE configurations; transistor as a switch; amplifiers 
9 
Operational Amplifier and its applications 
inverting & noninverting amplifiers, adder, integrator, differentiator, waveform generator, comparator, Schmidt trigger. Digital integrated circuits – NAND and NOR gates as building blocks, XOR gates, half and full adder. 
Computer Science 

1 
Data structures 
array, stack, queue, linked list, binary tree, heap, AVL tree, Btree. 
2 
Discrete Mathematics 
recurrence relations, generating functions, graph theory  paths and cycles, connected components, trees, digraphs. 
3 
Programming languages 
Fundamental concepts  abstract data types, procedure call and parameter passing, dynamic memory allocation, at least one of C, C++, Java and Python. 
4 
Design and analysis of algorithms 
Asymptotic notation, searching, sorting, selection, graph traversal, minimum spanning tree. 
5 
Switching Theory and Logic Design 
Boolean algebra, minimization of Boolean functions, combinational and sequential circuits  synthesis and design. 
6 
Computer organization and architecture 
Number representation, computer arithmetic, memory organization, I/O organization, microprogramming, pipelining, instruction level parallelism. 
7 
Operating systems 
Memory management, processor management, critical section problem, deadlocks, device management, file systems 
8 
Formal languages and automata theory 
Finite automata and regular expressions, pushdown automata, contextfree grammars, Turing machines, elements of undecidability 
9 
Database management systems 
Relational model, relational algebra, relational calculus, functional dependency, normalization (up to 3rd normal form). 
10 
Computer networks 
OSI, LAN technology  Bus/tree, Ring, Star; MAC protocols; WAN technology  circuit switching, packet switching; data communications  data encoding, routing, flow control, error detection/correction, Internetworking, TCP/IP networking including IPv4 
Engineering & Technology 

1 
At least one of C, C++, Java, Python. 

2 
Gravitation, moments of inertia, particle dynamics, elasticity, friction, strength of materials, surface tension and viscosity. 

3 
Laws of thermodynamics and heat engines. 

4 
Electrostatics, magnetostatics and electromagnetic induction 

5 
Laws of electrical circuits – transient and steady state responses of resistive and reactive circuits. 

6 
D.C. generators, D.C. motors, induction motors, alternators, transformers 

7 
Diode circuits, bipolar junction transistors & FET devices and circuits, oscillator, operational amplifier. 

8 
Boolean algebra, minimization of Boolean functions. 

9 
Combinatorial and sequential circuits – multiplexer, demultiplexer, encoder, decoder, flipflops, registers and counters, A/D and D/A converters. 
ISI Syllabus 2021 for M.Tech QROR (PQB)
S.No. 
Topics 
Part 1 Statistics (S1) 

1 
Descriptive statistics for univariate, bivariate and multivariate data. 
2 
Standard univariate probability distributions [Binomial, Poisson, Normal] and their fittings, properties of distributions. Sampling distributions. 
3 
Theory of estimation and tests of statistical hypotheses. 
4 
Simple and Multiple linear regression, linear statistical models, ANOVA. 
5 
Principles of experimental designs and basic designs [CRD, RBD & LSD], Full factorial design, Confounding and blocking in 2k factorial designs 
6 
Elements of nonparametric inference. 
7 
Elements of categorical data analysis. 
8 
Sample surveys – simple random sampling with and without replacement, stratified and cluster sampling. 
Probability (S2) 

1 
Classical definition of probability and standard results on operations with events, conditional probability and independence. 
2 
Distributions of discrete type [Bernoulli, Binomial, Multinomial, Hypergeometric, Poisson, Geometric and Negative Binomial] and continuous type [Uniform, Exponential, Normal, Gamma, Beta] random variables and their moments. 
3 
Bivariate distributions (with special emphasis on bivariate normal), marginal and conditional distributions, correlation and regression. 
4 
Multivariate distributions, marginal and conditional distributions, regression, independence, partial and multiple correlations. 
5 
Order statistics [including distributions of extreme values and of sample range for uniform and exponential distributions]. 
6 
Distributions of functions of random variables. 
7 
Multivariate normal distribution [density, marginal and conditional distributions, regression]. 
8 
Weak law of large numbers, central limit theorem. 
9 
Basics of Markov chains and Poisson processes. 
Part 2 “ Engineering Stream Mathematics (E1) 

1 
Quadratic equations, Roots of polynomial, AP, GP, HP, Divisibility and Prime numbers, Binomial theorem 
2 
Inequalities, permutation and combination, complex numbers and De Moivre’s theorem. 
3 
Elementary set theory, functions and relations, matrices, determinants, solutions of linear equations. 
4 
Trigonometry [multiple and submultiple angles, inverse circular functions, identities, solutions of equations, properties of triangles]. 
5 
Coordinate geometry (two dimensions) [straight line, circle, parabola, ellipse and hyperbola], plane geometry, Mensuration. 
6 
Sequences, series and their convergence and divergence, power series, limit and continuity of functions of one or more variables, differentiation and its applications, maxima and minima, integration, definite integrals areas using integrals, ordinary and partial differential equations (up to second order) 
Engineering and Technology (E2) Engineering Mechanics and Thermodynamics 

1 
Forces in plane and space, analysis of trusses, beams, columns, friction, principles of strength of materials, workenergy principle, moment of inertia, plane motion of rigid bodies, belt drivers, gearing. 
2 
Laws of thermodynamics, internal energy, work and heat changes, reversible changes, adiabatic changes, heat of formation, combustion, reaction, solution and dilution, entropy and free energy and maximum work function, reversible cycle and its efficiency, principles of internal combustion engines, principles of refrigeration. 
Electrical and Electronics Engineering 

1 
DC circuits, AC circuits (1φ), energy and power relationships, transformer, DC and AC machines, concepts of control theory and applications. 
2 
Network analysis, 2 port network, transmission lines, elementary electronics (including amplifiers, oscillators, opamp circuits), analog and digital electronic circuits, basics of computer architecture. 
Engineering Drawing 

1 
Concept of projection, point projection, line projection, plan, elevation, sectional view (1st angle / 3rd angle) of simple mechanical objects, isometric view, dimensioning, sketch of machine parts. (Use of Set Square, compass and diagonal scale should suffice). 
What is ISI Admission Test 2021 Exam Pattern for Part 1?
Particulars 
Details 
Questions 
MCQ or Descriptive 
Subject 
Mathematics of UG level 
Total 
30 Marks 
Duration 
2 Hours 
What is ISI Admission Test 2021 Exam Pattern for Part 2?
Particulars 
Details 
Questions 
MCQ or Descriptive 
Sections 
5 sections:

What are the Important dates related to ISI Syllabus 2021?
Events 
Dates 
Notification Release 
8th March 2021 
Application form Release 
2nd week of March 2021 
Last date to submit form 
2^{nd} week of April 2021 
Last date for fee payment 
3^{rd} week of April 2021 
Release of admit card 
June/ July 2021 
ISI exam 
18th July 2021 
answer key 
3rd week of July 2021 
Last date to submit objections 
4th week of July 2021 
Result Release 
Last week of July/ August 2021 
Release of 1st admission list 
August 2021 
When will the ISI Admit Card 2021 be released?
ISI Admit Card will be released by the Indian Statistical Institute (ISI). The ISI admit card contains information of the candidate and the examination. Students can download the ISI Admit Card through online mode by checking the official site. Students can get their ISI admit cards only from the online mode. Students should check all the details available in it. Students should download the ISI Admit Card and take printouts of the admit card which will be required for the exam. ISI Admit Card is a very important document that must be carried to the ISI 2021 exam without fail.
Syllabus 2021  FAQ
Category  Application Fee 
For general category candidates  Rs. 1250 
For SC/ ST/ OBC NCL/ PWD category candidates  Rs. 625 
ISI 2021 Form Fee by offline can be paid through Challan for cash payment at SBI branch.
ISI 2021 Form Fee by online can be paid by debit card/ credit card or net banking.
The exam date for ISI 2021 is 18th July 2021.
ISI 2021 will be conducted by Indian Statistical Institute (ISI).
ISI 2021 is conducted for admission in courses – B. Stat (Hons.), B. Maths (Hons.), M. Math, M. Tech (CS), MS (QMS), MS (QE).