What is the proper way to study Mathematics? | IIT prof's tips 

everywhere I go everyone assume that we are enrolled in some coaching... Atleast someone is focusing on people who want to learn on ourselves

Summary of the video 😅 Pick a good textbook: Focus on a book with strong explanations over one with many solved problems. Study the core concepts: Read and understand the theorems on your own. Reproduce the theorems: Without looking at your notes, try to rewrite the theorems from memory. Think about the implications: Consider what other results might follow from the theorems. Solve examples yourself: Figure out how the theorems apply to the solved examples before looking at the solutions. Solve problems in order: Start with easy problems and work your way up. Don't skip ahead. Analyze your solutions: After looking at a solution, reflect on why you got stuck and how you could have approached the problem. Analyze your successes: When you solve a hard problem, think about what helped you reach the solution.

The problem is self study is that the books are filled with such abstract definition that it's hard to understand the concept

This is one AMAZING video. I am an AI engineer myself and I love math. I have been studying math (and data structures for programmers) the exact same way throughout my life. So many points that you mentioned are already ingrained in my head and I'm glad that I most of the times predicted what you were going to say. Postmortem analysis of why you were not able to solve the problem and why your thinking didn't reach there, trying to find the solution yourself, questioning why you were able to solve the problem and not just moving on after solving it so you could re apply that thinking in the future, connecting what you've learned to what you're learning and clearing the confusion, brainstorming on corollaries surrounding the theorem and not just being satisfied after reading the theorem itself, concentrating on not just how but "why" of what you are reading, trying to predict or derive the conclusions yourself from the information you've read until now before completely reading the text, etc., are the paths to mathematical maturity. Plus, sometimes you DO have to brainstorm on easier problems to build that base before moving on to the complex ones. For e.g., it's better to first understand why area under a curve is the antiderivative and why integral is associated with "summing" before moving on to multivariate calculus. Understanding the absolute basic things like this help build the strong concepts. It still happens to me very often. Don't just understand Dijkstra's algorithm. Understand "why" it works. Don't just understand the formula of entropy. Understand "why" the formula of entropy is the way it is before moving to anything complex in information theory. And so on. So overall, this is a FANTASTIC video and should be shared with everybody who actually wants to be good at math.

Its a fact that nobody reads Math book everybody just rely on the teacher for theory and explanation and they put zero effort on understanding theory on their own and afterwards they directly jump on to problem solving . even I did this mistake in 10th grade but from now I will make sure that not to repeat this mistake wonderful video sir , THANK YOU EDIT - I had a misconception that by solving question you understand the theory completely but that's not true

..love this professor..for his right guidance and great mentor. .thnq

Totally agree sir. It baffles me that a lot of people don't emphasise on proving theorems and I'm glad you did. It is exactly when we prove theorems on our own, we get different ideas and be able to derive a few corollaries from them.

Yes Sir I'm taking drop with 92.98 percentile in 2024 due to health issues..my Target is mechanical engineering in IIT KHARAGPUR & WILL SEE YOU THIS MESSAGE 😊

This video is about how to properly study mathematics, aimed at students who are transitioning from school level mathematics (up to 10th grade) to higher level mathematics (11th and 12th grade). The speaker, a professor at IIT, emphasizes the importance of self-study in achieving mathematical maturity. Here are the key points from the video: Reliance on teachers for everything is not recommended. Students should rely more on self-study to develop a deeper understanding. Pick a good textbook that focuses on explanations and comprehensive coverage of theorems, rather than just a collection of solved problems. Examples of good textbooks include NCERT books and textbooks written by university teachers. When studying a theorem, don't just read it passively. Try to understand it line by line and then try to reproduce it from memory without looking at the book. This will help solidify your understanding. After studying a theorem, think about the implications of the theorem and what possible corollaries (related theorems) could be derived from it. This will help you develop your mathematical maturity. When going through solved examples, don't just copy the solutions. Instead, try to solve them yourself first by applying the theorems you just learned. Then look at the solutions to see if your approach matches. This will help reinforce your understanding of the theorems. Don't be afraid to solve easy problems. They are important for building a strong foundation and developing problem-solving skills. Don't look at solutions to problems immediately. Try your best to solve them yourself first. Then, when you look at the solutions, analyze why you weren't able to solve them and what you can learn from the solutions. After solving a difficult problem, analyze why you were able to solve it. This will help you identify the thought processes that lead to success.

This is SUCH great advice! I finally got good at math when I realized what, once understood, I needed to commit to memory, and what I needed to derive. It is analogous to the difference between axioms and rules of inference in advanced courses. It was also a relief to see this, finally.

Great advice! Self study and application is essential to concretise math from abstraction.

I was waiting for this vdo. Thanks sir

Yes, Sir. I totally agree with you. At the end of the day, it is all and all about you. Scientists/philosophers/researchers spend their time in solitude with their thoughts, let themselves contemplate the truth about various matters. Be it as simple as why does 1 plus 1 equals 2, when you realize it on your own, it will start helping you see the beauty of the subject that you want to pursue. You will start seeing the patterns/theories of what you have realized in various stuffs. You will start drawing those patterns together, and that is what makes any subject beautiful. You seeing the matter in your own perspective. Most of the times, it is about REALIZING the subject rather than just learning it. It may not be right always, but hey, science has always been a good friend of yours, it allows for mistakes to happen and lets you analyse it from the scratch. And teachers, here, play a very important role, like Sir told, in giving a more mature perspective. After all, be it any field of science, all of them are subjects based on perspectives of studies. And pure mathematics, does hold value for perspectives, approach and thoughts. While problem solving may only chisel your skills, it is, indeed YOUR INSIGHTS that will be your strength. As a person once said, scientific achievements have always taken place when one "Stops learning and Starts Thinking".

Everything that you say sir, makes sense for an average student exclusively if he's a freshman at +1 - JEE

Main points of this video 1. Self study is the key of deep learning 2. Understand the Theorem by yourself deeply by using good books. 3. Now close the book and write down the theore without looking 4. Take a question and apply your knowledge of Theorem in it. 5. If you not get the solution then see the solution and ask why i couldn't think this way and if you able to reach the solution also question how i'd manage to think that way. These suggestions are really valuable for comprehensive and deep learning of mathematics.

I really admire u sir... Both mother znd son watching u coincidentally

I self-study a topic before class and do the homework problems so that I know what I’m struggling with. It gives me a clear understanding with examples to show the teacher WHERE I am stuck. It’s not easy, since you have to get the work done in advanced and push really hard to be ahead the entire class, but worth it when the tests come.

Sir , please continue making JEE related videos for JEE Aspirants. Thankyou so much for your hardwork 🙏

Thankyou * INFINITE sir ....I was waiting for this video for a very long time

Sir, it would be also great if you do more polls like the newest one you did with an interesting problem :), it is really fun and an exciting challenge to solve a problem like the one you chose this time :)

Thankyou sir.. because of your videos I was able to get where was I going wrong and get to know the mistakes for my lower marks even after completing the syllabus.

You make some very good points on the role of a teacher and an emphasis on self study. I am a 68 year old and not a mathematician by training but nevertheless help younger members of an extended Indian family particularly when they reach out to me before exams as they are having difficulties. It's often too late as they need more time to gain insights into topics. Recently my wives niece approached me and said that she wanted help on a number of topics like ratios and circle theorems etc. I said what is the problem and she said she can do the easy ones but not the hard ones. I explained that they are all easy but reason you find some some problems hard is that you have not gained the true insight of the subject. She was not aware of what a quadratic equation was but could factorize a quadratic expression simply by putting in the variable x in two brackets and find the appropriate numbers so that when expanded the original expression was obtained. She did not know that each bracket was a factor of the original expression until I pointed this out.

Thank you sir for guiding us. I really learn so many things from you. And I add in my study also and even benefit me in my productivity in study.❤❤

'Whether it is easy or hard treat every problem with respect' ~ Sir JC That level of dedication and sincerity one must have 😊

Very very true but realising after 40 years. Hope I will guide my son on this

Thank you professor

thank you so much for uploading this video

My success behind calculus is self study.

Thankyou for the problem sir enjoyed doing it ❤❤❤

First of all thank you so much sir for making video at this topic & i totally agree with your words but Sir you also know that we students have back to back pressure of daily studies such as Study new topic, completing syllabus, solving problems and revision of previous chapters and having scheduled time for one subject in a day...BUT the type of STUDY STYLE which you are suggesting is Very time consuming and (like doing PhD in a chapter) i agree and i have also done this type of thing and i mastered those chapters but it's too much time consuming and as an aspirant if we go with that strategy we invest so much time in one chapter.

A lot of really solid advice.

Sir please make a video on what we actually study in engineering and also about different branches as most of us are unsure about this. We don't want to regret one of the most important decisions of our life.

Really a fruitful video. All students should follow the way describe by the respected professor to learn mathematics properly. Yes Mathematics can't be taught it is to be learnt. Very good video sir. Thank you very much for the video, which must make many students enriched. Sincere regards. 🙏🙏🙏🙏🙏

Thanks Prof. Helpful suggestions 😊

Thank You So Much Sir,. You just gave me very valuable information.

Thank you sir for your guidance....

This is the real meaning of maths and everyone needs to learn that maths is not just about fast and accurate calculations ... it's moreover about the skill of analysis prediction and comprehensive critical thinking which a student must develop in early stages and as Indian maths is in out blood we just need to extract it through critical thinking (kind of overthinking on a simple problem to get complex solution or making simple solutions to complex problems ). THE DAY on which you achieve the level of acceptance to maths that you find Multiple methods and uses of a simple problem to get accurate answer you will be a great mathematician... This guy is the best mentor for maths trust him and try to get best out of you In limited lifetime you have .❤❤

Thank you sir for such a wonderful video. I never really comment much on yt, but its been quite a while since i have been watching you, and your videos are really helpful. Looking forward to definitely meeting you someday.

I was impressed when he said that may you would score good marks by any book that only focus on marks but it will not help in developing maths intelligence...

I am so happy that I came across this topic that is given by you sir. Let me share my journey with the mathematics during my diploma studies in Electronics and Telecommunications in Bangalore. To start with I have to state that I could score only 41% in my high school final in 1958 that too in second attempt. Joined in the polytechnic here in 1981 ( Evening college). During the 1st year I was afraid of the maths because of my poor mark's in the school final experience. Some how the maths study was going on well because of the teacher. Still to get more deeper I bought 4 different maths books by 4 different authors and studied. This self study helped me a lot. By the time the exam came I was so confident that I will score 100% to that extent I had prepared myself. But I got only 82%. Because there was no time left to attempt all the questions though I was knowing to answer it. Among all the subjects only the Beautiful Maths gives the happiness to the mind since we don't need any one to say it is correct or not. We can know it ourselves. This I am writting at the age of 80 years as (Flsah back). Thought it will be an encouragement to those who study higher mathematics. Once again thanks for the video sir.

Thanks you sir for this♥️♥️

My advice: Understand why the answer to whatever problem IS the answer. Work on proofs Try to find different ways of doing the same problem. Actually understand and imagine the problem and numbers in your mind. Let your mind be creative. Don’t restrict yourself to one method. Don’t be afraid to try a new method or a different approach out by yourself for a problem. If you come to a dead end, at least you tried something new.

Extremely happy that sir decided to do these videos right when I started my JEE prep for 2026.

Thank you sir, i think this is more general way to study any subject of logic

Sir, I am a student who is just about to begin his first class of class 11 in a few days' time. Thank you so much for making these videos. As a JEE aspirant, I cannot overstate how valuable your videos have been in showing me the path I should take. Thanks to your videos, I can now avoid the study mistakes I would have done otherwise. I have a few questions: 1. I always face a problem related to competitive exams (such as Olympiads) - speed. When facing a new problem, I have a tendency to find very unoptimized, long-winded solutions which waste a lot of time (For example, my first derivation of heron's formula went on for three pages; after solving it I realised that there was an alternate solution which took only one page). No matter how much I practise, I have not been able to overcome this problem. Since unique, never before seen questions are quite common in Olympiads and such, I really struggle with time management. Is there any solution to this? 2. Besides NCERT, which book would you suggest for studying mathematics? 3. While preparing for JEE, can I have side activities like coding, playing video games/outdoor activities, etc.? Again, thank you for making these amazing videos. I am really excited of what you might bring to the table in the future! I eagerly await your response.

Sir I'm a student who really has a dream to enter into IIT. As you said here, I always used to study maths on my own, I myself will read the introduction, theories and start to solve problems on my own. It really helps me. Mathematics is not just a subject, it is my love ❤ your encouragement really helps me, thank you sir

Sir you are absolutely right but not getting the solution in right time will also hinder us to progress further and solve more of the questions, whats your take on time management and for solving these problems?

Thanks a lot sir this video really made difference Now i can grasp maths more efficiently Plz sir make a video for physics and chemistry

You are spot on 🙏 ! But.........To go deep in understanding a topic, free and relaxed mind is needed. Unfortunately, when the student comes back home (after 8 hours of school and transport), has to do useless homework for several subjects, there is hardly any time of free mind to THINK! Second, the school teachers get students to do sums from private textbooks which are of higher level or ideally should be covered in higher classes. The teacher feels proud, the more difficult sum a student can solve. This causes student to lose interest in Maths, frustration sets in and student starts hating this lovely subject.

Thank You very much sir :)

Thank you so much sir

I did rely on self study quit a bit but sometimes a friend could explain certain concepts in a way that the professors didn't that made it finally click for me. It also seemed that at a certain point, the higher maths were easier for me to grasp. I suspect it was due to plenty of practice I had in the lower maths and a wider knowledge base to draw upon.

Sir kya ap logo ko nahi lagta ki Jee advanced ke liye 3 attempt hone chahiye ek bar student ke point of views se dekye 😢 except jee adv baki aur jitne bhi is desh me competitive exam hote hai sab me multiple attempt hote hai . Sir please ek bar bas student ke point of views se soch lijiye ga .😔

Thank you sir.. but make a video on revision and how to learn things more and more efficiently, there are a lot of subject to participate in any kind of competitive exam .. Please sir make a video

A good spiritual video

Sir as you said that the books shouldnt just focus on the practise question but also on the theory as well, could you please suggest some books for students preparing for jee in clas 12. Is cengage new edition good ??

thank you very much sir can you please suggest some good books from which we can study for our jee preparation

Hello sir, I totally understand all the points you mentioned and I think they're all valid. Self study can indeed prove to be very beneficial in improving your ability to think critically. But I have some questions: a. What books do I refer? I think NCERT is indeed good but then Its definitely, for sure, not capable of training a person's brain and making him capable of attempting advanced questions, or perhaps even Mains questions considering how hard they are these days, yes, they can clear out the basics very well but they're definitely not enough material for advanced (even for theory). b. About teachers, I did try studying math by myself, I used Cengage books, I don't know if the books are good enough (which leads me back to the previous question), but yes I did try studying them, I looked at the solved examples and found out that in every other solved example, a different method is used to solve a question which induced a lot of confusion in me and I failed to solve questions. BUT BUT BUT, when I referred to Mohit Tyagi sir's videos, my entire perspective towards that chapter changed, I was able to solve Questions that I couldn't even think of being able to attempt, and all that credit solely goes to Mohit Tyagi sir's teaching. What are your thoughts on this phenomenon? c.Aboit the part when you said we need to think of the theorems ourselves before looking at the proofs, but personally, as a dropper (targetting jee adv 2025), I don't think I have enough time for that, instead of trying to think of new ways to prove theorems, isn't it just better to think of new ways to solve a particularly difficult question? If I'm wrong, please correct me and please suggest some ways for me to manage my time more effectively 🙏. Thank you sir, waiting for your reply 😁.

Sir could you please suggest the theory books

At 12:43 I got the master key of conceptual clarity . Thanku so much sir🫡🫡🥲

I always believed maths theory should always be learned by one’s self, when we stop relying on teacher for theory we can discover the concepts and then clear misconceptions about concept when solving problems by yourself, the ultimate formula to become a great problem solver is learn theory on your own + solve questions based on what you learn. This is what I learnt from this video thank you prof, I am 11th std student from south India

In the era of clickbait and view farming, sir you are one of the last people who actually bother with giving genuinely good information and advice Am really looking forward to binge watchimg your video once my JEE Advanced is dome upcomimg week. Wish me best for it. Thanks

Thank you

very true

Hello sir, I've chosen pcm for 11th grade this year, and your videos are very helpful, i am doubtful i might not score well in boards in maths, but that was because of exam fear and time pressure, though i love maths as a subject i don't understand why while solving it in exam i fail to score well

I am someone who failed miserably at Jee. Now I am preparing for CAT. Thanks a lot for the guidance sir

Namaste Sir, Sir i have a request please make a video for students who have really wants to prepare for jee and what measure they should take before starting their preparation. And why you should prepare for jee.

Thankyou❤

Agreed sir

All my life i was either homeschool and i was always had a solid grip on my concepts but ever since i joined school (which was decent) for board exam that is where my scores dropped dead and i started straight up failing on exams . The teacher would walk in to the class grab a horrible local board book full of terrible concepts read it as it is as if we did not had the knowledge to read basic English and solve the exam give rest of the exercise (which was the actually hard) in the homework than later on fail us on exams . I wish i went for O level and A level atleast i would've had a better experience . Now i have entrance exams in well known universities and i am losing my mind studying the very basics . I hope i make it 😌💞

Sir would you recommend some of the major mathematics books i,e abstract algebra, linear algebra, real analysis, geometry, complex analysis ( mostly theoretical not problem solving) etc. which written in simple language and easily understandsble for students which can help us to develop a strong root in Mathematics and help us in further high study in Mathematics . Plsssss sir 🙏 🙏

Greetings to you professor from Guyana. I really do appreciate your take on the study of math but how do you explain that after a few weeks of learning the concepts they are forgotten? One has to go back to the examples to retrace some steps after which the procedure will slowly 'comes back'. Is that 'learning' in the first place? Secondly, what would be your recommendation of the best math textbooks for self study? I know you said here you aren't giving any names of textbooks but I am kindly asking you to pick out a few of the all time staples. Thanks.

Respected Sir, I have just entered class 11 and was doing Hall and Knight from class 10.Should I take another guide book or just stick to the earlier. I am also from SEBA. Kindly reply.

sir please make video for those students who are preparing for jee advance without any coaching.......

Sir make a video for students in Grade IX And X to manage coaching with schools.

Sir i have taken commerce with maths and i am not great but i am also not bad if i practice i know i can do. But the problem is i can't rely upon my teacher as there are only 2 classes in a week of 35 min from which teacher waste half of the time so please can u tell some tips and these tips are really great that u gave.

Very nice words sir

What math textbooks would you recommend that fit the described necessities from the video. I ask because you provided a excellent physics textbook that is concise whilst not sacrificing vital information.

Math is a very beautiful subject. My only problem is the way its taught. Schools make exams as the whole point of learning things.

The end goal is earn a temper of solving problems in a percipacious manner 15:17

Very helpful video sir Sir, I am a student from class 11. I Practice maths even from different book like Rd Sharma.butt sir whenever I went to exam,I don't know why ,I can't answer some questions.it seems like I didn't study anything. unfortunately I did . I want to get full marks but can't.....and those silly mistakes.....

@Jeevanjyoti da: By chance came across your channel, wish there was something like this when I took JEE. Maybe would have cracked it 😁

sir but i have not done these things in my cls 11 and 12. is it possible to develop these skillls in my drop year pls reply

What are the best books to follow for maths ? Reccomendations would be highly appreciated?

sir make a video on engineering and computational mechanics and i may get this branch at nit jamshedpur should i take ?

SIR I USE CENGAGE IS THAT SUFFICIENT FOR ADVANCED LVL

I'm glad that your advices are more cohesive and includes students of all age groups and not just the ones who are preparing for competitive exams and so on. You very well know that the major problem with our education system lies in the roots and it should be tackled from there. The only sensible person on this platform that actually cares about the true fruit of education.

Sir please suggest a book

Sir will work hard and try to meet you in IITK wish me luck ❤❤

Sir may be first one should follow one’s own path in understanding the concept. There is no the one way….only success make the method and failure to clear clear the method. Let the people follow their own method. Bruce Lee told that he was not afraid of person who is versatile in breadth but of the person who practiced the kick 1000 times. Let them follow their own method

It would be great if you suggest one good book of mathematics also keeping in mind IIT Jee perspective but at the same time which has theory and illustrations both and would help to learn the subject as it is and not just pattern matching..The main issue is not being able to find a relevant good book..because some books have less theory..some have more, it is all a mess... Btw Sir, your advice and genuine explanation on different issues is such an epitome of your intelligence and profound observation skills..Thank you..

Yes

Hello professor, I am the father of a 29 yr old who is studying to get into a phd program, by writing nbhm, net. In India, there are age limitations to getting a job in academia. With that in mind would you recommend to look for another career and keep math as a hobby? Any answer / guidance would be greatly appreciated. I am sure many people would like to know this. Very helpful video as usual, I also appreciated you making the video discussing age limitations in academia jobs (and other job sectors as well).

sir can you suggest some good books for jee maths

Pls tell us about branches like industrial and production engineering, metallurgy,ceramic etc ,is there any point taking these branches?

sir I struggle with co-ordinate geometry a lootttt. I literally gave 2 days yet I get stuck to make basic solutions. I'm strong at calculus and algebra but vec-3d and conics are my weakest of weaakessstt

Sir! I dont know would you answer this or not ! Have you ever set the JEE Advanced question paper or do you know any colleague setting the paper if yes! How do you set so tough paper ? What is the philosophy behind setting such paper and framing questions? And isnt it unfair to students who cannot afford coaching?

I'm doing Bsc in mathematics and I think I'm yet not mathematically matured. Though i want to, I think I get lost in the race of marks and gpas. Fortunately I got an internship this summer in IITG, but now I'm afraid that my learning techniques are poor. I definitely will try this method. Thank you sir 🙏🏻

Where was the problem uploaded?

Nice Guidance sir. Can anyone guide me textbook to understand linear algebra . Thanks