IIT JAM is not only a perfect opportunity for the ones who have always dreamed of pursuing SOME degree from IITs but also for the ones wishing to delve deep into Economics
IIT JAM 2023 notification has been released by IIT Guwahati, the exam conducting body for this year.
Here in this article, Edusure School brings you all the important updates about the IIT JAM and its notification released till now.
The exam will be conducted for seven subjects, namely, Physics, Chemistry, Geology, Mathematics, Mathematical Statistics, Biotechnology and Economics. Admission is offered to the qualifying candidates in M.Sc (2 year), Masters in Economics (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree & other Post-Bachelor’s Degree & Integrated Ph.D courses.
This article is focused on general information on IIT JAM and specifically the M.Sc Economics course.
APPLICATION FEES :
IIT JAM Eligibility:
APPLY ONLINE/ OFFICIAL WEBSITE (LINK ACTIVATE 07/09/2022): https://jam.iitg.ac.in/index.html
|Exam Duration||3 hours|
|Number of Papers and Total Marks||Seven papers in total with 100 marks each|
|Total Number of Questions||60|
|Marking Scheme||Differential marking scheme carrying 1 mark and 2 marks|
|Language/Medium of Questions||English|
|Colleges Accepting IIT JAM Scores||IITs, IISc Bangalore, NITs and CFTIs|
|Total Number of Seats||3,000 (approx)|
|Exam Level||Postgraduate Exam at National level|
|Exam Frequency||Once a year|
|Mode of Exam||Computer-Based Test (CBT)|
|Total Number of Applicants||84000 approx|
The IIT JAM 2023 exam will be conducted in two sessions-
|IIT JAM 2023 Exam Date||Session Wise IIT JAM Exam Time||Test Papers and Codes|
|12th February 2023 (Sunday)||1 (Forenoon) 9.30 am to 12.30 pm||Chemistry (CY)
|II (Afternoon) 2.30 pm to 5.30 pm
Mathematical Statistics (MS)
The syllabus of IIT JAM Mathematics 2023 includes the 10+2+3 level topics:
|Unit – 1: Sequences and Series of Real Numbers|
|Convergence of sequences bounded and monotone sequences, Cauchy sequences, Bolzano-Weierstrass theorem, absolute convergence, tests of convergence for series – comparison test, ratio test, root test;
Power series (of one real variable), radius and interval of convergence, term-wise differentiation and integration of power series.
|Unit – 2: Functions of One Real Variable|
|Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, Taylor’s series, maxima and minima, Riemann integration (definite integrals and their properties), fundamental theorem of calculus.|
|Unit – 3: Functions of Two or Three Real Variables|
|Limit, continuity, partial derivatives, total derivative, maxima and minima.|
|Unit – 4: Integral Calculus|
|Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.|
|Unit – 5: Differential Equations|
|Bernoulli’s equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, method of separation of variables, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.|
|Unit – 6: Matrices|
|Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors.|
|Unit – 7: Groups|
|Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange’s theorem for finite groups, group homomorphisms.|
|Unit – 8: Finite-Dimensional Vector Spaces|
|Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem.|
The IIT JAM 2023 syllabus for statistics comprises mathematics (30% weightage) and Statistics (70% weightage).
|Unit – 1: Sequences and Series of real numbers: Sequences of real numbers, their convergence, and limits. Cauchy sequences and their convergence. Monotonic sequences and their limits. Limits of standard sequences. Infinite series and its convergence, and divergence. Convergence of series with non-negative terms. Tests for convergence and divergence of a series.
Comparison test, limit comparison test, D’Alembert’s ratio test, Cauchy’s 𝑛 𝑡ℎ root test, Cauchy’s condensation test and integral test. Absolute convergence of series. Leibnitz’s test for the convergence of alternating series. Conditional convergence. Convergence of power series and radius of convergence.
|Unit – 2: Differential Calculus of one and two real variables: Limits of functions of one real variable. Continuity and differentiability of functions of one real variable. Properties of continuous and differentiable functions of one real variable. Rolle’s theorem and Lagrange’s mean value theorems. Higher-order derivatives, Leibnitz’s rule and its applications. Taylor’s theorem with Lagrange’s and Cauchy’s form of remainders. Taylor’s and Maclaurin’s series of standard functions. Indeterminate forms and L’ Hospital’s rule. Maxima and minima of functions of one real variable, critical points, local maxima and minima, global maxima and minima, and point of inflection. Limits of functions of two real variables. Continuity and differentiability of functions of two real variables. Properties of continuous and differentiable functions of two real variables. Partial differentiation and total differentiation. Leibnitz’s rule for successive differentiation. Maxima and minima of functions of two real variables. Critical points, Hessian matrix, and saddle points. Constrained optimization techniques (with Lagrange multiplier).|
|Unit – 3: Integral Calculus: Fundamental theorems of integral calculus (single integral). Leibnitz’s rule and its applications. Differentiation under integral sign. Improper integrals. Beta and Gamma integrals: properties and relationship between them. Double integrals. Change of order of integration. Transformation of variables. Applications of definite integrals. Arc lengths, areas and volumes.|
|Unit – 4: Matrices and Determinants: Vector spaces with real field. Subspaces and sum of subspaces. Span of a set. Linear dependence and independence. Dimension and basis. Algebra of matrices. Standard matrices (Symmetric and Skew Symmetric matrices, Hermitian and Skew Hermitian matrices, Orthogonal and Unitary matrices, Idempotent and Nilpotent matrices). Definition, properties and applications of determinants. Evaluation of determinants using transformations. Determinant of product of matrices.Singular and nonsingular matrices and their properties. Trace of a matrix. Adjoint and inverse of a matrix and related properties. Rank of a matrix, row-rank, column-rank, standard theorems on ranks, rank of the sum and the product of two matrices. Row reduction and echelon forms. Partitioning of matrices and simple properties. Consistent and inconsistent system of linear equations. Properties of solutions of system of linear equations. Use of determinants in solution to the system of linear equations. Cramer’s rule. Characteristic roots and Characteristic vectors. Properties of characteristic roots and vectors. Cayley Hamilton theorem.|
|Unit – 1: Probability|
|Random Experiments. Sample Space and Algebra of Events (Event space). Relative frequency and Axiomatic definitions of probability. Properties of probability function. Addition theorem of probability function (inclusion-exclusion principle). Geometric probability. Boole’s and Bonferroni’s inequalities. Conditional probability and Multiplication rule. Theorem of total probability and Bayes’ theorem. Pairwise and mutual independence of events.|
|Unit – 2: Univariate Distributions|
|Definition of random variables. Cumulative distribution function (c.d.f.) of a random variable. Discrete and Continuous random variables. Probability mass function (p.m.f.) and Probability density function (p.d.f.) of a random variable. Distribution (c.d.f., p.m.f., p.d.f.) of a function of a random variable using transformation of variable and Jacobian method. Mathematical expectation and moments. Mean, Median, Mode, Variance, Standard deviation, Coefficient of variation, Quantiles, Quartiles, Coefficient of Variation, and measures of Skewness and Kurtosis of a probability distribution. Moment generating function (m.g.f.), its properties and uniqueness. Markov and Chebyshev inequalities and their applications.|
|Unit – 3: Standard Univariate Distributions|
|Degenerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (of first and second type), Normal and Cauchy distributions, their properties, interrelations, and limiting (approximation) cases.|
|Unit – 4: Multivariate Distributions|
|Definition of random vectors. Joint and marginal c.d.f.s of a random vector. Discrete and continuous type random vectors. Joint and marginal p.m.f., joint and marginal p.d.f.. Conditional c.d.f., conditional p.m.f. and conditional p.d.f.. Independence of random variables. Distribution of functions of random vectors using transformation of variables and Jacobian method. Mathematical expectation of functions of random vectors. Joint moments, Covariance and Correlation. Joint moment generating function and its properties. Uniqueness of joint m.g.f. and its applications. Conditional moments, conditional expectations and conditional variance. Additive properties of Binomial, Poisson, Negative Binomial, Gamma and Normal Distributions using their m.g.f..|
|Unit – 5: Standard Multivariate Distributions|
|Multinomial distribution as a generalization of binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions and related properties.|
|Unit – 6: Limit Theorems|
|Convergence in probability, convergence in distribution and their inter relations. Weak law of large numbers and Central Limit Theorem (i.i.d. case) and their applications.|
|Unit – 7: Estimation|
|Unbiasedness. Sufficiency of a statistic. Factorization theorem. Complete statistic. Consistency and relative efficiency of estimators. Uniformly Minimum variance unbiased estimator (UMVUE). RaoBlackwell and Lehmann-Scheffe theorems and their applications. Cramer-Rao inequality and UMVUEs.
Methods of Estimation: Method of moments, method of maximum likelihood, invariance of maximum likelihood estimators. Least squares estimation and its applications in simple linear regression models. Confidence intervals and confidence coefficient. Confidence intervals for the parameters of univariate normal, two independent normal, and exponential distributions.
|Unit – 8: Testing of Hypotheses|
|Null and alternative hypotheses (simple and composite), Type-I and Type-II errors. Critical region. Level of significance, size and power of a test, p-value. Most powerful critical regions and most powerful (MP) tests. Uniformly most powerful (UMP) tests. Neyman Pearson Lemma (without proof) and its applications to construction of MP and UMP tests for parameter of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.|
|Unit – 9: Sampling Distributions|
|Definitions of random sample, parameter and statistic. Sampling distribution of a statistic.
Order Statistics: Definition and distribution of the 𝑟 𝑡ℎ order statistic (d.f. and p.d.f. for i.i.d. case for continuous distributions). Distribution (c.d.f., p.m.f., p.d.f.) of smallest and largest order statistics (i.i.d. case for discrete as well as continuous distributions).
Central Chi-square distribution: Definition and derivation of p.d.f. of central 𝜒2 distribution with 𝑛 degrees of freedom (d.f.) using m.g.f.. Properties of central 𝜒2 distribution, additive property and limiting form of central 𝜒2 distribution.
Central Student’s 𝒕-distribution: Definition and derivation of p.d.f. of Central Student’s 𝑡-distribution with 𝑛 d.f., Properties and limiting form of central 𝑡-distribution.
Snedecor’s Central 𝑭-distribution: Definition and derivation of p.d.f. of Snedecor’s Central 𝐹-distribution with (𝑚, 𝑛) d.f.. Properties of Central 𝐹-distribution, distribution of the reciprocal of 𝐹– distribution. Relationship between 𝑡, 𝐹 and 𝜒2 distributions.
|Unit – 1: Microeconomics|
|Consumer theory: Preference, utility and representation theorem, budget constraint, choice, demand (ordinary and compensated), Slutsky equation, revealed preference axioms.
Theory of production and cost: Production technology, isoquants, production function with one and more inputs, returns to scale, short run and long run costs, cost curves in the short run and long run.
General equilibrium and welfare: Equilibrium and efficiency under pure exchange and production, welfare economics, theorems of welfare economics.
Market structure: Perfect competition, monopoly, pricing with market power, price discrimination (first, second and third), monopolistic competition and oligopoly.
Game theory: Strategic form games, iterated elimination of dominated strategies, Nash equilibrium, mixed extension and mixed strategy. Nash equilibrium, examples: Cournot, Bertrand duopolies, Prisoner’s dilemma.
Public goods and market failure: Externalities, public goods and markets with asymmetric information (adverse selection and moral hazard)
|Unit – 2: Macroeconomics|
|National income accounting: Structure, key concepts, measurements, and circular flow of income – for closed and open economy, money, fiscal and foreign sector variables – concepts and measurements.
Behavioural and technological functions: Consumption functions – absolute income hypothesis, life-cycle and permanent income hypothesis, random walk model of consumption, investment functions – Keynesian, money demand and supply functions, production function.
Business cycles and economic models (closed economy): Business cycles-facts and features, the Classical model of the business cycle, the Keynesian model of the business cycle, simple Keynesian cross model of income and employment determination and the multiplier (in a closed economy), IS-LM Model, Hicks’ IS-LM synthesis, role of monetary and fiscal policies.
Business cycles and economic models (open economy): Open economy, Mundell-Fleming model, Keynesian flexible price (aggregate demand and aggregate supply) model, role of monetary and fiscal policies.
Inflation and unemployment: Inflation – theories, measurement, causes, and effects, unemployment – types, measurement, causes, and effects.
Growth models: Harrod-Domar, Solow and Neo-classical growth models (AK model, Romer model and Schumpeterian growth model).
|Unit – 3: Statistics for Economics|
|Probability theory: Sample space and events, axioms of probability and their properties, conditional probability and Bayes’ rule, independent events, random variables and probability distributions, expectation, variance and higher order moments, functions of random variables, properties of commonly used discrete and continuous distributions, density and distribution functions for jointly distributed random variables, mean and variance of jointly distributed random variables, covariance and correlation coefficients.
Mathematical statistics: Random sampling, types of sampling, point and interval estimation, estimation of population parameters using methods of moments and maximum likelihood procedures, properties of estimators, sampling distribution, confidence intervals, central limit theorem, law of large number.
Hypothesis testing: distributions of test statistics, testing hypotheses related to population parameters, Type I and Type II errors, the power of a test, tests for comparing parameters from two samples.
Correlation and regression: Correlation and types of correlation, the nature of regression analysis, method of Ordinary Least Squares (OLS), CLRM assumptions, properties of OLS, goodness of fit, variance and covariance of OLS estimator
|Unit – 4: Indian Economy|
|Indian economy before 1950: Transfer of tribute, deindustrialization of India.
Planning and Indian development: Planning models, relation between agricultural and industrial growth, challenges faced by Indian planning.
Indian economy after 1991: Balance of payments crisis in 1991, major aspects of economic reforms in India after 1991, reforms in trade and foreign investment.
Banking, finance and macroeconomic policies: aspects of banking in India, CRR and SLR, financial sector reforms in India, fiscal and monetary policy, savings and investment rates in India.
Inequalities in social development: India’s achievements in health, education and other social sectors, disparities between Indian States in human development.
Poverty: Methodology of poverty estimation, Issues in poverty estimation in India.
India’s labour market: unemployment, labour force participation rates.
|Unit – 5: Mathematics for Economics|
|Indian economy before 1950: Transfer of tribute, deindustrialization of India Planning and Indian development: Planning models, relation between agricultural and industrial growth, challenges faced by Indian planning Indian economy after 1991: Balance of payments crisis in 1991, major aspects of economic reforms in India after 1991, reforms in trade and foreign investment Banking, finance and macroeconomic policies: aspects of banking in India, CRR and SLR, financial sector reforms in India, fiscal and monetary policy, savings and investment rates in India Inequalities in social development: India’s achievements in health, education and other social sectors, disparities between Indian States in human development Poverty: Methodology of poverty estimation, Issues in poverty estimation in India India’s labour market: unemployment, labour force participation rates.
Differential calculus: Limits, continuity and differentiability, mean value theorems, Taylor’s theorem, partial differentiation, gradient, chain rule, second and higher-order derivatives: properties and applications, implicit function theorem, and application to comparative statics problems, homogeneous and homothetic functions: characterizations and applications.
Integral calculus: Definite integrals, fundamental theorems, indefinite integrals and applications.
Differential equations, and difference equations: First order difference equations, first order differential equations and applications.
Linear algebra: Matrix representations and elementary operations, systems of linear equations: properties of their solution, linear independence and dependence, rank, determinants, eigenvectors and eigenvalues of square matrices, symmetric matrices and quadratic forms, definiteness and semidefiniteness of quadratic forms.
Optimization: Local and global optima: geometric and calculus-based characterisations, and applications, multivariate optimization, constrained optimization and method of Lagrange multiplier, second-order condition of optima, definiteness and optimality, properties of value function: envelope theorem and applications, linear programming: graphical solution, matrix formulation, duality, economic interpretation
You must plan your preparation with the help of this detailed IIT JAM 2023 Syllabus of your subject discussed here along with solving past IIT papers along with ISI and DSE past papers
Edusure School offers specialised guidance focused for preparing for IIT JAM, with Online Live Classes and Streamed lectures with a dedicated team of Subject-wise Experienced Faculty Members.
Complete Printed Study Material, Practice Sets and IIT JAM Previous Years’ Solved Papers as well as class recordings will be provided.
Regular Online Topic-wise Tests followed by doubt solving sessions.
With consecutive success of producing AIR 1 in IIT JAM both in 2021 and 2022, and an impressive list of students who have topped the entrances and made to their college of choice
Edusure proudly announces its IIT JAM 2023 focused new batch starting today!!
See you in class!