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Updated on 16th January, 2024 , 7 min read
IIT JAM Latest Updates:
The syllabus for IIT JAM Mathematics 2024 encompasses subjects such as integral calculus, linear algebra, and real variables. Formulated by the conducting body, this mathematics syllabus aligns with the standards of a graduate-level education. Those aspiring to pursue an M. Sc in Mathematics at IIT will find the article valuable, covering all necessary and crucial topics.
Before delving into the syllabus details, candidates should familiarize themselves with the paper's structure and marking scheme. This understanding will aid in assessing the syllabus comprehensively and preparing effectively. The examination comprises three sections—“A,” “B,” and “C”—with a total of 60 Multiple Choice Questions (MCQs) amounting to 100 marks.
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Every year, one of the participating institutes administers the IIT JAM exam. The IIT JAM 2023 Exam is being held at IIT Guwahati.
The exam authority added a new subject, Economics, to the IIT JAM Syllabus in 2021. This will be continued in subsequent years of the exam. As a result, the IIT JAM subject list includes Physics, Chemistry, Mathematics, Biotechnology, Statistics, Economics, and Geology. This article contains the entire IIT JAM Mathematics syllabus.
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The following are the important topics, along with their weightage, based on previous year's paper analysis:
Topic | Weightage |
Real Analysis | 21% |
Calculus of Single Variable | 18% |
Linear Algebra | 14% |
Calculus of Two Variables | 14% |
Vector Calculus | 12% |
Differential Equation | 11% |
Abstract Algebra | 10% |
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Section | No. of Questions | Marks per Question | Total Marks | Negative Marking |
Section A | 10 | 1 | 10 | ⅓ |
20 | 2 | 40 | ⅔ | |
Section B | 10 | 2 | 20 | N/A |
Section C | 10 | 1 | 10 | N/A |
10 | 2 | 20 | ||
60 | 100 |
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The 10+2+3 level topics covered in the IIT JAM Mathematics 2023 syllabus include Sequence & Series, Function, Vector, Differential Equations, and so on. These are some of the most highly rated chapters in Mathematics.
The Mathematical Statistics (MS) test paper is divided into two sections.
The topics covered in the IIT JAM Mathematical Statistics Syllabus 2023 are listed below.
Sl.no | Topics | Sub- Topics |
Unit - 1 | Sequences and Series of Real Numbers | Real number sequences, sequence convergence, bounded and monotone sequences, real number sequence convergence criteria. There are also Cauchy sequences and sub-sequences, as well as the Bolzano-Weierstrass theorem. There are also series of real numbers, absolute convergence, tests of convergence for series of positive terms that include comparison tests, ratio tests, root tests, and the Leibniz test for alternating series convergence, among other things. |
Unit - 2 | Differential Equations | Bernoulli's equation, exact differential equations, integrating factors, orthogonal trajectories, homogeneous differential equations, variable separation method, linear differential equations of second order with constant coefficients, parameter variation method, Cauchy-Euler equation. |
Unit - 3 | Integral Calculus | Integration is defined as the inverse process of differentiation, as well as definite integrals and all the properties associated with the calculus fundamental theorem. Aside from that, there are double and triple integrals, information on changing the order of integration, the process of calculating surface areas and volumes using double integrals, and calculating volumes using triple integrals. |
Unit - 4 | Linear Algebra | Finite-dimensional vector spaces with linear vector independence, basis and dimension, and linear transformations, details on matrix representation and also range space with null space, concepts on rank-nullity theorem. It also covers Rank and inverse of a matrix, determinant and all the solutions of linear equation's systems. On the contrary there are consistency conditions along with eigenvalues, and also eigenvectors for matrices, Cayley-Hamilton theorem, etc in this section. |
Unit - 5 | Functions of Two or Three Real Variables | Limit, continuity, partial derivatives, total derivatives, maxima and minima are all included in this unit. |
Unit - 6 | Finite-Dimensional Vector Spaces | Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem are all covered in this unit. |
Unit - 7 | Matrices | Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, and eigenvectors are all covered in this unit. |
Unit - 8 | Groups | Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms. |
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Units | Topics | Sub topics |
Unit-1 | Probability | Experiments at Random. Sample Space and Event Algebra (Event Space). Probability is defined using relative frequency and axiomatically. Probability function properties. Probability function addition theorem (inclusion-exclusion principle). Probability based on geometry. Boole's and Bonferroni's inequalities. Multiplication rule and conditional probability. Total probability theorem and Bayes' theorem. Events are pairwise and mutually independent. |
Unit - 2 | Univariate Distributions | Random variables are defined as follows. A random variable's cumulative distribution function (c.d.f.). Random variables, both discrete and continuous. A random variable's probability mass function (p.m.f.) and probability density function (p.d.f.). Distribution (c.d.f., p.m.f., p.d.f.) of a random variable function using variable transformation and Jacobian method. Moments and mathematical expectation. A probability distribution's mean, median, mode, variance, standard deviation, coefficient of variation, quantiles, quadriles, coefficient of variation, and measures of skewness and kurtosis. The properties and uniqueness of the moment generating function (m.g.f.). The applications of Markov and Chebyshev inequalities. |
Unit - 3 | Standard Univariate Distributions | Degenerate, Bernoulli, Binomial, Negative binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Double exponential, Gamma, Beta (of the first and second types), Normal, and Cauchy distributions, as well as their properties, interrelationships, and limiting (approximation) cases. |
Unit - 4 | Multivariate Distributions |
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Unit - 5 | Standard Multivariate Distributions | The multinomial distribution and its properties (moments, correlation, marginal distributions, additive property) are a generalization of the binomial distribution and its properties. The bivariate normal distribution, as well as its marginal and conditional distributions, and their related properties. |
Unit - 6 | Limit Theorems | The interrelationships of probability and distribution convergence. The Weak Law of Large Numbers and the Central Limit Theorem are used in applications (i.i.d. case). |
Unit - 7 | Estimation |
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Unit - 8 | Testing of Hypotheses | Type-I and Type-II errors, null and alternative hypotheses (simple and composite). A critical region. The level of significance, the size and power of a test, and the p-value. Uniformly powerful critical regions and powerful (MP) tests. Uniformly most powerful (UMP) tests are performed. Pearson, Neyman Lemma (without proof) and its applications to the development of MP and UMP tests for single parameter parametric families. Likelihood ratio tests for univariate normal distribution parameters. |
Unit - 9 |
Sampling Distributions
| Random sample, parameter, and statistic definitions. A statistic's sampling distribution.
Definition and derivation of p.d.f. of Snedecor's Central F-distribution with (m, n) d.f. The properties of the Central F-distribution, as well as the distribution of the reciprocal of the F-distribution. The relationship between the t, F, and 2 distributions. |
Sl.no | Topics | Recommended Books |
1. | Books for Linear Algebra
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2. |
Books for Abstract Algebra
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3. |
Books for Real Analysis
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4. |
Books for Vector Calculus and Differential Equation
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IIT JAM 2023 Application Form, Registration (Started) - Apply Online Here
By - Prachi Bhatia 2023-04-07 09:10:22 , 5 min readIIT JAM Mathematics Syllabus - Weightage of Subjects, Detailed Syllabus
By - Kitiyala Jamir 2024-01-16 06:15:48 , 7 min readIIT JAM Physics Syllabus 2024 - Weightage of Topics, Important Chapters, Recommended Books
By - Kitiyala Jamir 2024-04-02 05:55:30 , 5 min readYou can practice Abelian and non-abelian groups in the section Group Theory, as well as details on permutation groups and Lagrange’s Theorem only for finite groups, and you must have a basic understanding of quotient groups.
It is best to practice all sections of the syllabus for high marks, so you should focus on all topics in Mathematics as this is the scoring subject.
The syllabus for the IIT JAM 2023 exam is available on the exam’s official website as well as on this page. On this page, candidates can also download the IIT JAM 2023 syllabus in PDF format for each subject.
Candidates can view the updated JAM exam syllabus 2023 as well as the JAM 2023 application form on the official website of IIT Roorkee.
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