IIT JAM Mathematics & Mathematical Statistics Syllabus

Mathematics (MA)

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: L imit, 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 and minima.Integral Calculus: Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.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.

Linear Algebra and Algebra:
Matrices: Systems of linear equations, rank, nullity, rank-nullity theorem, inverse, determinant, eigenvalues, eigenvectors.Finite Dimensional Vector Spaces: Linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem.Groups: Cyclic groups, abelian groups, non-abelian groups, permutation groups, normal subgroups, quotient groups, Lagrange's theorem for finite groups, group homomorphisms.

MATHEMATICAL STATISTICS (MS)

The Mathematical Statistics (MS) Test Paper comprises following topics of Mathematics (about 30% weight) and Statistics (about 70% weight).

Mathematics
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.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.

Statistics
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.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 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 normal, 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 construction of MP and UMP tests for parameter of single parameter parametric families. Likelihood ratio tests for parameters of univariate normal distribution.

IIT JAM Exam Pattern

IIT JAM Exam Pattern : IIT JAM (Joint Admission Test for M.Sc.) is an entrance examination conducted by the Indian Institutes of Technology (IITs) for admission to various M.Sc., M.Sc.-M.Tech., M.Sc.-Ph.D., and other post-bachelor's degree programs in science disciplines. The conducting body for the Joint Admission Test for Masters (JAM) has been released the IIT JAM Exam Pattern  on its official website.

The IIT JAM Examination will consist of seven subjects: Biotechnology, Chemistry, Economics, Geology, Mathematics, Mathematical Statistics, and Physics. The medium for all subjects will be English only. The examination will be conducted as a Computer-Based Test (CBT).

Candidates should carefully review the IIT JAM  Exam Pattern, which includes details on exam duration, marking scheme, question types, and total marks. Understanding the exam structure thoroughly will help aspirants prepare effectively and perform confidently in the test.

In the Examination, there will be seven subjects, and it will be a Computer-Based Test (CBT) with English as the medium. The duration of the exam is three hours, and it consists of 60 questions and carries 100 marks. The paper is divided into three sections: A, B, and C. Section A has 30 Multiple Choice Questions (MCQs), Section B has 10 Multiple Select Questions (MSQs), and Section C has 20 Numerical Answer Type (NAT) questions. For MCQs, there is a negative marking for wrong answers, while MSQs and NATs do not have negative marking. Eligible Persons with Disabilities (PwD) may get one hour compensatory time and be ascribed as per the Government of India guidelines.

IIT JAM Exam Pattern Overview

IIT JAM exam, also known as the Indian Institutes of Technology Joint Admission Test, is a national-level post-graduate degree examination. It is conducted for admission to various post-bachelor's degree courses. The exam will be held online on the 15th of February (tentative). It consists of multiple-choice questions (MCQs) and numerical answer type (NAT) questions.

Regular Classroom Program

Regular Classroom Program for IIT JAM MATHS These are the full length programs for the IIT JAM MATHS Aspirants which are hunting down classroom preparing programs for their exams. These classes are flowed to such an extent that it continues running over the time period of 4-6 month, when classes are coordinated 5-6 days in seven days contributing 4-6 hours step by step. The program is laid out in such a path, to the point that each and every hopeful can understand the topics of subject and gets identical opportunity to learn not like the other coaching institute which overburden the mind of student with extensive instructive modules and due to this they get puzzled with the course. There is a novel method to follow in the Infomaths and that framework is to perceive the student as per their understanding level and help them to crack the examination as per their understanding. We all know that the understanding level of the large number of students isn't same and students feel the frenzy in requesting their various issues from time to time so we isolate them as per their understanding level and make segregate bunches for them under the program named as Basic Building Measures (BBM) which has two fragments 1. BBM – Tests: When Student goes to the classes, after 2-3 classes on each point we offer them these tests which is called BBM Test and as demonstrated by the outcome of these tests we isolate them according to their outcome and give them extra thought so not just topper student and also normal student would clear their exams. 2. BBM – Classes: After the BBM Test happen seclude groups of students are made and therefore their examinations do in view of their understanding level. With the objective that student got select and organization would get best result. So it is a win-win situation both for student and our Academy. Infomaths is acclaimed among the student in view of this exceptional approach which is followed in our establishment and other coaching are not enthused about knowing the student and guide them as per their understanding level with the objective that he/she takes the most preferred benefit from our coaching.

 Weekend Classroom Program 

JAM MATHS Weekend Classroom Program This program is proposed for the working student and the student who are not prepared to join the reliable classroom program due to any reason. The time period of classes will be 10 to 12 hours on Saturday and Sunday. Student can get notes from the regular classroom student or note down their own particular to keep the pace with others and in this way they have the ability to crack the exams while doing their jobs or go to the colleges or universities. In this manner, this program is useful for them and that student said it is a boon for them in light of the way that as a result of this program they can fulfill their dreams of clearing JRF without leaving their occupations or school classes. This Program is productive for those students who are living near to our coaching centresdue to the fact that they can without being in any kind of pressure join the classes on weekends and prepared to satisfy their fantasy of getting JRF and LS.JAM MATHS Weekend Classroom Program This program is proposed for the working student and the student who are not prepared to join the reliable classroom program due to any reason. The time period of classes will be 10 to 12 hours on Saturday and Sunday. Student can get notes from the regular classroom student or note down their own particular to keep the pace with others and in this way they have the ability to crack the exams while doing their jobs or go to the colleges or universities. In this manner, this program is useful for them and that student said it is a boon for them in light of the way that as a result of this program they can fulfill their dreams of clearing JRF without leaving their occupations or school classes. This Program is productive for those students who are living near to our coaching centresdue to the fact that they can without being in any kind of pressure join the classes on weekends and prepared to satisfy their fantasy of getting JRF and LS.

 Online Video Lecture 

JAM MATHS Online Video Lecture Our Distance Learning Program is designed to keep the classroom mood alive, so that students will not be felt boring while watching the lecture on the Video. Since our Video Lectures are directly recorded from regular classroom session not from Studio which will be the main reason that our Video Lectures are alive not like other institutional Video Lectures. Our Video Lectures are Mobile and Desktop compatible, so that you can start learning whenever you want. Students can opt for Video Lectures if they are not able to come to attend our regular classroom session. All the concepts of IIT JAM [MATHS] are completely described in our Video Lectures and you can practice questions on behalf of concepts which are described in our Video Lectures. Our Video Lectures are backed with support for email and Skype ID. You can query your Question or doubts on the Email ID: infomaths32@gmail.com Highlights Of Our Video Lecture Our Video Lectures are Classroom Recorded High Definition Quality Videos High Quality voice Ask your doubts on Email Skype and on Phone Videos are made by Industry Expert.

 Study Material 

IIT JAM MATHS Study Material There are many students who are unable to join the regular classroom program for that kind of students we have another option, i.e. Study Material which are designed by our expert panel, they do it in such a way that the student who read it can understand each and every concept which are going to cover in the exams and practice pool of examples and questions so they can easily handle the problems in the exam on that topic in an easy manner. Our panel updates it regularly so that you have an exact understanding of current pattern of the exam and you do not need any kind of book for any topic other than our study material. If you are booking worm then our study material is enough for you to crack the IIT JAM Stats Exam with good rank. Advantage Of Our Study Material The booklet will cover all the necessary topics Design by Industry expert Study Material will be dispatched in single time Pool of Questions Based on the current exam pattern Written in such a manner so that students can easily understand.

Test series 

Infomaths also has test series for IIT Jam Statistics aspirants which are designed by industry leaders. They designed the test series in such a way that you not only practice questions with our test series, but we also assist you, “how to crack the exam”. Our test series is available online so that you have the freedom to conduct the test as per your own comfort and timings. Our 360 degree analysis which is performed online on the basis of your performance will assist you in the preparation of the competitive exams and scale your performance among the competitive students all across the nation. The result of each exam will be declared on the next day of the exam (in the morning session) and will be available for next two days on your panel with full analysis of exams and your performance in the exams. Our online test series are not identical to regular student but it is merged with test series, which are acquired by our regular students of our academy. In this way you can compete with the most serious and generic aspirants which are lacking in other test series available in the market. Hence, students have the facility to check their knowledge among the most competitive environment before the actual exam. Highlights Of Our Test Series Standard Quality Questions Questions are placed as per the weight age of the question in the exam Availability of question on each concept Practicing these questions can help you in understanding the whole concept. Topic or concept wise test and Full length test available. Get Answer and solution post test Analysis of your performance Availability of similar pattern as per the exam Attempt the exam as per your norms.