A piece of advice for IIT JAM Mathematics Aspirants

Dear Friends

Hii

I am Shivam Maurya, I have done my post-graduation from IIT Bombay in Mathematics.

General Question that arises in your mind

Question: What is list of good colleges for perusing M.sc in Mathematics?

· Indian institute of Science(IISc)

· Chennai mathematical institute(CMI)

· Tata institute of fundamental research(TIFR)

· IISER’s

· IIT’S

NIT’S

· Delhi University

· Banaras Hindu University

There are other good Universities and Colleges.

Question: What is a different entrance examination for admission in that college. CMI, TIFR, DU, BHU, and AU take their own entrance examination but IISC, IISER, IIT’S, and NIT’s take admission on the basis of your rank in JAM.IISER and IISC have additional interview rounds.

Question: What is JAM?

Jam is being conducted from 2004 to provide admissions to M.Sc. (Four Semesters), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, etc. Programs at the IITs and Integrated Ph.D. Degree Programmes at IISc for consolidating Science as a career option for bright students. These postgraduate programs at IITs and IISc offer high-quality education in their respective disciplines, comparable to the best in the world. The curricula for these programs are designed to provide opportunities to the students to develop academic talent leading to challenging and rewarding professional life.

Question: When registration for JAM starts?

The first week of September(only online)

Question: What will be the date of examination?

Second or third week of February

Question: What will be the mode of examination and duration?

It will be three hour Test and the mode will be online.

Question: What are the minimum education qualification and eligibility requirements for admission?

Mathematics for at least two years/four semesters the qualifying degree, the aggregate marks or CGPA/CPI without rounding-off (taking into account all subjects, including languages and subsidiaries, all years combined) should be at least 55% or 5.5 out of 10 for General/OBC (NCL) category candidates and 50% or 5.0 out of 10 for SC/ST and PwD category candidates.

Question: What is the syllabus for JAM MA(mathematics)?

Sequences and Series of Real Numbers: Sequence of real numbers, the convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms — comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima, and minima.

Functions of Two or Three Real Variables: Limit, continuity, partial derivatives, differentiability, maxima, and minima.

Integral Calculus: Integration as the inverse process of differentiation, definite integrals, and their properties, fundamental theorem of 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: 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, variable separable equations, linear differential equations of second order with constant coefficients, Method of variation of parameters, Cauchy-Euler equation.

Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems.

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.

Linear Algebra: Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix,determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices,Cayley-Hamilton theorem.

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

The most of the above question was quite formal now informal.

Question: What is the time duration required for the preparation of JAM?

It depends upon your learning ability, mathematical concepts but 6–10 months and 2–4 hr in a day will be taking you to good results.

Question: What are important materials required?

It is one of the most important questions where most of you got to mess up.

Actually, its answer can differ from person to person.

I will advise you to follow the steps.

· First go through the syllabus

· Try to underline what you have covered till now in your B.sc syllabus note there can be some topics in JAM which you will cover after JAM exam in your college so you also need to cover it before JAM.

· Now revise one of the topics you like the most such as linear algebra, sequence, and series, group theory, etc.

· Now go through the previous year's question of JAM and try to attempt the question of that topic. Here you will taste the level of JAM.

· If you solved some question or able to understand the question properly that indicates you have good basics in that topic.

· But your work not over yet. Although your basics clear but don’t leave that topic like that, you can put such a subject in a category that your basics clear and this topic required less time, you need to solve more and more questions from where I will state later.

· If you are not able to solve questions or not able to understand please don’t lose interest here. It simply indicates it required more attention and concepts. Now go to the question, see what concepts required, Have you learned that concept?

If no go through it. Try to make separate short notes of all topics which contain formula, concepts, and theorems if you learn some concepts through question try to include that also in your short notes.

· As soon as you go through the basics of all topics will be good for you.

· Now suppose you are now in the state that you have learned most of the basics of the topic (covered college notes and college books).

· Go through the year-wise question paper try to sit the whole three hours and try to solve as much you can in that attempt.

· After that analyze the question which topics have more questions, which topics question you are able to solve, which topics question you are not able to solve, which topic questions you are not able to even understand.

· Categories on the basis of that and divide your time and attention according to that.

Question: What is subject-wise marks distribution?

Question: What is topic-wise advanced material?

NOTE: JAM Previous year question paper is mandatory for all the topics.

Linear Algebra- *N.N Bhattacharya

*Schaum outline of linear algebra

*NET, GATE question paper (solve only that which covered under jam syllabus)

*samvedna publication linear it contains all JAM, NET, Gate, and other question paper.

Real Analysis — * Shanti Narayan S.CHAND publication

*R Kumar (Brilliant Series)

*SC Malik

(choose only one of the above)

* NET, GATE question paper (solve only that which covered under jam syllabus)

* Samvedna publication real analysis it contains all JAM, NET, Gate and other question paper

**Caution: check answer and concept in samvedna real analysis there can be some printing errors.

Abstract algebra- *N.N Bhattacharya

* Ram Ji Lal algebra (part 1)

*Gallian abstract algebra

*Dummit Foote abstract algebra(optional)

* NET, GATE question paper (solve only that which covered under jam syllabus)

Remark: N.N Bhattacharya and Ram Ji Lal book are books are sufficient but if you have time go through the Gillian in last Dummit Foote.

Calculus of single variable: *Try to go with IIT JEE book calculus book(Arihant) and question paper

Calculus of two variables: *Shanti Narayan book

*Samvedna publication

Vector Calculus:* Shanti Narayan

*Samvedna publication vector analysis

Differential equation: * MD Rai Singhania

*BR Chaudhary

(choose only one of the above)

Attention: All the above advice is mainly for that student who wants to do self-study otherwise in the coaching institute there will be other materials please don’t mess up with all that.

In the last I want to advise, generally, student give too much attention to real and algebra and ignore other topics please don’t do that as you can see there is good weightage of other topics too.

If you have any other doubt related to preparation feel free to contact me on my email Id or Facebook.

Thank You

Shivam Maurya

M.Sc Mathematics

IIT Bombay

Email: shivam.maurya362@gmail.com

Facebook: www.facebook.com/cvaam