IAS Mains 2020 Preparation Strategy for Mathematics Optional

Updated On -

May 27, 2020

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Abanti Pramanik

Exams Prepmaster

There are several subjects which you can choose for the optional papers in IAS Mains and one of them is mathematics. A number of students choose this subject as it is entirely logic-based and you can either do a sum correctly or it will be wrong. While this means a student confident with their preparation can secure exceptional marks, those who are not very good at calculation should refrain from choosing the subject. It is hailed as one of the toughest subjects to choose from by many aspirants, but there have also been candidates who have emerged successful in the exam with flying colours by choosing this as an optional paper. Hence, its effects on the candidates’ performance is rather ambiguous.

If you opted for maths optional, you have to follow a dedicated preparation strategy for the same. This post shares in detail the different approaches that you can have regarding this subject to ensure that your preparation does not fall short during the exam.

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Why choose Maths Optional for IAS Mains?

Before we delve into the preparation strategy, it is very important to understand for the candidate the advantages and disadvantages of choosing maths as your optional paper. IAS Mains has a huge syllabus leaving aside the optional paper and to ace the exam, smart studying is more important than in-depth studies.

Benefits of choosing Maths Optional

The following are the advantages of choosing maths as the optional paper-

  • Mathematics is a scoring subject. There is no theory to memorize, and your performance entirely depends on your understanding of the underlying logic behind the different topics. If your preparation is good and you have speed and accuracy in calculation, you can score way more than what is possible with any humanities subject.
  • The syllabus is static and hence you need not worry about the preparation for a year going to waste since it got updated by the upcoming exam. Candidates who are attempting for IAS the second time or more, find this feature very advantageous.
  • The competition is much less than other optional papers as very few candidates choose maths.
  • Assessing the performance right after the exam is much easier since there is no subjectivity in maths and the marks depend only on right or wrong calculation.
  • Maths is particularly suitable for candidates who are not fond of or have the ability of memorizing.

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Drawbacks of maths optional

However, maths also have a few drawbacks which are as follows:

  • It takes up a long time to prepare the entire syllabus and its syllabus does not overlap with any other general studies paper.
  • Since the topics are not subjective and nothing is left to the interpretation of the examiner, there are no marks for attempted but incomplete answers. Hence, the margin for error becomes very less.
  • The paper is thoroughly technical and hence, candidates who do not have an aptitude in technical studies will find it difficult to grasp the syllabus.

Success rate of choosing maths optional

According to the annual report from UPSC, in 2015, 258 candidates had opted for maths optional and 31 of them had cleared the exam. The success rate was 12% for that year. From 2011 to 2015 the success rate of the subject has increased from 8.3% to 12 %. However, the number of candidates opting for maths optional has slowly declined over the years. A number of toppers in IAS have emerged in all these years who had this subject as optional. 2006 IAS Topper Mutyalaraju Revu had maths as optional and Anuvab Singh who ranked 8th in 2017 had scored 375 out of 500 in optional by choosing this subject.

Who will benefit the most by choosing Maths Optional?

Students who had B.Sc. in mathematics or B. Tech will find the syllabus of math optional papers most relevant to what they have learned in their graduation so far and thus benefit the most. However, many students, despite their technical background, have apprehensions about choosing the subject.

This is primarily because they lack confidence about their logical, calculative, and analytical ability and also their speed and accuracy with such topics. But if you do not have such troubles and think you can complete the syllabus, maths can prove to be very advantageous as it is very scoring.

Many of the topics in the syllabus are from higher secondary level and common to all but there are also several important topics that are taught in graduation or B.Tech, making the subject a difficult choice for candidates with Humanities background. The syllabus calls for 4-5months of preparation with 12-14 hours of weekly practice.

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Maths optional syllabus for IAS Mains

There are two papers for maths optional and the syllabus are as follows:

Paper-I Paper-II
Analytical geometry Algebra
Linear algebra Real analysis
Calculus Complex analysis
Dynamics and statics Numerical analysis
Vector algebra Computer programming
Ordinary differential calculus  Mechanics and fluid dynamics
- Partial differential equation

These are the basic topics and there are further subdivisions under them which together makes the syllabus rather big.

Best reference books for Maths optional

The following are the best reference books that you can choose from. It is best to keep the number of books and study materials limited to avoid confusion and keep your study plan concise:

  • Linear Algebra: A.R.Vasista, Schaum Series
  • Calculus and Real Analysis: S.C Malik and Savita Arora, Shanti Narayana
  • 3-D Geometry: P.N. Chatterjee
  • Complex Analysis: Schaum Series, J.N. Sharma, Ponnu Swami, G K Ranganath
  • Dynamics & Statics: A.R.Vasista, M. Ray
  • Mechanics and Fluid Dynamics: M.D. Raisinghania, R.K. Gupta, J.K. Goyal and K.P. Gupta, Azaroff Leonid
  • Calculus and Real Analysis: S.C Malik and Savita Arora, Shanti Narayana
  • Ordinary Differential Equations: M.D. Raisinghania, Ian Sneddon
  • Algebra: Joseph A. Gallian, Shramik Sen Upadhaya
  • Numerical Analysis: Jain and Iyengar, K. Shankar Rao, S. S. Sastry
  • Computer Programming: Raja Raman
  • Mathematical Analysis by Malik and Arora
  • Ordinary and Partial Differential Equations by MD Raisinghania
  • Advanced Differential Equations by MD Raisinghania
  • Krishna Series on Matrices
  • Krishna Series on Differential Calculus
  • Krishna Series on Integral Calculus
  • Krishna Series on Analytical Geometry
  • Krishna Series on Statics
  • Krishna Series on Dynamics
  • Krishna Series on Vector Calculus
  • Vector Analysis: Schaum’s Outline Series by Murray Spiegel
  • Abstract Algebra, Group Theory by R Kumar
  • Abstract Algebra, Ring Theory by R Kumar
  • Real Analysis by MD Raisinghania
  • Krishna Series on Complex Analysis
  • Operations Research by JK Sharma
  • Engineering Maths by Grewal
  • Numerical Methods by Jain and Iyengar
  • Fluid Dynamics by MD Raisinghania
  • 3-D Geometry by N. Chatterjee
  • Algebra by Shramik Sen Upadhayay
  • Linear Programming by Shanti Swarup, S D Sharma

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General tips to score more in maths optional papers

In order to organise your study plan effectively, there are a few generic tips that must be followed for improving your overall speed and accuracy with mathematical problems:

  • Nothing can beat rigorous practice for acing maths. Regularly practising a variety of problems from each topic will improve your critical and logical thinking. It will also make mental calculations faster and more accurate.
  • Practice will also ensure that your observation is keener and hence silly mistakes are avoided. Missing out on noting a tiny symbol or a decibel point can entirely change the outcome of the sum hence this is another important factor that should always be practiced.
  • Develop a habit of reading the question very carefully and simultaneously write down the figures that are already given.
  • Solving the problem should be done step by step and in a crisp and organized manner so that the examiner is able to understand the method you have followed. Step-jumping is not a problem, but haphazardly solving the problem with scattered steps all over the paper is a habit that must be avoided.
  • Do not try to memorize the base logic behind a topic, rather understand the concept in-depth. Memorizing in maths works as far as the formulas are concerned but not beyond that.
  • Prepare formula sheets for every topic and keep it handy. As you practice more and more sums from each topic applying these formulas, they will automatically get memorized.
  • When you are beginning to solve a math paper- be it a mock test or simple practising of what you have learned so far, make sure you have a calm mind. While one correct sum will boost your confidence and make the entire process much faster, a wrong attempt will simply further agitate you and the net result of the entire study session will be negligible.
  • If you have a senior or a mentor to guide you, take their help in preparing a list of books to be followed for different topics. This way when you start studying a specific topic in maths optional, you can have all the necessary notes and books at hand and do so in an organised manner and get maximum utility of your time.
  • Check through the previous maths optional paper to get an idea about the repeated topics and pattern of questions so that you can take the preparation accordingly.
  • Lay emphasis on the methods of proving theorems. This often comes as a part of a question and even in situations when you are unable to remember the exact theorem behind a specific question, you can derive it from scratch. Proof of theorems specifically come in paper-II.
  • Enroll in tests series for maths optional if you can. They help to gain confidence about the subject and also improve your time management and thus help you to attempt and finish the maximum number of questions possible within the designated time.
  • Check your answers right after finishing solving a question while doing a practice paper. This way, you can spot errors while the sum is still fresh on your mind and rectify the mistakes better so that they do not get repeated in the future.

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Paper-wise Important tips for maths Optional

We will now share paper-wise tips for different important topics which are often repeated over the years in IAS Mains Maths Optional Papers.

Important tips for topics in Paper-I

  • Paper-I is easier than paper-II as it comprises topics that are in the higher secondary level and more based on calculation than derivations.
  • For analytical geometry, emphasis on problems related to skew lines, cones and conoids, and sphere. Check the solved problems provided in the books and try to follow the same pattern while solving a new sum related to these topics. The questions may be asked in a different manner, but the approach of solving the question will remain the same once you understand what you are expected to find.
  • In calculus, focus more on calculus of many variables- this topic is common for paper-I and II with slight differences which means you can prepare the topic simultaneously for both the papers.
  • Statistics and Dynamics is an important topic, so try to solve as many problems of different difficulty levels, as you can from this chapter.
  • Ordinary differential equations are relatively simple even though the topic appears very vast. Once you complete practising sums for all types of differential equations the section is done and since the sums are of the same pattern and rather simple, this topic does not take too much time to prepare.
  • For vector analysis, you must have a thoroughly clear conception of the theorems associated with it so that you can do the applications accordingly.

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Important tips for topics in paper-II

  • Paper-II is more conception-based and has sums related to the derivation and proving theorems, which make it difficult for many candidates. If you can master these types of problem-solving, this paper will prove to be an advantage for you and also enhance your preparation for paper-I.
  • In abstract algebra, you have to memorize all the theorems. But you can skip practicing the derivation of large theorems which are usually not asked in the paper.
  • In real analysis, emphasis on Riemann Integral, Series and Sequence of functions and Improper Integrals which are repeated on several occasions for maths optional in the past few years.
  • Linear Programming is another very important topic, and you cannot leave out any part of this while practicing the sums.
  • Mechanics and Fluid Dynamics had a fair share of questions in the previous year. In UPSC you will often get questions that are a mix of PDE, Numerical analysis and Fluid Dynamics which make it much trickier. See all the solved examples from your reference books and lay special emphasis on sums related to Kinematics of Fluids in Motion, Sources and Sinks, Vortex motion, and equation of motion of Inviscid Fluids.
  • Complex analysis is an important but also very easy section from this paper and Cathy’s Theorem is particularly important from this topic.
  • Computer programming section requires adequate practice but on the brighter side, it comprises basic programming which is easy to master.

Check IAS 2020 Preparation Tips, Important Books and Exam Pattern

Acing in maths optional for IAS Mains 2020 exam is possible when you dedicate enough time to practice and revise all the topics and relevant formulas. With the prelims exam of IAS Mains 2020 postponed, you have enough time to cover the syllabus. If you think maths is your forte, this is a good topic to choose even though it is unconventional. We hope the tips shared above will assist your preparation and wish you all the very best!

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