Topic wise syllabus coverage in Maths optional – Kanishak Kataria (Rank 1)

Hi everyone!

Following on from my previous post I am giving a detailed topic wise syllabus coverage. It will give you some idea as to how should Maths be approached topicwise. It is advisable to read the previous post first before continuing here.

Topic wise coverage

Paper 1:

It is lot easier than paper 2 but HIGHLY prone to silly mistakes. So do not take it lightly and practice as much as you can. Also, it has more scaling then paper 2. So any mistake will hurt you much more.

Linear Algebra:

  • Very scoring topic. With consistent practice you can assure yourself of full attempt. There isn’t much variation in type of questions asked.
  • Important areas: Linear Transformation, Matrix of LT, Linear Equations, Bases and Dimension
  • Proofs: Don’t waste too much time on them. 
  • Basic understanding of definitions is very important.


  • Do it in continuation with Real Analysis (As has been done in IMS notes). 
  • Important Areas: Lagrangian Multipliers, Jacobian 
  • Practice all types of problems involving Multiple Integrals.
  • Single variable calculus is very easy.
  • Remember important integrations to save yourself time. Keep a sheet of such integrations and revise them time to time.
  • Beta and Gamma functions can become handy in solving integrations involving sin and cos functions. Do not fully ignore these topics.
  • Curvature has been asked in the past. But keep it at lowest priority.

Analytic Geometry:

  • Till conicoids,
    • It is a very intuitive and scoring topic with certain guarantee of attempting the question.
    • Practice is important to recognise which type of parametric equation should you start with like assuming symmetric vs asymmetric form of line before starting the problem. 
    • Locus problems are quite common and you should be thorough in it.
    • The Line is an important and scoring topic.
  • Post conicoids,
    • Subsequent topics are challenging for sure.
    • Little amount of cramming is needed to remember various formulas and approaches.
    • Short notes are very handy in this section.
    • With practice you will be able to identify particular models.
    • Learn how to start a given problem, many question are repeated in the exam. 

Do not leave conicoids. As per your bandwidth pick important topics based on PYQs. Atleast cover all the problems discussed in the test series.

Ordinary Differential Equations:

  • Very simple topic. Remember the formula and apply it.  
  • The only challenges are multitude of formulas and avoiding silly mistakes. I did a lot of silly mistakes in my 1st iteration from the notes.
  • 2nd order LDE with Variable coefficients is a portion which needs much practice.
  • Laplace transformation should also be covered as there is a tendency to ask questions from it. 
  • Some problems might seem easy but involve some tricks to integrate. Such tricks you can remember only when you solve the problem once. Keep a shortnotes book handy to note such examples.

Dynamics and Statics

Easier as compared to the other 2 physics topics from Paper II. 


  • SHM, Catenary, Cycloidal motion, Projectile etc — cover all different question types. They follow a specific procedure which you need to replicate in each problem.
  • It can be a scoring alternative – an X factor – in your preparation if you are comfortable in them. But focus only if you have covered the other topics.
  • Its marginal utility isn’t that high, more so if you get a favourable question distribution in final exam where you can ignore all the questions from these topics.


  • Virtual work is a very simple and scoring concept.
  • If not all, cover atleast the previous year questions involving Principle of Virtual Work.

You should be proficient in all the 10 pointer compulsory problems asked from these topics in UPSC and test series. An easy question from this topic might make your job of picking non-compulsory questions in Paper I — Part II much easier.

Vector Analysis: 

  • Important topics: Serret-Fernet Formulae, Divergence and Curl are very important topics.
  • Solve ALL the problems on the Green, Gauss and Stokes theorems asked in UPSC and in test series. The more you practice them, the lesser you will commit silly mistakes.
  • Change of axes and showing invariance is important.
  • Overall a scoring topic. Please cover it fully.

Paper 2: 

It has more challenging topics but not undoable. Lesser scaling than Paper 1, so if you attempt more, you will score more.

Modern Algebra:

  • One of the most feared topics. If you haven’t encountered the terms before, there are chances that you will feel lost. As a result, this topic will need more than average time.
  • The only answer to the fear of Modern Algebra is revision, revision and loads of revision. 
  • Topics up to Homomorphism of rings are manageable and relatively easier to understand but you need practice to solve the problems. 
  • From Fields onwards, you have to struggle much more – but that’s why you opted maths, didn’t you?!
  • If you cannot understand anything, please be more strategic and cover according to PYQs. Do not waste too much time by getting stuck.
  • Try to be thorough with all the PYQs and test series questions. Discussions with friends also helps. With multiple revision you will begin to have more clarity. 
  • Keep handy negation examples in hand like Quaternion group! Such problems are very easy to score from.

One important TIP: Homomorphism is a very very important topic and also one of UPSC’s favourite. If you understand it, a lot of problems become easier.

Also IMS notes are sufficient, don’t start chasing textbooks. There isn’t much difference between the two. Almost everything important in the books is there in the notes. Just revise as much as you can. Clarity increases with more revisions.

Real Analysis:

  • Amongst the tougher topics.
  • Try to cram all the convergence tests for sequence and series and practice as much as possible.
  • Continuity is a favourite concept for UPSC. Reimann integral and Uniform convergence as well.
  • You should not fret too much over proofs. They have very high CBA and should be done only if you have too free time!

The only way out is practice and revision. To put things into perspective, I would just say that in the 5 day gap during Mains, 50% of my time was devoted to Modern Algebra and Real Analysis.

Complex Analysis:

  • This topic is trickier than it looks. Much practice is needed.
  • Cauchy theorem and Contour integration are the frequently asked concepts. Learn all the tricks in contour integration problems.
  • Other important concepts: Taylor and Laurent expansions, convergence and singularities.
  • In addition to IMS notes, you might need to refer to Krishna book for better understanding of few topics.
  • Atleast try to look at the solutions to select PYQs provided by IMS.

Partial Differential Equations:

  • Linear PDE with constant coefficients is quite similar to ODE. 
  • Non Linear PDE problems are little difficult. Learn Charpit’s method (even though not in syllabus) and cram Cauchy characteristics method. Cauchy method should be used only when explicitly asked in exam. If nothing is mentioned, use Charpits.
  • Physics application problems should be practiced as they are asked as 15-20 pointers and are quite scoring and follow a fixed pattern.
  • Reduction to canonical form questions are also quite frequent.

Linear Programming Problems:

  • The easiest topic to prepare but HIGHLY PRONE to silly mistakes.
  • In a paper with limited space, any silly mistake means 0 marks because with all the tables, there isn’t any space to correct mistakes and redo the problem. 
  • Solve ALL the PYQs. There are many edge case problems given in the notes, you should have done them atleast once.
  • Be thorough in all the problems and don’t intermix the steps and get confused.
  • Try to improve your overall speed and accuracy.

Computer Programming and Numerical Analysis:

  • CP was easy for me to prepare plus IMS notes are little excess which can lead to time wastage. Try to cover from PYQs. Maxterm and Minterm concepts should be known.
  • Algorithm and flow charts should be done only after reading Numerical Analysis. Draw all the flowcharts by yourself. And don’t just read from books/notes.
  • Numerical Analysis is a scoring yet difficult chapter. Biggest challenge is to remember all the formulas correctly.
  • Error approximation is being given importance now and should not be untouched. Try to do for standard methods like Newton-Raphson etc

Fluid Dynamics and Mechanics

  • 10 pointers are manageable and 15-20 pointers are repetitive. If you get hold of this topic, again it can act as an X factor but don’t spend too much time into it.
  • Do a thorough Cost Benefit Analysis with respect to other topics and GS prep. If you do have time, cover this topic by solving the PYQs.
  • Repeat attempters shouldn’t ignore it. 
  • Moment of Inertia, Lagrangian and Hamiltonian in Mechanics along with Continuity equation, Sources and Sinks in Fluids are easier topics. 

Lagrangian and Hamiltonian problems are very scoring and follow a fixed pattern. If you can learn that, a lot of scoring options open up in Paper II-Part II.

I covered these topics from Vajpayee Sir’s DIAS videos and IMS notes (solved examples). The videos aren’t that conceptually enriching but they do help in boosting the confidence. My biggest take away was that in topics like Fluid, 10 pointers are scoring whereas 15-20 pointers repeat. So, if I cover all PYQs and few model problems, there is a chance that I might actually attempt a few difficult problems in exam and get some partial marks.

I got the videos from a friend of mine. They are probably available on Neostencil. Still I would say that they are not worth spending time and money into! If you can manage them easily, good for you else leave them.

Recommended order of topics to finish syllabus:

Topic(approximate number of days to complete)

  1. Ordinary Differential Equation (10 days)
  2. Partial Differential Equation (10 days)
  3. Vector Analysis (10 days)
  4. Linear Programming Problems (7 days)
  5. Modern Algebra (30 days)
  6. Linear Algebra (15 days)
  7. Real Analysis + Calculus (45 days)
  8. Complex Analysis (15 days)
  9. Analytic Geometry (15 days)
  10. Computer Programming and Numerical Analysis (10 days)
  11. Dynamics and Static (10 days)
  12. Mechanics and Fluid Dynamics (15 days)
  • First 4 topics are to get into rhythm of solving maths problems. They are more “application of formula” based.
  • Next 4 topics are little taxing but you will be at peak of studies and can sustain it. Some portions of Modern Algebra and Linear Algebra also overlap like Vectorspaces and Groups.
  • Linear Algebra and Calculus provide little relief from theoretical problems.
  • Complex Analysis has a minor overlap with Real Analysis (convergence etc.) which might be helpful.
  • Analytic Geometry and Computer Programming and Numerical Analysis again get you into that application based topics, thus breaking your saturation from theoretical topics.
  • Remaining physics topics should be done as per your own level of overall preparation. Doing them at last won’t break your rhythm in other topics.
    • Few topics like PDE, Complex etc should be done as prerequisites to Fluid Dynamics.
  • Also you can mix topics depending on your comfort level.
    • You can put either Analytic Geometry or Numerical Analysis in between Modern Algebra and Real Analysis so that you get refreshed between two heavy weight topics.
    • LPP and Vector Analysis are floating topics which can be done anytime.

Total estimated time is around 6-7 months. This is just a rough approximate. You can reduce this time depending on your time allocation to optional vis-a-vis GS at the start. I would advise you to devote at least 6 hours daily during initial days, so that you can finish the syllabus on time. If your 1st revision is done before Prelims, you are in a wonderful position from Mains perspective and the burden of optional would reduce substantially.

In my last two posts, I have tried to cover as many dimensions as possible. I have always focused on finding my own path. These posts should only act as a guiding light in case of confusion. You are the best judge for yourself, so try to formulate your own strategy.

Stay motivated and just remember why you opted for Mathematics as an optional. It is a double edged sword with high risks but if you execute your plans perfectly, the rewards are much higher!

Hope these posts helped you 🙂

Best of luck!

95 thoughts on “Topic wise syllabus coverage in Maths optional – Kanishak Kataria (Rank 1)”

  1. Hi, Kanishak! I’ve been attending IMS classes from 2 weeks. I’m confused if I should continue or not, reason being the extreme slow nature of classroom teaching and hence not so good productivity. Can you please give your two cents on this?

    1. It’s upto you, if you are gaining something out of classroom coaching or not. As I had mentioned in previous post, I realised IMS classes are too slow and then started attending multiple classes and reading different topics simultaneously on my own. Classes only helped me maintain sincerity (5.5 hours daily for 4 months) and I could talk to few people and discuss doubts.
      Just remember that you have to be self-dependent in UPSC. Don’t rely on someone else fully. Utilize whatever you have to the fullest. If your productivity is high with same level understanding outside of IMS classes, then you don’t need to attend them. But if it is not, classes will provide you some sort of routine at least. Rest you can evaluate on your own. 🙂
      Best of luck!

      1. Thanks a lot, bhaiya! For now, I sit in the last and read and solve on my own, occasionally listening to imp things from Sir. And, thanks a lot for all the guidance. (It has helped me immensely coming from a similar background as you)

          1. I attended IMS from 11:30 to 4:30 for 4 months. Also, studied for 1-1.5 hours at home.

      2. Sir how u hv practised questn??? From book ki solved problems ya fir ims solved questions for each topic.

  2. You talked about IMS notes. Are they the same notes that IMS send through correspondence because I am in Bangalore and can’t afford to go to New Delhi

    1. Thank you so much sir❤
      I am facing many problems in Complex Analysis(wether to do proofs or not). Can you please upload CA short notes on the Dropbox because the only topic left to upload is that.
      Again thanks a ton Sir ?

      1. You can refer to Krishna Series book for better understanding in CA. Proofs are something which may consume a lot of time. Please refrain from getting stuck because of them. Focus on applications more.
        I have uploaded my Complex Analysis notes also.

    2. Yes they are the same. You can either get them through coaching directly or get in touch with any of the shops in ORN (Kumar Book Centre or Imagerunners), they will send you the xeroxed notes directly.
      Mind you, the IMS notes are handwritten.

  3. Sir, the headings given in the UPSC Mathematics optional syllabus are very exhaustive.
    So, do the notes provided by you in the Dropbox contains all the topics?
    Or I have to complete the books recommended from cover to cover?
    Please assist.
    Hoping for a positive response.

    1. UPSC syllabus is like bible for all the aspirants – be it any subject or paper. You should cover all the topics mentioned as much as possible. My notes are only for reference. Do not try to read from them directly. They are compiled using IMS notes and only contain information which I felt needed revision. If you want to read from good quality notes, you can refer to IMS notes by Venkanna Sir.
      I haven’t followed any book, so cannot comment on that. But as per my best knowledge, no book needs to be read cover to cover. You have to identify the relevant topics and read them. Syllabus and PYQs help you make that decision.

  4. Hi sir,
    I have started my Maths preparation 8-10 days back. I have completed linear algebra(Matrix part) and currently doing ode from IMS notes. I had these topics in my engineering so I am enjoying solving them but regarding the topics like Modern algebra, real analysis, static and dynamic and fluid mechanics which are rated difficult by many aspirants… how good is coaching from IMS for these topics? I’m from Navi Mumbai and I have no prior knowledge about these topics. Where can I find solutions to the PYQ ? How to master theorems?

    This initiative is wonderful. I loved the part where deadlines are mentioned for each topic it will help me a lot to keep me in check. Thank you sir and Congratulations for cracking CSE.

    1. From what I know, you will not be getting IMS coaching for only those few topics plus I would not recommend joining classes only for them.
      The notes for Physics topics are also little exhaustive and you need to pick and choose what topics from read from.
      PYQ solutions aren’t available that easily. You need to make use of internet extensively. Also IMS uploaded some solutions before Mains 2018 on their test series portal.
      For Theorems you need to revise multiple times and also try to apply them in problems. Only then you will be able to master them.

      1. What was your strategy for MA, RA and Static and Dynamics? Did you refer to YouTube Videos for clarity of topics?? From which topics theorems are asked the most? Any tips for difficult topics? Thank you, sir.

        1. MA, RA — loads of revision and practising same problems again and again

          Dynamics and Statics — was comfortable in Physics. There are 4-5 models like constrained motions and Virtual Work etc. Practiced all the problems on them.

  5. Hi Kanishk,
    I live in Pune.I am working professional.
    I have been attending online ramanasri coaching.
    Currently limit and continuity topic is going.
    I am not able to grasp much and looks like have to write and memorise step and to make out most for syllabus in small time.what would u suggest from below.
    1.Add IMS notes to the material.
    2.Add standard books as mentioned in blogs by nitish.
    3.standard books for reference + practice – IMS notes
    4.Rely on Ramanasri material.
    What are your suggestions over the same.Thanks in advance for time and initiative.

    1. I will advise against adding too much material to the notes you already have. I have no idea about quality of Ramanasri material. If it is reliable stick to it, otherwise make use of standard books or switch to IMS notes. In Mathematics you have to write a lot and learn all the steps, you cannot rely on just “reading” from notes. You will have to struggle through some topics like MA and RA but if you are able to manage them, excellent returns are possible.

    1. I am afraid there is no one stop source for the solutions. You need to solve and cross check with your peers. If you join the test series at IMS, you may get the solutions probably before the Mains.

  6. Sir i just wanted to ask that is IMS coaching helpful .
    Along with vajiram regular batch .
    Can we manage 2 batches of IMS

    1. Everything is manageable as long as you are willing to work hard. I went to IMS from 11:30 to 4:30 and then Vajiram from 5:00 to 7:30 for a period of 4-5 months. But you should be comfortable in the topics you have covered. Don’t just sit through the classes. IMS coaching is helpful only if you utilise it in the correct manner. Otherwise it will consume a lot of your time.

  7. Thank you sir for the suggestion. please throw some light on the vajiram and ravi insta account.As I am using it to filter out my newspaper topics for The Hindu.

    1. You should never filter topics from some institute’s list. First read the newspaper by yourself, then at the end you can cross check just to see if you missed out on something. Develop the habit of identifying relevant topics on your own. If you do not do that, it will backfire in the longer run.

  8. First of all thanks a lot sir for guiding us for very unpredictable exam. Really we need a such type of guidance that you provide us because there are lots of noise of guidance available in social media and everywhere …

    Finding such type of reliable guidance is very difficult for freshers .

    My question is that how to do study of mathematics ?
    means we only solve problems , by looking solved problems in IMS notes ( we never think about that problems ) . Because Prudhvi Tej sir told that this is not worth for exam.

    Please tell us sir method of preparation ???

    Finally heartly congratulations for your dedication …

    1. Thank you for your kind words.
      I have shared my guidance on Mathematics in these posts.
      For “How to do study of Mathematics?”, I would just say that practice as much as possible.. Don’t “look” at the problems. Solve them by yourself initially, even if you know it fully. In later revision you can just skim over them.
      I don’t know what Prudhvi said but as per my knowledge he studied mathematics with a constraint of very limited time availability (with most of it being done post prelims). So he had to rely on some hacks to quickly finish the syllabus. There is no guarantee that it will work for you.
      I had more time than him and finished the syllabus before Prelims, hence the difference in approach.
      Do not mimic his approach or my approach. Just see what is more relevant for you and then “adapt” as per your needs.

  9. I’m thinking I can complete syllabus within 2 months after seeing syllabus and some previous years Questions… still now I’m in that thoughts only …but does it looks foolish to think like that? .. I got this doubt after seeing your strategy.. videos..
    I need to know that though if I heartily do my preparation.. can’t I finish within 2 months..

    1. Everything is possible. I have heard about people finishing Maths syllabus in 3 months. It all varies from person to person. The schedule which I shared is from a general point of view. But 2 months is very less time in my opinion (if you input 5-6 hours).
      You need to cover the syllabus extensively and practice as well. If you are able to master in 2 months, kudos to you! You can become the next topper with mathematics 😉
      But for that your daily time allocation for Mathematics has to be upwards of 8-9 hours and you may get burned out also. So think accordingly.
      And one last tip.. don’t just “think”, you have to actually do it!

    1. It is important in order to revise quickly, otherwise you might feel little lost.
      Also given the volume of formulas you need to cram, it is imperative to have a small formula sheet ready for quick glances.

  10. Thanks you very much sir …

    Really ,
    if such type of guidance is always with us while preparing then all of us have great privileged and get confident to clear the exam .

    And this is more beneficial for us that you are always solving our queries while preparing. Sometimes times very small queries create very big problems …

    I hope that you will always with us during preparation for your valuable guidance …

  11. First of all thanks to sharing strategy about maths becoz noone shared this type of info before.
    I want to ask that i live in pune so how should i get ims notes to refer? Is there a need to refer reference books apart from ims notes? I have done engineering so i donot have knowledge about modern algebra and real analysis. I started reading real analysis from MD Raisinghania but i am not understanding it so i felt nervous that how can i complete it with this subject also i feel nervous about modern algebra.
    Can u plz suggest how can i understand that sub and complete it with time?
    I have given JRF math exam in that the maximum paper is of real analysis so i scared that the maximum mark topic i am not understanding. Can u plz give me suggestion.
    Thank you.

    1. IMS notes can be purchased from coaching or any of the Xerox shops in Delhi (they can even post them to your place).
      They are quite extensive and you do not have much need for standard books but they might be required for a few topics.
      Modern Algebra (MA) and Real Analysis (RA) are 2 of the toughest topics. You can get confidence only through revision. Also try to mix theory with examples in these subjects. You might get into the tendency of only reading theorems. You will understand the concepts and retain better if you solve some problems using them. Just remember that if you prepare these 2 topics, rest of the course is easily sorted out.

      1. Sir I’m doing IMS coaching. MA and RA both topics are going on simultaneously in coaching. I’m thinking that i should prepare separate notebook for imp and tough questions with proper solution (including PYQs) for these topics. What will be your suggestion if i do same? Is it correct time or not? Because whatever important topics you have told are not covered yet. So plz guide sir…

        1. Yes, you can do so. It will be handy to revise from those notes later on. IMS schedule is different with multiple batches going on. I recommended a schedule for someone studying on their own. It is upto you to follow it or not. It is neither necessary nor sufficient!

          1. Thank u sir. Had u made any different notes for revision(like i asked i.e notebook for imp questions) . Because in my opinion just reading the theoretical notes might not benefit as much..

          2. Yes. I have already shared the notes on dropbox. It contained important theorems, formulas and trick/good questions. I used them for Last Minute Revision during Mains.

          3. How did u kept revised other topics while u were preparing in first four months. And how many topics u were able to manage simultaneously(I’m not going to do the same. I know there is difference in every one’s ability. But it will help to manage syllabus in limited time.)

          4. My Maths revision was done in the month of January and February 2018 after I had finished the syllabus by October 2017.
            I didn’t revise the older topics in the first 4 months. I only did maximum 2 topics simultaneously – mostly RA and MA. Other than that I finished all the topics much faster than the coaching by keeping a good pace (Like LPP was done in ~4 days and Vector in 5-6 days). As a result, sometimes I was also able to revise the topics automatically if they were being taught in the class.

  12. Hi sir, I am currently doing my final year in Mechanical Engineering from IIT Delhi. I have 27 credits left in my final year. I have started my GS coaching from vajiram. It will be tough for me two attend 2 coachings 1 for maths and 1 for GS during college time. So I have decided to complete maths on my own.
    So will that be appropriate to complete syllabus through IMS notes and few books for standard topics or do I need to join some classes for few toughest topics?

    1. You can complete using IMS notes and standard books. If you feel lost, then go for the coaching route.

  13. Hello sir,
    Thanks for this initiative and congratulations for the rank.

    Sir, I want to switch my optional to maths because i cannot handle my previous optional. I am damn interested in maths. Can i cover it by myself through ims notes without their coaching?

    1. Yes the notes are good. But you have to work hard in Mathematics. It is a bulky optional for sure. Self-study is required, coaching wouldn’t spoonfeed you everything.

  14. Sir, from your EXPERIENCE , don’t u think that there are many outdated questions in the IMS ( book printed) notes as well. Means such type of questions never asked or rarely asked. Is it beneficial to do such question or focusing and revising repetitive pattern is enough?
    I’m asking this because u told many times that don’t leave a single question? I hope u r getting me. Because in ur revision u did only imp marked question. And those questions about which I’m asking hopefully might not in your marked question list. So plz guide.

    1. You need to be dynamic and understand by yourself which questions are important. Many questions become outdated so focus more on question models from recent years instead of those in 1990s/2000s. But remember UPSC can anytime ask older questions also as Maths is static, so you need to be little aware about it. Do not leave a single question in 1st iteration and then during revision you can be selective.

  15. Hi Kanishak,

    Thank you very much for sharing your strategy and encouragement on maths as optional.

    While practising sums in test series/ PYQs , where do you match the solutions for questions which are not covered in IMS resources ? Did you refer the standard books ?

    I am asking this because, having decided to take up maths as an optional, I need to prepare all by myself..

    Thanks in advance!

      1. Hello Kanishk sir
        Please upload 2018 maths IMS Test Series papers .Dropbox link is not working. I read all your blogs.

  16. Hello sir
    Can you check my time table that it efficient or over exhausted
    I take 2 batch in IMS 11:15-1:45
    And 5:15 -7:45 in between I have vaji ram and Ravi…2-4 so I can’t adjust my time for self study as only 2-3 hr daily to gs and maths
    Plzzz suggest me a right way for the preparation. Plzzz sir

    1. I cannot comment on your timetable. Do whatever you are most comfortable in. Don’t lose on important time but at the same time don’t burn yourself out.

    1. I prepared them myself using the important formulas from Numerical Analysis topic. Base material was IMS notes for cross checking.

  17. Hello sir,
    Congratulations for your success and big thanks for this blog.
    Are the IMS notes sufficient or do I need standard book?
    If I need standard books then which one ?

  18. Hey Kanishak!

    Is there any reliable source to cover the flowcharts and algorithms for numerical methods? I have checked Nitish K’s blog, the flowcharts and algorithms’ look different from that on the internet.

    1. I used IMS notes and then made all by myself. You can use my notes as well or google it. Just remember, there is no single way of making the flow charts.

  19. Hello sir,
    Thanks for this wonderful initiative and congratulations for the rank.

    I am doing self-study for Mathematics optional relying on IMS Notes for most of the topics. As I am studying by my own in my hometown, I am not able to find a serious peer group with whom I can match my answers or clear my doubts. Shall I come to Delhi and join coaching for this. If not What is the way out ? Can you please guide me ?

    1. You can search for online groups through platforms like forum and telegram. I would advise against the decision of moving to Delhi solely for this reason. There is no certainty of finding a reliable and motivated peer group even in Delhi.

  20. plz sir share some tips for real analysis and abstract algebra.
    I’ve no one to guide and I’m following standard books such as Malik & Arora for Real Analysis & Gallian for Abstract Algebra.
    Any advice would be helpful.
    Thank you

  21. Hello Sir,
    I have finished the first 4 topics but I don’t remember all the formulas and tricks concretely. Should I revise them or continue with the syllabus and do the revision at the end? And should I keep solving the PYQPs, test series along with the IMS notes or do these at last?

    1. You can leave revision for later. After reading just try to solve questions.
      If you have time, you should solve PHQs as well. Test series can be done later.

  22. Sir, I have done and in mathematics. I have two question
    1. I am thinking to make notes in first reading or it’s better to make notes after first reading…..and I want to when you have given time to first and second revision ??
    2. is IMS notes sufficient or I have to prefer in addition to books ???

    1. Generally it’s difficult to make sense of topics in 1st reading. So it’s preferable to make notes during revision. My first revision was in Jan 2018 and then second was in the one month just after prelims.

      IMS notes are quite comprehensive. If you can understand from them, then you are good to go. Else supplement them with standard books. You need to be dynamic in your perspiration.

  23. Hello Sir,
    Congratulations on the rank and you have started a great initiative. You have simplified maths optional preparation for people like us.

    The topics from modern algebra seem to be very counter-intuitive and from IMS notes I have to see 70% of the solutions from the notes. Not able to solve most of the questions by myself. What should I do?

    1. Just keep practising and try to not look at the solutions. That’s the only way out. I also had to struggle a lot in this topic but never gave up. The more you revise the more you will be able to solve by your own. If you have time, refer to some other notes/lecture for better understanding.

  24. Hi Kanishak,

    Congratulations on your success.

    I would like to ask a question. It is said that there are various questions in Maths optional final exam directly from standard books (Solved problem, Examples, etc.). But since I am just starting it and have the paucity of time, I am inclined towards using only the IMS notes. So I have following doubts:
    1. Did you face any problem regarding this or IMS notes cover all possible questions or the startegy to solve it?
    2. Did you solve questions from standard books in between or just focussed on IMS material, PYQP and Test series?
    3. Or is it just not true to have most of the questions from standard books?

    1. 1. IMS Notes sufficed for me.
      2. Latter
      3. You never know where a question is going to be asked from. Focus on concepts and cover few examples from them. Then you can answer any question.
      I never prepared thinking that question can be asked from this or that book.

  25. Hello Kanishak,
    I really liked your approach towards every topic in math and I am following that schedule also with minor changes as per my need. My doubt is how you are managing time for GS with it…like your schedule indicating GS timetable also in parallel to maths and current affairs…so that I can have a balance. If you have answered somewhere mentioning your how your daily schedule was(I know it changed with time), how it changed with time and how much time u allowed to every gs topic with maths going side by side…will surely help.
    I know I am asking a lot. Hope u understand my dilemma of maintaining the balance.
    It was inspiring to see how your work paid off 🙂

    1. Please watch my video with Chamomile Tea with Toppers. I do not remember exact time allocation. But yes GS did suffer a lot in initial few months due to Maths.

      1. Sir,
        I went through your video and I found you stressed quite a lot on newspaper reading. So whether you were preparing notes simultaneously or just reading it and went through coaching institute materials (magazines ) at the end.
        In short what should be the best way to make most of current affairs and if possible suggest magazines if you followed anyone especially for mains point of view ?

  26. Hello sir , Read newspaper take lot of time plzz suggest a better option for it and plz suggest a magzine that is useful as in market there lot of magzine and I am confused about the magzine . And my optional is maths and plz suggest that how I tackle modern algebra I m facing lot of problem in it.plzz help me…

  27. Sir, were you able to manage PYQs and practice problems in first phase for all topics ? Had you left any topic for next time preparation (i. e. In January)?

  28. Sir,which book is best : Schaum’s outline or Krishna series for complex analysis & for other topics too. I have IMS notes of all topics in pdf form.

  29. Sir I m facing problem in algorithms and flowcharts . I m not able to understand the loop within loop concept. I have maths in my graduation subject but since I don’t have engineering background my lots of time get consumed in it and I am not getting output..

  30. Hello kanishk sir…inspired a lot with your guidance …I just wanna check the way you made your short notes..but it is not available in drop box…can you please check post once..

  31. Thank u sr,but I am little confused that should I take mathematics as optional because I am pursuing my second year of graduation with humanities stream. I did so due to some problems but I have a genuine interest in mathematics and I have completed linear algebra and linear programming. Can you guide me sr pls???

  32. Greetings, sir.

    I am a Btech graduate(from Bangalore) with 7 gpa(65%-70%) in engineering mathematics 1,2 and 3(I only studied during the last 4-5 days before the exams). I am not an IITian. But over time, I developed inordinate interest in Math, and when I decided to pursue UPSC CSE(about a month or two ago), I chose Math as my optional without even a second thought. I began my preparation with GS as usual, and as time flew, I began developing fear for Math’s abstractness/vastness. Is there a way to decide whether or not I have the right mindset for math, and whether or not I should choose Math as my optional subject? I remember you suggesting the readers to first study easier topics like Linear Programming in order for them to realize what’s in store if they chose math, but I believe that LPP is a little too easy to firmly decide if I’ll be able to sustain my efforts, come what may. Could you please help me decide if Math is the right optional for me? If yes, then how do I begin studying/which topic should I start with(given that I am starting from scratch, and that I have forgotten Engineering Math)?


  33. Hlo sir.
    Sir me 2021 IAS k liye prepration krr rhi hu or maine 2017 me bsc pcm se ki the abhi sir maine maths k pyqs dekhe the to paper 1 to smhj aa rha h but paper 2 smhj nhi aa rha h uske liye koi tips nd sir starting kaise kre pls help.

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