Preparation Guide for IIT-JAM mathematics

What is JAM:

JAM stands for Joint Admission Test for M.Sc. Every year JAM is conducted by one of the old IITs. Registration starts in the first week of September and continues till the first-second week of October. Each year the exam is held on the second Sunday of February.

For engineers like me who wish to pursue higher studies in Mathematics, JAM is the most useful (and arguably perhaps the easiest) examination. With a valid JAM scorecard, you can apply to all IITs, all IISERs as well as IISc. As of now, however, NITs don't allow B.Tech degree holders to seat for the counseling. In this blog post, I will discuss how someone might start preparing for this exam from engineering backgrounds as well as I would address some general questions I often receive regarding this exam.

When should one start preparing:

Of course as early as possible. In my personal case, I started preparing seriously in my fifth semester, which means I got roughly 2 years before the examination. However, I also studied for TIFR/ISI/NBHM, etc which requires a completely different preparation strategy. So I personally feel if someone is solely targeting JAM, one good year is all that s/he needs.

How should one start (Which topic is to be prepared when):

This question is really interesting. I mean it is always tough to study something deeply and consistently which is mutually exclusive to your syllabus. After all, it takes some time to plunge into the abstractness of higher mathematics. In my opinion, one should always start with Real Analysis. This part covers a large portion of the total syllabus and includes sequence and series, continuity, differentiability, integration, etc. I do believe almost all of us have studied these topics in one or the other Engineering Mathematics course (albeit not in much depth), so if you start this early, you would be able to recapitulate most of the topic and practice accordingly. The best part about starting with something in which you have some knowledge is that you will be able to finish this early (as it is not completely unknown) and you will have sufficient time to prepare for newer topics.

After one is done with Real Analysis, I would say Linear Algebra should be targetted next. In my opinion, this part is the easiest in the entire syllabus. For JAM, you are required to know very basic concepts of vector space, linear transformation, and the theory of matrix algebra.

Next one should practice Differential Equations. This is mostly the same as the 10+2 level differential equations, one or two elementary concepts are new such as ode of order 2, and Cauchy-Euler equation.

Vector Calculus should be the next priority. I wouldn't say it is very hard but I would admit that this part certainly demands great practice.

And finally, we have Abstract Algebra. This is completely a new thing and I have seen many math honors students skipping this part in JAM. The weightage carried by this topic is quite small (<10%). If you want to master this, you really need to invest a good amount of time, For JAM, you can easily get a good rank even without studying it, but almost all the other examinations give quite a good weightage to this topic, and you will be putting a really bad impression if in any interview you say that you don't have a good grip over this part. 

Lastly, I would always say that start preparing more than one topic simultaneously. I mean, for example, it should not be your goal to study Real Analysis for the first two months and Linear algebra in the third month. Because if you do so, by the time you finish linear algebra, you would have forgotten 70% of what you studied in real analysis. Remember constant practice is the most needed key to crack JAM. It is completely up to you to decide the study schedule.

How many hours does one need to put in:

This is a very vague question, to be honest. It entirely depends upon individual merit. Still, on an average, you need to study hard for 4-5 hours, to say the least. 

Conceptual understanding vs Practice:

Practice is the key to success in JAM. If you closely follow the papers of the last 5-6 years, you will understand that for more than 60% of the paper, they repeat almost the same kind of problems. So if you really toil hard, you should not have much trouble covering these. Having said that, each year they set 5-6 very beautiful and challenging problems, solving those require deep knowledge and understanding; but then again, you can easily clear the exam without even attempting those problems. Unlike ISI/CMI/TIFR, you can pass JAM with flying colors even if your basics suck but you manage to cover it by practicing hard. 

Coaching class vs self-study:

 Again this question is really subjective and varies from person to person. However, if you ask for my point of view, I personally prefer self-study to coaching class and never took any kind of coaching for IIT-JAM. But I would say that if you think coaching class can be beneficial for you, I don't see any reason why you shouldn't join one.  I am also not very fond of online video lectures, I personally feel if you invest, for example, say 2 hours in a video lecture and 2 hours in studying a book, the later one will be proven much more fruitful. Again this is my personal choice and by no means, I'm trying to discourage you from taking video lessons.  Regarding test-series, I would highly recommend buying a subscription of any good online test series (although I hadn't bought any), as it will help you to understand your strength and weakness, also will teach you about time management. And most importantly, buy a book that contains detailed solutions of previous years JAM papers. Personally, I followed the book by Arihant Publishers, it contains some silly printing mistakes, but overall it is a good one.

A 'special' method I personally used:

This is a very simple method but tremendously useful(for me at least). Whenever I was studying, I used to keep a particular notebook with me in which I wrote down all the useful formulas which were either difficult to remember or confusing or not readily available or completely new to me. Don't take me wrong, don't just write down all the formulas you come across, as it would make that notebook another short textbook and you will be having a hard time finding anything. Be choosy and include only those formulas/facts which you consider to be particularly useful and need a ready reference. For example, I'm including a page from my 'special notebook' here.

Books to study:

There are many good books available for JAM aspirants, you should pick the books those suit you the best. Here I am going to make a list of the books I personally used

• Real Analysis: Introduction to Real Analysis by Bartle & Sherbert, Wiley Publishers, is in my opinion, the best book available out there for real analysis (for JAM purpose). The book covers everything in a very lucid yet detailed manner. Apart from this one, I also followed Principles of Mathematical Analysis by Walter Rudin, McGraw Hill Educations Publishers ( this book is not essential for JAM though). 
• Linear Algebra: I studied linear algebra from Linear Algebra Done Right by Sheldon Axler, Springer publishers, and Linear Algebra by Friendberg-Insel-Spence, Pearson India. Apart from these two, the books by Gilbert Strang and Hoffman-Kunze are also quite good.
• Abstract Algebra: Abstract Algebra by Dummit and Foote, Wiley Publishers is arguably THE best book for learning Abstract Algebra. I made my 100% preparation for abstract algebra from this book only. The book by Joseph Gallian is also good, and occasionally I referred to that one as well.
• Calculus: I studied it from Thomas Calculus, Pearson; be it multivariable calculus or vector calculus, I stuck to this book only.
• Differential Equations: I personally prepared from the book by William Boyce and Richard DiPrima, Wiley publishers. But I heard that for differential equations, the book by M.D. Raisinghania is excellent too. 

Some final words:

• Use the math stack exchange website if you are stuck at some problem and couldn't find a way out. The people there are really helpful and if you post a problem, you will get a solution in no time. However, they expect you to at least try that problem and show your progress to them, no matter how trivial it is.
• Get good sleep. No need to burn the midnight candle on the day before exam, as it might very well be counter-productive.
• A small tip for NAT questions. You will see that in some questions, they will ask you to write your answer rounding off to say 2-3 decimals and won't mention anything like this in the other questions. Where they mention writing the answer up to some decimals, the answer to that question will be a fraction, and where they don't mention such things, the answer to that particular question will be an integer. 
  

So here for example, if you got an answer of say 2.3 to question-48, you can be sure that your answer is wrong since it is not telling you to round off your answer. So the answer to question 48 has to be an integer

• Learn to chill. You don't have to study all day and occasionally you must take a whole day off. I am an avid anime watcher and PUBG player, and by no way I allow these to affect my study. If you manage your time properly, your hobby won't harm you anyway but give your mind some fresh air.
• Lastly, please take good care of your health before the exam. I am telling you from my own experience. I fell terribly sick before JAM; so sick that I couldn't even seat for my GATE exam which was scheduled on the day before JAM. I somehow managed to write the JAM but my illness costed me dearly in terms of many silly mistakes (I wasn't able to concentrate properly), otherwise, I could have very well secured a rank under 10.

About the author:

Mr. Arnab Chowdhury has secured an All India Rank of 56 in JAM mathematics in the year 2020! He also was selected to TIFR Banglore for their I-PhD program. He also, like Tushar Arora(Link to his post about his journey into Mathematics after Engineering) achieved these while still in the final year of engineering. We, the MAE(Mathematics after Engineering), and PAE (Physics After Engineering) community are proud of his achievement and thank him for the inspiration & hope he has given us with it. We wish a bright future ahead for him in the research domain.

Also, do visit all other useful content of our blog 
Mathematics after Engineering.

Here is the link for our WhatsApp group of members all of whom are engineers who actively discuss and help each other out in entering mathematics stream after engineering.