IIT JAM Mathematics syllabus download PDF, ECONOMICS, GEOLOGY, MATHEMATICS, MATHEMATICAL STATISTICS, PHYSICS, CHEMISTRY, BIOTECHNOLOGY, Joint Admission Test for M.Sc has released the notification regarding Online form submission of M.Sc Admission test, Interested candidate can check eligibility, Application fees, Age, Qualification, Eligibility, and many more things. If you are interested in downloading the IIT JAM Syllabus you can download your syllabus in pdf format, the link is given below. Official website of IIT JAM https://jam.iitr.ac.in/
Table of Contents
Indian Institute of Technology
|Title||IIT JAM syllabus https://jam.iitr.ac.in/|
|Notification date||coming soon|
|Last date||coming soon|
|Sate||BHILAI, BHUBANESWAR, BOMBAY, DELHI, DHANBAD, GANDHINAGAR, GUWAHATI, HYDERABAD, INDORE, JODHPUR, KANPUR, KHARAGPUR, MADRAS, MANDI, PALAKKAD, PATNA, ROORKEE, ROPAR, TIRUPATI, VARANASI|
|Department||Conducted by IIT Roorkee|
IIT JAM Mathematics Syllabus 2023
|Real Analysis||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.
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.
|Multivariable Calculus and Differential Equations||Functions of Two or Three Real Variables:|
limit, continuity, partial derivatives, total derivative, maxima
double and triple integrals, change of order of integration, calculating surface areas
and volumes using double integrals, calculating volumes using triple integrals.
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
|Linear Algebra and Algebra||Matrices: |
systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant,
Finite Dimensional Vector Spaces:
linear independence of vectors, basis, dimension, linear
transformations, matrix representation, range space, null space, and rank-nullity theorem.
cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups,
quotient groups, Lagrange’s theorem for finite groups, and group homomorphisms.
IIT JAM Economics Syllabus
|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 return 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)
|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
|Behavioral 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|
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, the 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, the 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)
Statistics for Economics
|Probability theory||Sample space and events, axioms of probability and their properties, conditional|
probability and Bayes’ rule, independent events, random variables, 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
the 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, the 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, the goodness of fit, variance and
covariance of the OLS estimator
|Indian economy before 1950: |
Transfer of tribute, the deindustrialization of India
Planning and Indian development: Planning models, the 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 labor market: unemployment, labor force participation rates
Mathematics for Economics
|Preliminaries and functions: Set theory and number theory, elementary functions: quadratic, polynomial, power, exponential, logarithmic, functions of several variables, graphs, and level curves, convex set, concavity and quasiconcavity of function, convexity, and quasi-convexity of functions, sequences, and series: convergence, algebraic properties and applications, complex numbers and its geometrical representation, De Moivre’s theorem, and its application|
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
Optimization: Local and global optima: geometric and calculus-based characterizations, 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
IIT JAM Mathematical Statics Syllabus
|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 𝑛𝑡ℎ 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.
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, Lebnitz’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. Lebnitz’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).
Integral Calculus: Fundamental theorems of integral calculus (single integral). Lebnitz’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.
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.
|Probability: Random Experiments. Sample Space and Algebra of Events (Event space). Relative frequency and Axiomatic definitions of probability. Properties of the 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.|
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.
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
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..
Standard Multivariate Distributions: Multinomial distribution as a generalization of the binomial distribution and its properties (moments, correlation, marginal distributions, additive property). Bivariate normal distribution, its marginal and conditional distributions and related properties.
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.
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.
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 normals, and exponential distributions.
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 the construction of MP and UMP tests for the parameter of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.
IIT JAM 2022 Syllabus
JAM 2022 Highlights
- JAM 2023 Examination will be conducted ONLINE only as a Computer Based Test (CBT) for all Test Papers.
- JAM 2023 will have seven Test Papers, namely, Biotechnology (BT), Chemistry (CY), Economics (EN), Geology (GG), Mathematics (MA), Mathematical Statistics (MS), and Physics (PH).
- All the seven Test Papers of JAM 2023 will be of entirely objective type, with three different patterns of questions, namely (i) Multiple Choice Questions (MCQ), (ii) Multiple Select Questions (MSQ), and (iii) Numerical Answer Type (NAT) questions.