UPSC Topper Utsav Gautam’s Preparation Strategy for IAS (UPSC CSE) Mathematics Optional

Updated On -

Mar 4, 2021

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Sudeshna Bhar

Exams Prepmaster

Utsav Gautam qualified IAS UPSC CSE exam with 33rd rank in 2017 in the 4th attempt without any sort of help from coaching centres. He has completed a B.Tech graduate in Electrical Engineering from IIT Delhi. Read UPSC Topper’s Utsav Gautam’s Interview

He has chosen Mathematics as the IAS UPSC CSE Optional Paper. In his 4 attempts, he has secured 238(122+116) in 2014, 195 (122+73) in 2015, 288 (145+143) in 2016 and 310 (147+163) in 2017 in the Mathematics optional papers.

In the following article, the preparation books and strategies followed by UPSC Topper Utsav Gautam has been discussed in detail.

UPSC Topper’s Strategy: Cause of Choosing UPSC Mathematics Optional

  • The topper’s scores in Mathematics creates an illusion of mathematics being a scoring subject. Due to the scaling method, he got 73 in Mathematics Optional Paper-II in 2015. As he was in the lower percentile of candidates, scaling decreased his marks as well.
  • There is time to cover the basics of the optional subject. Therefore, one must be comfortable and learn to improvise the difficulty level of the optional paper.
  • Before choosing maths, candidates should be comfortable with easy topics such as linear algebra, Calculus, Ordinary and Partial Differential Equations and Complex analysis.
  • Candidates must possess inherent skill in maths and extreme likeness for this subject to master it for IAS (UPSC CSE) Mains Exam.

UPSC Topper’s Strategy: Booklist for Mathematics Optional Paper 1

Utsav Gautam did not take any sort of coaching for the IAS (UPSC CSE) Mathematics optional paper which led him to take reference from several books. Here is a list of books and strategy for the IAS UPSC CSE Mathematics optional paper.

Linear Algebra

As it is one of the easiest positions in Mathematics paper 1, the key line is to save time with maximum accuracy. Linear Algebra book and Matrices Book by Krishna series is sufficient to cover this section. One should go through the Schaum series as well.


Questions from this section are straightforward most of the times. The essential books 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, Shanti Narayan must be studied. Series Integral Calculus by A.R. Vashishtha (Krishna Series) also can be studied to prepare and practise for the definite integral question.

Analytical Geometry

Books such as Analytical geometry by Shanti Narayan (S Chand) or Series Analytical Geometry by A R Vasishtha(Krishna Series) are crucial to be followed. The Krisna Series contains more solved question papers which will help to understand the trend.

On the other hand, questions pertaining to conicoid are not easily solved. Therefore, for some particular questions, how to start the solving process must be remembered.

Ordinary Differential Equation

For Laplace, a selective chapter from the advanced differential equation, Book of M.D. Raisinghania (S. Chand) is required to study. Focus on solving previous years’ paper with 100% accuracy.

Vector Analysis

Vector Analysis by Krishna series will be enough to cover the syllabus of this topic. For further practice, the last 15 years papers would be enough.

Statics & Dynamics

For both of these topics, Krishna Series would be sufficient. The maximum number of questions from these two topics are coming from these books only.

UPSC Topper’s Strategy: Booklist for Mathematics Optional Paper 1

Here are recommended books for the respective topics used by Utsav Gautam during his preparation for Mathematics optional of IAS (UPSC CSE) Mains Exam

Modern Algebra

Group theory by R Kumar and Ring theory by R Kumar( Vardhaman Publications) is the primary recommendation for this topic. The question of the last 2 years has been really tricky. UPSC also asked questions on proof of theorems. Therefore, the approach should be basic first and then move to a higher level of difficulty.

As some of the students study Modern Algebra for the first time, it creates a lot of challenging portions. Therefore, give this topic ample time to study and practice.

Real Analysis

Books such as Elements of Real Analysis (S. Chand) and Mathematical Analysis by S.C. Malik and Savita Arora must be followed. For the past few years, the question asked by the UPSC from this topic is almost unpredictable. Therefore in his opinion, the right approach is to make sure that the easy questions are not left unanswered.

Complex Analysis

For this topic, the Complex Analysis by Krishna series would be sufficient. The questions are quite straightforward.

Linear Programming

As it is one of the easiest topics in Mathematics optional, Linear Programming by R.K Gupta would be enough. However, sufficient practice and diligence are required and make sure that there are no difficulties in answer writing.

Partial Differential Equations

For exercising boundary value problems, M.D. Raisinghania along with sufficient internet research would be more than enough.

Numerical Analysis

Jain & Iyengar book or any book which is there in state engineering college mathematics course can be studded to cover this topic

Fluid Mechanics

M D Raisinghania should be the primary source of study. As this section is very challenging and the best aid is to memorise by practising the examples given in the book. According to Utsav Goutam, if there are tough questions asked from the outside of the book, it is almost impossible to answer.


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

UPSC Topper’s Strategy: IAS (UPSC CSE) Mathematics Optional Preparation Tips

  • Try to solve the last 20 years of previous years question papers. If there is not sufficient time, in the above section of the article, the mandatory topics for previous years papers have been mentioned.
  • Revision is also another mandatory thing for mathematics Optional subject as well as IAS (UPSC CSE) Mains. Fluid mechanics, mechanics requires a revision of 4 times at least, Statics, dynamics, modern algebra is required to be revised 3 times and the rest of the topics must be practiced at least 2 times.
  • Focus on finding the correct method of the answer. Small and silly mistakes will drain most of the marks if not carefully treated.
  • Revise every formula once every 2 weeks to avoid forgetting them.

Check UPSC Topper Minal Karanwal’s Interview

For the prelims exam, he basically took immense help from google and Wikipedia. However, at the time of IAS Mains preparation, it was minimal.

At the time of preparation, he mostly used electronics gadgets such as desktop, laptop, tablet and mobile for preparation and spent 1 - 2 hours on the online websites for exam preparation.

*The article might have information for the previous academic years, please refer the official website of the exam.