How to Prepare UPSC Mathematics Optional subject 2021 – IAS Mains


Prepare UPSC Mathematics: Check out How to Prepare UPSC Mathematics Optional subject 2021 – Study Strategy. UPSC Mains Mathematics Optional subject Preparation Tips are provided here. UPSC Notification 2021 has released. Today we’ve provided a Preparation strategy for UPSC Mathematics optional Paper. UPSC has already announced the IAS / Civil Services Exam Dates (यूपीएससी गणित वैकल्पिक विषय). Before going to start the preparation strategy for UPSC, know UPSC Mains Syllabus. You can check Suggested Strategy for Mathematics optional for the UPSC IAS mains exam.

How to Prepare UPSC Mathematics Optional Subject

Mathematics is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature.

  • know your UPSC Civil Services Exam syllabus
  • Select Best Reference Books
  • Prepare a Study plan
  • Prepare own Preparation Notes
  • Practice Previous Question Papers
  • Practice few Mock Test Papers

Why Mathematics optional?

Mathematics is the most advantageous and the highest scoring optional. You have been solving Mathematics questions since elementary school. Think about it; After spending more than 15 years in the field of Mathematics, if you are being manipulated to change your path for an irrelevant option with just 6 months or one year of preparation, you are actually leaving your area of proficiency and are indirectly trying to take up the challenge of competing with the masters of their respective fields.

UPSC Preparation Tips

UPSC Aspirants should follow exam tips to write the exam. Preparation tips are needed for any exam. UPSC exam should be conducted once in every year. Planning and hard work are very important to face any competitive exam. Below are some of the tips for preparation. The Paper I of Mathematics Optional paper Linear Algebra, Calculus, Analytic Geometry, Ordinary Differential Equations, Dynamics & Statics, Vector Analysis. But Paper-II of Mathematics optional deals with Algebra, Real Analysis, Complex Analysis, Linear Programming, Partial differential equations, Numerical Analysis and Computer programming, Mechanics, and Fluid Dynamics

Step 1: Know UPSC Mathematics syllabus

In the previous article, we’ve provided UPSC Mains Mathematics Syllabus. You can check and find what are the applicable topics and chapter for UPSC IAS Mains 2021 Exam.

CheckUPSC Mathematics Syllabus 2021 – IAS Mains Optional Subjects

Step 2: Select Best Reference Books for UPSC Mathematics

To prepare UPSC Mathematics Optional Subject, UPSC aspirants should prepare some reference books. We’ve already provided UPSC Reference Books for All optional papers. You can check our best-recommended books for the IAS exam at the given link below. The suggested books are included in optional and language Subjects.

Check – UPSC Mains Mathematics Reference Books

Recommended books for Mathematics:

  • 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
  • Ordinary Differential Equations: M.D. Raisinghania, Ian Sneddon
  • Vector Analysis: A.R.Vasista, Schaum Series
  • Algebra: Joseph A. Gallian, Shramik Sen Upadhaya
  • Complex Analysis: Schaum Series, J.N. Sharma, Ponnu Swami, G K Ranganath
  • Linear Programming: Shanti Swarup, Kanti Swarup, S D Sharma
  • Numerical Analysis: Jain and Iyengar, K. Shankar Rao, S. S. Sastry
  • Computer Programming: Raja Raman
  • 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

Step 3: Prepare a Study Plan

The study plan is very important for every exam preparation. It plays a key role in the success of getting a good score in the UPSC exam.  Prepare a study plan for the UPSC exam. Make a monthly plan, weekly plan and daily schedule to prepare UPSC Mathematics Optional Paper. Allot the time for exam preparation and set the time for playing, eating, watching TV, and studying.

Daily prepare a few hours and spend at least 8 hours for IAS exam preparation.

UPSC Mathematics Preparation Plan for 3 months

If you have 3 months of preparation time for the UPSC Mains exam, you can prepare 8-9 hours per day.

UPSC Preparation Plan for Mathematics (Before 3 Months)
SubjectAllocation Time
Paper A – Indian Language1 hr daily
Paper B – English1 hr daily
Paper 2 – General Studies 11 hrs. daily
Paper 3 – General Studies 21 hrs. daily
Paper 4 – General Studies 31 hrs. daily
Paper 5 – General Studies 41 hrs. daily
Paper 6 – Mathematics Optional Paper 1 1 hrs. daily
Paper 7 – Mathematics Optional Paper 21 hrs. daily

Step 4: Prepare UPSC Mathematics Important Topics

Mathematics Paper I Important Topics

  1. Paper I being easier compared to Paper-II, all the topics have to be covered in detail.
  2. For Analytical Geometry, read all the solved examples given in the above-mentioned books. Regularly revise particularly skew lines, spheres, cones, and conoids. In many problems you would have to remember how to start the problem i.e. you would have to mug the approach to solve specific problems.
  3. For Calculus, focus more on Calculus of many variables. This is well covered in Malik and Arora. Also many topics of Paper I and Paper II overlap, which can be prepared simultaneously from the above-mentioned book.
  4. In Statics & Dynamics, try to solve all the problems. You can leave very complex problems which are usually given at the end of every chapter.
  5. Make the formula sheet for every chapter and revise it regularly. Otherwise, you might forget many formulas in the exam.
  6. Practice makes perfect. Try solving problems with pen and paper with the book closed, instead of just reading.

Mathematics Paper II Important Topics

  1. Usually, Paper-II is tough for many. Hence if you are able to master it, then you will able to score very high compared to others
  2. Abstract Algebra  Memorize all the theorems. Skip proofs of theorems that are big, particularly in Permutation groups, Cayley’s theorem, PID, Euclidean Domain and UFDs. On the other hand, if you are comfortable with Abstract algebra and want to do it in a detailed manner, I will shortly share various e-books, pdfs, etc.
  3. For Real Analysis,  Focus more on Riemann Integral, Improper Integrals and Series and Sequences of functions.
  4. Linear Programming: I feel books for MBA like JK Sharma are written more clearly that Krishna Series.
  5. Mechanics and Fluid Dynamics: From last year UPSC has started mixing questions from PDE, Numerical Analysis and Fluid & Rigid Dynamics.  Fluid dynamics cover Kinematics of Fluids in Motion, Equations of Motions of Inviscid Fluids, Sources and Sinks, Vortex Motion. No need to see proof of any theorems. From Navier Stokes equations, just try to see only solved examples. For Rigid Dynamics, cover those topics mentioned in the booklist above.

As you know the marks of the optional paper are crucial to deciding your ranking in the final list, you to have to perform exceptionally well in the paper of your choice. Since the rest of the papers are compulsory for all, its only the optional paper that can make or break your fortune. So don’t try to do selective reading and gamble, as there is only one optional paper now.

Final Step: Prepare UPSC Mathematics Previous Question Papers & Practice papers

Download UPSC Mains Mathematics Question Papers. We’ve provided UPSC mains Mathematics Previous Question papers for download in PDF format.

Click Here: UPSC Mains Mathematics Question Papers 2018 Download in pdf

Who should opt for Mathematics?

The students who have studied B.Sc Mathematics/ B. Tech. can take Mathematics as the optional in this examination. In fact, Mathematics is one such option which gives you the advantage of a much higher score than what one could manage with other humanities subjects and thus, the chances of getting the best ranks are much better. However, there is a certain phobia about choosing Mathematics as optional amongst the students. Let us examine this problem through an observational analysis of the situation.

How much time does it take to prepare?

Prepare UPSC Mathematics: 4-5 months, if you study Mathematics 12-15 hours per week. This should be enough. Also, it depends on how much can you recall your graduation concepts.

Ideally, aspirants need 4-5 months to complete the optional subject solely. Here we are giving the best suitable strategies for Mathematics optional for UPSC IAS Mains Exam.

  • Aspirants should have an exhaustive knowledge about the syllabus of Mathematics optional.
  • Your high school maths teacher was right when she reiterated the importance of practice to score well in your maths paper. Although answer writing is essential for any UPSC civil services paper, it gets double the import in the maths paper. Practicing makes you faster in your problem-solving.
  • Avoid silly mistakes like ignoring a ‘+’ or ‘-’ sign, copying numbers wrong, or making simple addition/subtraction mistakes. These can be very costly. Practice till you are perfect.
  • Go through a problem carefully. Write down what is given in the question. Then work out the answer step-by-step.
  • Always understand the question correctly before venturing to work out the solution. Once you start writing the answer and it is incorrect, you lose precious space in the question-answer booklet. And later, even if you figure out you have to rework your answer; you might not be able to because of a space crunch.
  • Always prepare and keep a formula sheet handy with you. This will help you memorize certain formulae that would be required to solve the problems.
  • Always solve mathematical problems with a relaxed mind. Panic can cause confusion and you will end up faring badly in your UPSC optional paper.
  • The essential part of UPSC IAS Exam preparation is solving the previous year’s UPSC Mains questions papers. For Mathematics also aspirants should go through the Previous year question paper to extract an idea about exam patterns, trends, etc.

This article titled “How to Prepare UPSC Mathematics Optional subject – Study Strategy – Suggested by Toppersयूपीएससी गणित विषय gives detailed information about the tips for the preparation of the UPSC 2021 exam for all optional papers. Additional information like Reference books for UPSC Mains, IAS Previous question papers are also given above. Students should follow those tips and prepare well for the exam and download the links for more information about UPSC.