JAM MATHEMATICS

ABOUT JAM

The Indian Institute of Science Bangalore (IISc) and Indian Institutes of Technology (IITs) conduct the Joint Admission Test for M.Sc. (JAM) for admission to Integrated Ph.D. Degree Programmes at IISc Bangalore and M.Sc. (Two Years), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, M.Sc.-M.Tech., M.Sc.-M.S.(Research)/Ph.D. Dual Degree and other Post-Bachelor's Degree Programmes at IITs. The main objective of JAM is to consolidate Science as a career option for bright students across the country. It is expected that the research infrastructure, the inter-disciplinary interaction and the vibrant academic environment of IISc Bangalore and IITs will motivate these students to pursue R&D careers in frontier areas of basic sciences as well as inter-disciplinary areas of science and technology.

WHAT IS NEW?

JAM 2017 Examination will be conducted ONLINE only as a Computer Based Test (CBT) for all Test Papers.
All the seven Test Papers of JAM 2017 will be of fully objective type, with three different patterns of questions as follows:

1. Multiple Choice Questions (MCQ) : Each MCQ type question has four choices out of which only one choice is the correct answer.

2. Multiple Select Questions (MSQ): Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices.

3. Numerical Answer Type (NAT) Questions: For each NAT type question, the answer is a signed real number which needs to be entered using the virtual keypad on the monitor. No choices will be shown for these type of questions.
All candidates have to apply only ONLINE.
NO hardcopies of documents (except challan) are to be sent to the Organizing Institute. The documents (if applicable) are to be uploaded to the online application website only.
No hardcopy of JAM 2017 score card will be sent to the JAM 2017 qualified candidates by the Organizing Institute. It can only be downloaded from JAM 2017 website.

IMPORTANT DATES
September 02, 2016 Commencement of ONLINE Registration and Application Process
October 10,2016 Last Date for Payment of Fee through Challan
October 14,2016 Closure of ONLINE Application Procedure
February 07, 2017 JAM 2017 Examination
March 23, 2017 Announcement of JAM 2017 Results

QUESTION PATTERN - JAM 2017

JAM 2017 examination will be conducted for the seven test papers, namely: Biological Sciences (BL), Biotechnology (BT), Chemistry (CY), Geology (GG), Mathematics (MA), Mathematical Statistics (MS) and Physics (PH). All seven test papers will be of fully objective type, with three different patterns of questions as follows:

Multiple Choice Questions (MCQ): Each MCQ type question has four choices out of which only one choice is the correct answer.

Multiple Select Questions (MSQ): Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices.

Numerical Answer Type (NAT) Questions: For each NAT type question, the answer is a signed real number which needs to be entered using the virtual keypad on the monitor. No choices will be shown for these types of questions.

PATTERN OF TEST PAPERS

The JAM 2017 examination for all the seven test papers will be carried out as ONLINE Computer Based
Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. For all the seven test papers, the duration of the examination will be 3 hours. The medium for all the test papers will be English only. There will be a total of 60 questions carrying 100 marks. The entire paper will be divided into three sections, A, B and C. All sections are compulsory. Questions in each section are of different types as given below:

SECTION – A: contains a total of 30 Multiple Choice Questions (MCQ) carrying one or two marks each. Each MCQ type question has four choices out of which only one choice is the correct answer.
Candidates can mark the answer by clicking the choice.

SECTION – B: contains a total of 10 Multiple Select Questions (MSQ) carrying two marks each. Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices. The candidate gets full credit if he/she selects all the correct answers only and no wrong answers. Candidates can mark the answer(s) by clicking the choice(s).

SECTION – C: contains a total of 20 Numerical Answer Type (NAT) questions carrying one or two marks each. For these NAT type questions, the answer is a signed real number which needs to be entered using the virtual keyboard on the monitor. No choices will be shown for these types of questions.

Candidates have to enter the answer by using a virtual numeric keypad.

MARKING SCHEME

In all sections, questions not attempted will result in zero mark. In Section – A (MCQ), wrong answer will result in negative marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer.
For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section – B (MSQ),
There are no negative and no partial marking provisions. There is no negative marking in Section – C that is for NAT questions.

ONLINE TEST RULES
  • An on-screen virtual scientific calculator will be available for the candidates to do the calculations. Physical calculators, charts, graph sheets, tables, cellular phone or any other electronic gadgets are NOT allowed in the examination hall.
  • A scribble pad will be provided for rough work and this has to be returned back at the end of the examination.
  • The candidates are required to select the answer for MCQ and MSQ type questions, and to enter the answer for NAT questions using only a mouse on a virtual keypad (the keyboard of the computer will be disabled). At the end of the 3-hour window, the computer will automatically close the screen from further actions.
  • REGULAR CLASSROOM PROGRAMS

    REGULAR CLASSROOM PROGRAMS

    These are very comprehensive programmes which run over the span of 4-6 months depending on the course. Under these programmes the classes are conducted 4-6 hrs per day for 5 to 6 days in a week. The class schedules are designed in a manner that every student in the class gets equal opportunity to learn and apply.

    As the understanding level of all the students in a class may not be uniform, we try to distinguish weaker so called average students in the class and work over them. For such students we have developed Basic Building Measures (BBM) which has two components

    1. BBM- Tests: After 2-3 lectures on any topic the academy offers a test to all the students. This test (Called BBM Test) contains very basic and fundamental questions about that topic. The performances over this test are analyzed comprehensively and on the basis of their performance, those students are identified who could not cross minimum thresh hold and requires extra care.

    2. BBM Classes: The students Identified by BBM tests are clubbed into various groups and dedicated faculty are assigned to each group. These groups are given extra classes (BBM Classes). In these classes, this faculty helps the students clear their doubts and concept so that they too can equally participate in the regular classes along with the so called average plus students.

    The RCPs of Rising Star Academy are complete in its nature. In the span of almost half a year we try to bridge the gap between your degree and learning so that you can appear in any competitive exam of your eligibility and interest.

    Syllabus / Books

    JAM: MATHEMATICS

    Sequences and Series of Real Numbers: Sequences and series of real numbers, Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibnitz test for convergence of alternating series.

    FUNCTIONS OF ONE VARIABLE:

    Functions of One Variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem, Maxima and minima.

    Functions of Two Real Variables:limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

    Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

    Differential Equations:Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy-Euler equation.

    Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.

    Group Theory: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups (only group theory).

    Linear Algebra:Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skew-symmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

    Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series.

    JAM: MATHEMATICAL STATISTICS (MS)

    The Mathematical Statistics (MS) test paper comprises of Mathematics (40% weightage) and Statistics (60% weightage).

    MATHEMATICS Sequences and Series: : Convergence of sequences of real numbers, Comparison, root and ratio tests for convergence of series of real numbers.

    Differential Calculus: Limits, continuity and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables.

    Integral Calculus:Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.

    Matrices:Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric, skew-symmetric and orthogonal matrices.

    Differential Equations:: Ordinary differential equations of the first order of the form y' = f(x,y). Linear differential equations of the second order with constant coefficients.

    STATISTICS

    Probability:Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes' theorem and independence of events.

    Random Variables: Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.
    Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.

    Joint Distributions:Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables.

    Sampling distributions: Chi-square, t and F distributions, and their properties.

    Limit Theorems:Weak law of large numbers. Central limit theorem (i.i.d. with finite variance case only).

    Estimation:Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, Rao-Blackwell and Lehmann- Scheffe theorems, uniformly minimum variance unbiased estimators. Rao-Cramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.

    Testing of Hypotheses:: Basic concepts, applications of Neyman-Pearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.

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