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

hello everyone in my previous two videos I have discussed the biggest mistakes which students make while studying physics and chemistry and I've also shared a few tips on how to improve their study habits and in this video I'm going to do the same for mathematics now because mathematics is inherently different in its nature from physics and chemistry I first decided to make a poll uh through a community post and uh I am not actually surprised by the results of this poll so uh the question was what system do you follow when preparing mathematics and more than um close to 50% of the students said that they relied on teacher for Theory and examples and then they tried the problems on their own and uh a certain fraction of the students said that they relied on the teacher for theor and examples and then they went about learning the problems from the solved examples so uh almost 60% of the students uh from the response it is clear that there is a clearcut Reliance or even I would say an over Reliance on the teacher for the theory and the uh the introduction to the subject the the discussions so all the theoretical kinds of discussions the students are relying on the teacher so this kind of an over Reliance on the teacher is something which is not actually good and this is one of the main points of this uh of this video that this kind of Reliance on the the teacher is not something which is going to help you to ultimately achieve mathematical maturity and unless you achieve mathematical maturity you are not going to be able to actually grasp mathematics at its very core you may be going from one class to at higher class but actually you are not learning mathematics as it should be learned so what should be done so instead of overly relying on the teacher you should be doing self-study so yes in mathematics also even though many people say that mathematics is about practice I would say that a significant portion of mathematics involves some very very deep self-study this is one crucial aspect which is missing from many of the guidance that is given by our school teachers this is unfortunate but this is true and Mathematics is such a subject which really cannot be taught by Any teacher a teacher can only be there as a guide can only give pointers to you in certain directions but it is you who yourself have to follow these directions on your own path and figure out things for yourself so self- study is the first step which you need to actually do in order to uh have a proper grasp of mathematics and this is something which is actually very much missing in the vast majority of the students as the poll has clearly shown mind you that there is a certain fraction of students in the poll who have mentioned that they do completely self-study but that also has certain issues that when you completely do self-study you you miss out on a certain perspective from a more mature person so that also is request so an ideal situation an ideal situation would be when a teacher gives you an introduction to the subject and then you do self-study and then you go about solving problems so all of these three aspects in conjunction are what contributes to making your study of mathematics your preparation of mathematics complete and comprehensive now so in this video what I'll do is first of all I'll point out certain things what you can do in regards uh with regards to self-study so first and foremost pick up a very good textbook not the commercial kind of books which only focus more on giving you lots and lots of solved problems so these books are very attractive from the uh Viewpoint that they help you get good marks but remember that getting these good marks in the board exams and the school LEL exams um this is certainly good but just because you are getting good marks doesn't actually mean um and and this is not your fault at all doesn't actually mean that you are learning mathematics so uh if you are time and again getting almost 100 out of 100 in mathematics but this score is based on your preparation which is very fast very comprehensive but this comprehensiveness is based only on some kind of a pattern matching exercise then you are not really learning mathematics what you're doing is basically developing a Proficiency in pattern matching which is a good skill to develop I certainly agree to that but mathematics is not all about that so pick up a very good textbook where the theory is presented in a comprehensive fashion by a proper expert of the subject there there are some excellent School teachers who have written textbooks their Boards of teachers the ncrt books are written very well uh uh then at the higher levels also the university teachers for class 11 and Class 12 uh the university teachers they uh they have written some very good books uh and again the ncrt books are there so pick up a good textbook don't go for too many textbooks pick up one very good textbook and follow that religiously now what do you do actually in self-study so this discussion is more about how you go about doing things I'm not going to suggest this book or that book rather I'll uh tell you what you can do in the actual process of selfstudy so the first thing is that actually you need to study the theorems on your own and you need to go through the solv examples and even before that the discussions the explanations on your own line by line trying uh very hard to really understand understand and grasp The Core Concepts from it but that is not the end of it because mathematics is so very different from math from physics and chemistry what you have to do is after you have studied the theorem you have to close your book and without looking you have to try to reproduce the theorem on a piece of paper so that is how you exercise the theorem it may seem like ratification as some people call it like Road learning but it is not when you do the when you reproduce the theorem on your own it creates certain Connections in your brain with what you studied earlier and this has some very serious implications on what you're going to uh study ahead uh after you have done these two steps think very hard about the implications of the theorem unless you have done the theorem yourself on the on a piece of paper you'll not be able to do it so think about the implications of the theorem what I mean by that is so usually after a certain theorem or after certain theorems there are certain corollaries to it but in certain places there are no corollaries there are no subsequent discussions so you have to think for yourself what kinds of possible corollaries or some kind of adjacent explanations could be possible from a theorem now this is where you need I mean this is the place where you develop your mathematical maturity and this is also the place where the tips and pointers and the little guidance from the teachers actually help you out a little bit I I mean a lot so next is the solved examples so when going through the solved examples don't just treat the solved examples as some kind of different patterns which you have to learn and later on use in the unsolved examples rather treat the solved examples as opportunities for applying the knowledge of the theorems the knowledge that you have grasped from the explanations and the discussions don't look at the solution immediately first of all what you do is close close the solution read the solved example and then think for yourself how the various theorems that you have just studied how they apply in this uh in this solved example how they would apply in this kind of a in this question uh you must also try to think about possible connections with the theorems of the previous chapters unless you do this and if you just look at the solution immediately this thinking process that you absolutely must go through will not be there and your learning will not be reinforced your learning of the theorem will not be reinforced however if you do this by closing the solution and first thinking about the about the possible modes of going ahead with the solution even if you do not make any Headway into the solution yourself still you'll be able to make a clear cut reinforcement of your learning of the theorem so those things will actually get embedded it in your brain this is very very important so next we are going to solving problems and by the way after I have discussed this solving problems I'm going to announce the names of um the students who were able to solve the um the problem that I had posted in my community post uh that successfully solved that problem it was a little logical kind of geometrical problem so solving problems uh so many students make the mistake of treating certain easy problems as being beneath them yes they think that solving such kinds of easy problems will be like an insult to their intelligence this is kind of common um perhaps uh most common in among students who are preparing for some kind of competitive examinations like J because they think that they have to go for such a high level will they waste their time doing these kinds of simple problems but mind you mathematics is something and this I had emphasized um in my earlier video on problem solving and I I really insist that you please make it a point to go through that that rather lengthy video on problem solving where I have discussed all of these things in great detail so mathematics is such a subject where you really cannot proceed but without leveling up so you H really have to level up one after another so without first being absolutely proficient and expert in the very easy level problems how can you think of going to the higher level problems so only after you have you have convinced yourself that you are perfectly perfectly comfortable with the very easy level problems then only go to the certain certain higher level problems and then only go for more competitive level examination problems that that level and a Frank confession here during my own preparation when I was first studying in my class 11 12 I used to study problems or I used to do problems which were so easy that they would not even come in the board examinations they were so very easy but I never look down on them if if I could not solve a problem it was it was not because I was too above them it's just because that my mind had not acclimatized to the theorems to the concepts so you have to go through this process I mean nothing no problem is beneath you okay please do not ever think like this this is absolutely a wrong wrong way of going about things um whether it is easy or whether it is hard treat every problem with respect so the next thing is you must be trying the problems on your own nowadays there are lots of books available lots of resources available even on YouTube where Solutions are there my Earnest request to all of you is that you should not be looking at the solutions directly first of all try it on your own try your best exhaust all possibilities of uh that that you have at your disposal of tackling the problem on your own only and only then if you fail to make any of sort of Headway try to then look up the solution but then don't just get satisfied by looking at the solution and again this is something which is so very important I had mentioned it at length in my previous video on problem solving so do watch it uh still I'm mentioning it here because it is so very important that you should be uh looking at the solution through the lens of a postmortem analysis meaning that since you are not able to do it you must after looking at the solution try to think for yourself why was it that you were not able to solve it so this kind of a postmortem analysis is extremely extremely important to make you realize your shortcomings not just in for that particular problem rather in your overall thinking why you did not think in that that particular direction and it'll also be a reflection of your grasp of the theorem that you had studied earlier so as an application of that or perhaps your grasp of the connections that need to be made across different kinds of theorems another important point is that uh after you have successfully solved a difficult problem you must also make another attempt or you must make a full analysis of why you were able to solve it what was it that made you proceed in the right direction again this is something which I had discussed in my earlier video on problem solving so do make uh make it a point to watch it so uh these are the some of the broad points which I thought I'll discuss in relation to mathematics especially as it regards to making this big jump from the school level that means up to the 10th level from the 10th level to the 10+2 level where the level is really high now for the winner so uh the two students who had successfully solved the problem within a few minutes of each other the community post that had uh had made are serves Krishna and Krishna Prasad sures Krishna and Krishna Prasad so congratulations to both of you on solving the problems mind you there were quite a few other students who came very very close to the correct solution but they were missing a key part of the argument um uh here and there so uh that's it I have to be fair in my assessment uh but what made me really happy was that quite a few students actually figured out that uh this problem had to be done by the method of contradiction so congratulations to all of you who thought in the proper direction and came very very close to the actual solution so all all right so that's uh it uh thank you very much for Patiently listening to me and all the very best in your preparation of studying mathematics in in your in your preparation of mathematics and your uh in your journey of self-studying mathematics in a proper comprehensive fashion as it should be done thank you

Channel: jc

Views: 170,586

Keywords: jc, prof jc, IIT, IIT Kharagpur, IIT KGP, IITKGP, IIT prof, Mathematics, Mathematics education, School, School education, Teaching, Learning, Self-study, Problem solving

Id: DpQ8MKL18DU

Length: 15min 17sec (917 seconds)

Published: Sat Apr 27 2024