Disclaimer : All the things mentioned below is based on my experience. It is not the only strategy. I humbly believe in principle of Anekantavada.

Dear all,

I have written 4 mains with maths and secured variety of marks in them. I got 238(122+116) in 2014, 195 (122+73) in 2015, 288 (145+143) in 2016 and 310 (147+163) in 2017. I have interacted with numerous aspirants who took mathematics in these 4 years. I would like share various aspects that I have observed in these years. I did no coaching for maths. Neither did I join any test series.

Choosing Mathematics as an optional

Many aspirants take mathematics as an optional and after exhausting 2-3 attempts with maths, realized that maths was not the right optional for them. Changing optional is the most unfortunate thing that can happen to an aspirant. Therefore decision that whether to take maths or not needs a lot of self-assessment and introspection.

Aspirants many times are attracted by the high marks obtained by toppers every year, which gives illusion that maths is a scoring subject. People who are the top scorers in maths (lets say top 20-25 people) will get 280-300+ marks. Rest are bound to get less marks because of scaling. It is just the beauty of scaling method which leads to wide variety of score. I got 73 in paper II in 2015. Since I was in lower percentile of candidates, scaling decreased my marks by a big factor.

There is no time for learning basic mathematics while reading about the optional. One should be comfortable with basic topics. He/she should improvise on easy topics and learn the topics which are difficult by doing a lot of practice.

Usually Btech or BSc/MSc maths people take mathematics as optional. Before taking mathematics one should be comfortable with easy topics such as linear algebra, Calculas, Ordinary and Partial Differential Equations and Complex analysis. If one is not comfortable with these topics then he/she should think twice before talking mathematics.

Scoring good marks in maths requires competing with the aspirants who have some natural skill in maths, which even includes competing with finest IIT minds as well. There is no time for building base. Choose mathematics only if you have strong liking and interest in mathematics which includes possessing some inherent skill in maths. Students who have performed well in their Btech/Bsc in maths courses, can infer that they have some level of comfortableness in mathematics.

Coaching or no coaching

Ideally a person who is good in mathematics, will not feel any need for coaching. Unlike humanities optional where many aspirants take optional without having any background of it. Science optional (especially Maths and engineering optional) is taken by people who have some background for it. So there is not much case for taking coaching so as to get some acquaintance with maths. Except for some difficult topics like Abstract Algebra, fluid mechanics there is no need for any coaching guidance. Usually all recommended books contain solved examples which are more than sufficient for teaching a new topic. But still if one thinks of going to coaching, I would advise to do it for selected topics and not for all.

Joining Test series ?

As per present trend, UPSC maths paper level is quite tough which is not matched by any test series in the market. I think doing difficult problems from recommended books in a time bound manner is more fruitful than joining test series available presently in the market.

Recommended book list and Strategy

Paper 1

Linear Alegbra : this is the one of the easiest portion in paper 1. The key lies in finding the correct answer in minimum time. Linear Algebra book and Matrices Book by Krishna series is sufficient. One can read schaum series as well. Please do last 15 years UPSC question from this chapter for improvisation.

Calculus : Questions from this chapter are also straightforward. Books needed are : Shanti Narayan – Course on Mathematical Analysis (S. Chand), mathematical analysis by S.C. Malik and Savita Arora. For covering asymptotes and curve tracing, differential calculus by shanti Narayan needs to be studied. For practicing definite integral question (which is coming as 10 marker), Series Integral Calculus by A.R. Vashishtha (Krishna Series) can be studied.

Analytical Geometry : Analytical geometry by shanti Narayan (S Chand) or Series Analytical Geometry by A R Vasishtha(Krishna Series). Krishna series book contains more solved examples so I personally prefer it. Questions pertaining to conicoid are not easy, so for some selective good questions, how to start the question needs to be remembered.

Ordinary Differential Equation: M.D. Raisinghania (S. Chand). For Laplace, selective chapter from advance differential equation by M D raisinghania needs to be studied. Focus should be on solving question without doing ZERO calculation mistakes.

Vector Analysis: Vector Analysis by Krishna series. Solve at least last 15 year question from UPSC paper.

Statics : Krishna Series

Dynamics : Krishna Series

Solve relevant chapters from Krishna series for statics and dynamics. Mostly question is coming from these books only. If a new question comes in exam which is not easy, it becomes difficult to solve in that pressure situation.

For friction: Read Golden Statics By N.P Bali. It is there on google books.

Paper 2

Modern Alegbra : Group theory by R Kumar and Ring theory by R Kumar( Vardhaman Publications). Question in past 2 years have become very tricky. They are asking proof of theorems. So approach should be to cover basics first and get comfortable level in it and then go for learning higher stuff. This portion creates a lot of challenge for majority of students as they read modern alebra for first time in their student life. Therefore ample time and lot of revisions are needed.

Real Analysis : Raisinghania – Elements of Real Analysis (S. Chand) and Mathematical Analysis by S.C. Malik and Savita Arora. Since past 2 years, there has been some very unconventional questions from this portion. Some question in my opinion are meant to be bouncer, so nothing much can be done on that front. Therefore the best approach is to ensure that one should be able to solve easy and moderate level questions. Please do past 15 year papers from this portion.

Complex Analysis : complex analysis by Krishna series. This portion is quite straight forward.

Linear Programming : Linear Programming by R.K Gupta. One of easiest topic. But ensure by adequate practice and diligence that there is no mistake in finding answer.

Partial Differential Equations– M.D. Raisinghania + internet searching for practicing boundary value problem. I will also upload some material on this.

Numerical analysis : Jain & Iyengar book or any book which is there in state engineering college mathematics course. I will upload a pdf also soon.

Fluid Mechanics : M D Raisinghania. This portion is very challenging. Best bet is to memorise and practice examples form this book. If some tough question comes in exam which is not from this book, it becomes quite unapproachable.

Mechanics: Rigid Dynamics (Volume I & Volume II). It has similar case as that of Fluid mechanics.

General tips

Try to solve past 20 years question papers. If time doesn’t permits, atleast solve papers for the portion that I have mentioned.

Revision is the must thing. Even if you cover some tough topic and don’t revise it enough. Touch will be lost, and all the hard done earlier will go in vain. So revise, revise and revise. My typical revision schedule after prelims was like that

Fluid mechanics, mechanics : 4 times

Statics, dynamics, modern algebra : 3 times

Rest topics : 2 times

Focus and practice a lot on finding the correct answer. Silly mistakes can cost you dearly. As it did in my case.

Revise all formulas once in every 2 weeks

Paper 2 in 2016 and 2017 came very tough. I think this will become a norm. Please practice more for this paper.