How to Start with Research in School | Path to Ivy League Seminar

okay so thank you everyone for joining in today uh my name is as Das gupto I'm one of the faculty members uh at chenta Academy I also have shif with me shif is also a faculty member at chenta and he's one of the research advisers so today uh I want to talk about re sear opportunities at school this particular session will be recorded for later viewing um let me start the recording actually just for the sake of okay let's see or maybe shif can you start the recording at your end is that possible can you check maybe I have to do it I've started oh you have started okay thank you all right so um basically uh there is a new trend in the world of Academia especially in schools this is coming into particularly international schools but also several National level schools students are actively participating in research uh activities so they are writing papers they are um they're contributing to the domain of knowledge in mathematical Sciences biological sciences Humanities there is a lot of activity that especially in the um in the high school level from Grade 9 to 12 uh Chinta has a very active program on this we have uh started with these very intelligent smart kids who work on Olympiad level problem solving and then many of them transition into research because they want to get tougher challenges and I'll describe a little bit more on how they pursue this particular thing uh and how you can also do it you do not need to be part of Chinta for this you can do it on your own world of knowledge is really open for everyone so it's it's definitely possible to do it on your own um I will share with you all the resources that you can use to to start your own research journey and um how you can use it for University applications at a later stage if you want to do that because um we have we we counselors and we talk to people who work with University as applications especially in us and Europe and they increasingly tell us that a good a solid research project adds a lot of value to a particular students portfolio definitely I'll tell you more about that as well so the first thing first let me just uh go to the next slide one second this is a little slow here from at my yeah so the first and the foremost thing is basically about what research does to a particular child what we have noticed is that maybe a student begins their Journey with their University application or something else in mind because these are really young kids especially uh most of them are from Grade 9 to 12 so they start with this Viewpoint okay this is something that may help me in my University applications it's like a carrot that they have in in front of them so and and their parents also sometimes think in that way but what happens is that when they start working on the projects their entire mindset about pursuit of knowledge changes they have to get involved in a variety of areas so usually it is interdisciplinary in nature so they have to get into several areas of knowledge and they have to uh go deep into each of them so you cannot be superficial if you want to do something solid I'll give you one example this is a student with whom I worked last year Anika she's in Stanford right now so she worked on this particular uh project which involved hyperbolic geometry so the title of her of her project was hyperbolic geometry and an application in social sciences uh so she spent a lot of time a lot of time in learning hyperbolic geometry in learning group Theory when she was at school like in 11th grade and 12th grade she initially started with Olympic had preparation and then she had a um she wanted to move toward research as well show show show so she started with that and she took a lot of time to learn group Theory she took a lot of time to learn hyperbolic geometry and all of that came together into this particular project uh which is she talked the first part of this project was an exposition on hyperbolic geometry and group Theory and the second part was her idea idea about how to apply all of that in the context of social sciences uh the beautiful part of this entire Journey was like this that you know she started with group Theory and she was completely new to it but what we noticed is that she learned quite a bit of group Theory while she was in her 11th and 12th she worked really hard toward it and that really expanded The Horizon that really changed the way she thought about the entire problem of this social uh science I mean this particular problem was something related to some called social proximity uh which is kind of Novel uh how she used mathematics to treat that one thing I want to point out here is that there are several so-called research projects out there by high school students who which are really very superficial in nature that is what they do is they take a bunch of data and they fit it into a machine learning model this a very wellknown sort of a method of doing so-called research I will strongly recommend you to refrain from doing things like that because that sends a very bad signal to the reviewers or even if you're willing to apply to a university it sends a very bad signal that that you are trying to Corn your way into this process instead of that I'll talk about three steps of getting into research in a second um use that to display what I call depth of knowledge so let me uh proceed a little bit more into the next slide so you will get a sense of what I'm talking about uh there are really one second yeah there are really three things that we recommend when you start p puring research at school and the step one the first of it and that's really the most important step what we call is depth of knowledge so what is depth of knowledge depth of knowledge is basically you take one area of mathematical Sciences which is a bit beyond the school curriculum maybe and you really learn it remember if you try to fake your way into this first of all you will be fooling no one because people who will be looking at your paper they will immediately know they're experts usually so they will immediately know if you're trying to fool your way into it and secondly and which is more important you will be wasting valuable time of your own life into faking which is kind of pointless so the first thing and your research paper should really demonstrate this one thing that you have depth of knowledge in some area of mathematical science I'll come back to the previous example the one that Anika the project that Anika worked on she in the first part of the paper she showed that she has really gone into hyperbolic geometry and group Theory she has worked hard to learn all of that it's not a she's not a corner artist she has taken time to learn what they are time to think about those ideas how they come together so that's the first step choose an area one area that you like maybe it's number Theory maybe it's combinatorics maybe it's geometry whatever it is choose one area and make sure to gain depth of knowledge and one way to gain depth of knowledge is actually to use books that are authored by by real mathematicians so students often ask us about book suggestions so books that they ask us okay what book can I use for amc10 what book can I use for ioq and so and so forth and there are many manual type books out in the market like there are list of results and list of problems stuff like that we often suggest students to avoid avoid those sort of books instead use books that are written by real mathematicians because in those books they are not written as manuals for a particular exams but they have the capacity to open up your mind the same thing goes into this if you want to gain depth of knowledge in a particular area of mathematics or mathematical sciences that could include physics or computer science or machine learning or whatever it is then use a book that is authored by an expert a real practitioner of the field not some person trying to write a manual on it for some exam okay so uh one good place to see such book suggestions is stack exchange if you find an area interesting just Google geometry books for in stack Geometry book suggestions in stack exchange you will often get really good responses there by again people who are really involved in the field okay let's go to the Second Step which is equally important if you have done the first step properly then you can start with the Second Step which is equally important and the second step is really uh okay so it's it's taking a bit time to scroll I think see yeah okay the second step is about reading papers so this basically begins a bit later so suppose you have worked hard to gain uh um depth of knowledge in a certain field The Next Step would be to start reading papers from real journals now you have to be very careful here because there are so many so-called High School journals that have come up that actually charge students money to publish their material it's really a very big scam and universities actually considered those things in a in a very poor ta taste I can tell you firsthand because we have very close connections with several counseling or topnotch counseling organizations who work very closely with us and with University Representatives so we we get a sense of what's going on out there so when I say read papers from real journals I have mentioned a few uh for example mathematical Gazette is a very good Journal published by Cambridge University there are many problem many papers in there which are really accessible Quant and KL are two other very respected High School level journals which are published from Russia and Romania respectively there is one called one lesser less heavy Journal called Crocs mathematic Orum which is published from Canada so there are quite a few of them out there which have some original ideas some of these journals have articles which are expository in nature so those are not original ideas but some of those articles are really original they are they have some new ideas in them so that's the step two after you have worked really hard to G gain the depth of knowledge in a certain domain you can go to a particular journal to actually look up articles in and around that area so maybe you are interested in Geometry so look up articles related to geometry and make it a habit to read Journal articles I mean just like people read newspapers or Vlogs or uh I don't know you guys see Instagram whatever you do on a regular basis make sure reading journals is a habit like that now of course Journal articles are usually quite heavy in nature it's impossible to read them like you would read a news article so what I usually suggest is do not worry about the entire derivations and all the complexities that are presented in an article just scheme through the paper to see see if you see the main idea that is usually the first recourse now if you see the main idea and if you really like it then you can go deep into it and think more about it as a second thing keep a note of these particular Journal names because they they will be useful if you want to pursue this thing the third thing and this is usually the place where an advisor can come in but you can also really do it on your own you have to fix a research question now what we have seen over the that once you fix the research question once you fix the research question it gets transformed over the time so maybe you start with a research question you you pursue it really uh vigorously and over time you see the research question itself gets transformed so that could happen I mean that happens all the time but it's important to fix a problem and uh at this particular juncture really an advisor can help someone who is uh aware of lwh hanging fruits so in in in research Community they call it low hanging fruits I'll explain uh let me explain one in one line what that is maybe someone has worked on some research problem out there and there is a sub problem which is potentially very easy to solve but no one has really worked on it this is sometimes known as a lwh hanging fruit in the world of research so it's something that is readily doable but you know uh no one has really worked on it there are so many problems out there not every problem has been worked on by everyone so uh it's important if you can find an advisor to fix a problem a research question that you can work on so at this point before proceeding to the next slide uh I will ask um shif because shif has been advising some of the students who are um in the short summer research program this year at chenta so Shai you were uh so I think about 30 plus students are working on different projects is that correct correct around 30 of them are working yeah so they're working on very interesting research questions couple of them have some really they've already got they're nearing the results so can you describe one or two of those ideas that they without diverging the name of the students or anything because that might be so something can you can you can you tell us a little bit more about that sure uh so as Sir has talked about hyperbolic geometry and group Theory so there's one model in hyperbolic geometry called Point Care Unit dis model so you can think it of as the region in the coordinate plane that x² + y sare is less equals to 1 so and there it has got a very unique metric so think that you can think that each person in this region can be represented as a point on unit disk and then think it of is it like a disease outbreak so the nearer the points are the transmission probability increases so and the farther point the transmission probability decreases so the point car disc provides a way to understand and visualize relationship in space where distances grow exponentially As you move away from the center the model is particularly effective in capturing the spreads of diseases as the diss geometry can reflect the natural expansion of an out I see so this was one of the project another project involves so the so the student the students actually modeled disease outbreak using hyperbolic geometry is that something that these people are doing right right these two I see that's that's quite interesting actually so one thing I must mention before sh moves on to the next project description is that notice what H what they what they are trying to do they're using hyperbolic geometry which is like a very PE mathematics kind of a thing and they're applying that in the domain of something really handson like disease outbreak so this is this sort of thing is what is actually interesting what makes people pay attention because you know it shows that not only you used your mind to you know learn something deep deep in mathematics you were also trying to apply it into something that is real world one example I mean I I before you just tell us about the next one one example I can recall is of girl Friedrich gaus one of the greatest mathematician of all time he worked on differential geometry but he stumbled upon differential geometry while he was measuring land in Austria and uh he was actually you know uh given that Consignment by the king to measure land for tax purposes so while he was measuring land he noticed that there is a thing called curvature which then entered into the world of di differential geometry if I recall the story correctly so I mean it's it's very interesting when you intertwine pure mathematics with something that is real out there yes sh what about the next one can you tell us another one sure so like graph Theory it's a branch of mathematics that studies in some sort of an object where the categorical object are the nodes MH and which consists of edges between them so it can represent the connections or paths between two entities and what this is I'm mapping that into an urban planning problem so in an urban context nodes can represent various entities such as buildings or public amenities and edges can be weighted edges where the weights represent time I see so there's the concept called 15 minute City so 15 minute city is an urban planning concept that emphasizes creating a city where all essential services and amenities are accessible within a 15 minute what I see so this can be very easily modeled into a graph Theory problem and that is why there are various graph Theory algorithms like the minimal spanning three algorithm formed by cuscal algorithm and dexra algorithm talks about the shortest distance withes and we are combining those algorithms into finding a subgraph with maximum number of vertices and the diameter meter bounded with a bounded diameter I see and that will give us the 15 minute City model and we can apply into real world problems wow that is that is fantastic I mean graph theory is actually very close to my heart as well uh because it turns out that the stuff that I studied in group theory in Geometry group Theory uh there is a phenomena called relative hyperbolicity one of the description of it is using graphs which is uh so I had to study some of it I guess and this this is sounds very F very nice so yeah I mean uh one thing that I again I I suggest to all students is that you when you work on a problem make sure you start with something from beond mathematics something that is that has been well studied for some time because it will exhibit depth of knowledge and then you do the applied part which is handling some real world problem it gives a very good mix of ideas and it shows that you are not just saying things you have worked hard to learn something and then you are saying things which is which is very important actually in this particular domain okay so uh let me just finish this off before we move on to the um the the the the final part of today's discussion and that is you know um in at Chinta if you are if you are a member of Chinta for some time you know that there are there is a path to IV league program and uh this this particular program really has three components the first one is of course Olympia training where you learn how to you know two problems which are nonroutine in nature the second part is called research which is what we are talking about today asking questions that are kind of Unsolved that are out there you are learning deep mathematical science to pursue those questions creatively and the third part is leadership where you build products and services and you show that you are really engaged and you can work with a team so so these are the three components of it and uh why I say this again is that what we have found over the years is that all of these three components play a crucial role in uh building also your academic career uh for example if you are pursuing University applications either after school or after college one of the things that you could do a research paper usually culminates in a paper research project usually culminates in a paper so one way to go about it is you submit it as a additional material to University applications many students actually ask this question that where do we submit these papers that we have worked on one trap that is out there one scam that is out there are so-called journals High School level journals who would actually take some money happily take some money from you and actually you know um publish your so-called work many students actually fall into this particular scam that does not work really well the students who have worked with us and they've gone to places like Harvard Stanford they never did anything like that what you do is you work really hard to write a really well-crafted paper then you up submit it directly to the universities and you talk about the main result in the state statement of purpose this is at the school level I'm talking about of course if you're at a college or university level you should try to get published in some of the reputed journals uh in the school level what we essentially suggest is that while you are applying to the universities you submit the paper as an additional material there and talk about your journey toward those results in the statement of purpose that does really work so this is this is important and um if you I think we don't have oh we these are some of the areas of research that we work on pure mathematics Applied Mathematics artificial intelligence machine learning uh econometric statistical analysis of course these are the domains that we work on you don't have to work with us you can work with anyone whatever your interest area is but it's always a good idea to find a good advisor okay if you want to learn more about this sort of stuff then you can go to cha.com resesarch and you can find more information on that okay all right we will stop out the um Dem the presentation now and I will ask the audience if they have any question and if you are watching this in YouTube or Facebook you can also put a question in the comment section so if you have a question please click on the hand raise button there is a hand raise button in Google meet and you can ask a question all right if I'm assuming if there is okay pushkar go ahead yeah pushkar go ahead yeah my question was what is the right age or the right grade for student to start in investing into this research kind of problems so there are two ways we approach this one is that if you are in ninth grade or above then you can definitely go into it because many of our students do before 9th grade you should really invest your time into learning uh how to solve non-routine problems that is pursuing something related to olympiads like iqm or American math competition or whatever that really sharpens your mind and makes it ready for the next next stage so ninth grade is an ideal I would say time to get started okay let's go to shash Gupta uh hi sir hello sh so these research will be going on high school level but there are many other things going on on high school level and for like 10th graders like me uhhuh I have started the uh like the you know the first step right in which uh problem solving yeah is uh concerned uhhuh so there is uh I can uh like I cannot you know take uh borrow some time for the research right how that is that is true I mean shash you're right I mean there are students who are pursuing let's say if you're pursuing i j or something like that then you are already you know uh you you you have your time you have a severe time crunch but usually students who are working with us on research projects what we have noticed is that their their goals are like not not really iits their goals are MIT Stanford stuff like that but that is a that is a career discussion that you need to have with your family let's say if you want to go for places like iits then you can definitely you have to focus on IJ and that takes a lot of time and you probably won't have time for anything else but uh if you are planning for let's say MIT or Oxford or Cambridge or something like that then you have to strategize diff differently your preparation Pro process for example if you are planning for an MIT then you might do what I mentioned a bit earlier the path to Ivy League process where you do really well in an Olympiad you do really well in a research research project and you do really well in a leadership project so this is this is you have to you know think what is it that you are you know what is it that your goal is and accordingly do because it's a big decision you have to talk to your family and understand what are the possibilities okay all right let's go to gorang yes yes sir my problem is like that I study very well means that I study in depth a subject let's say in mathematics well I more studied in more interested in a pure mathematics side so I study the subject in depth but this caution of research always come into my my mind but I never I never made a decision or never the basic question of research came into the mind this I can study the subject but that caution for research that particular thing I should do research for it that don't come into my mind so how can I get that yeah that's a very Clarity basically Kang is asking that how to identify potential research questions so as I mentioned gorang uh you have to be familiar with Journal articles where you will read about other people thinking about problems and maybe while reading through those problems you will identify some problem where you have an idea that is really how it is done you know you look at what other it's not like you sitting under a tree and an apple Falls it's a very it's a story that we hear from our childhood but uh it's really more of Newton's other phrase that I stood on the shoulders of giants there is a book by Stephen Hawking called on the shoulder of giants what it really means is research does not happen in isolation you do not ask questions out of nothing it doesn't come to your it doesn't fall in your mind like a like an apple from a tree what you do is you read read read research papers which are in journals I mentioned some of the journals and then while you go while going through those papers while going through the problems that others have worked on some ideas come to your mind maybe we can extend this question maybe we can work something some more on that and really you will then notice that research is highly collaborative in nature if you even if you are not working with someone else you are highly dependent on other people's work so go ahead and read papers from some of the reputed journals that I mentioned and I'm sure you'll get some idea about some research questions okay so nikel is saying can I repeat the so I mentioned four Journal names one is KL one is Quant Kant or Quant this is from Russia and uh one is mathematical Gazette this is from Cambridge University this is a this is the strongest recommendation mathematical Gazette and krux mathematicum from Canada is another one which does a really good job okay let's go to w w you have a question yeah good evening sir yeah if someone is solely preparing for ismi is it a good idea to go for research if someone is not preparing for IV and right now uh if you if you are in grade 11 or 12 if if you're just focusing on isic CMI entrance then it is a it's not a good idea to go for research because you know I I mean things like isi and CMI entrances they're very involved in their own right so uh you you really have to work really hard um and I do not see that you will have a lot of time to accommodate uh something like research some students however who are taking isic CMI entrances they also take entrances called Step of Cambridge University maybe you have heard of step step is a very similar entrance as isi ncmi similar means well it's the step also has mechanics which is not there in isi ncmi entrances but the flavor of the questions in mathematics part they have a lot of similarity you can Google step if you don't know what it is so now if you're taking step because your preparation for isic CMI entrance will be also useful there and if you have at the back of your mind that okay maybe I want to go to Cambridge or something like that or even if you don't I or Oxford or whatever it is then then then you have to build a portfolio and then the research projects come in but if your sole purpose is to apply to up isi and CMI and focus just on that then I would suggest don't go for a research project right now finish your high school and then start with a research project because you know at that point your next step will be to go to a university for a PhD or a Masters or whatever it is and when you are again the same game begins when you apply for a PhD program they would want to know if the kid has a strong research background that is really helpful so After High School you can start with the project okay all right let's go to udav udav you have a question sir do you believe a child has to be very academically gifted to pursue mathematics uh does an average kid have a chance to pursue mathematics at a higher level yeah I mean you see in Chinta we use a word called gifted now it is often wrongly understood what do I mean by a gifted child we say that a child is gifted if he's he or she is interested in a subject and is able to engage with the subject for consistent amount of time 3 to four hours every day let's say maybe he's not superbly clever maybe he is not ramanujan or anything like that but he is able to he or she is able to engage with the subject that means sit with a problem scribble diagrams read all of these things which do not require exceptional intelligence in that sense we just require persistence and consistency if if you can do just that this is like raw labor then you are you you you can can take the joy of mathematics you can experience the joy of mathematics uh this is this is actually I think it's a very Colonial uh idea that if you are superbly clever only then you can do mathematics it's it's a very I think because the British came to India and they had this meritocracy going on people in India think of it like like that but I don't think people in other parts of the world who have never been called colonized they think of it like that just like any other sport let's say archery or something like that mathematics is just like that you just have to be consistent that's all if you think you can be consistent if you think you can engage and enjoy the subject for three to four hours every day then you are gifted gifted under quotes and then you can do it there is nothing nothing in it okay let's go to system the last question I don't know your name so I call your by your username go ahead Namaste sir am I audible yes you are go ahead sir uh actually being honest I have I haven't any question but I just want to tell you something yeah uh sir uh I will do a groundbreaking research in Comin aics that's it okay all the best for that then all right okay okay thank you guys for joining in today I wish you all the luck and have have fun with whatever you do and uh we will see you in the next session take care bye