MATHEMATICS Strategy, Booklist and Sample Answers – By Nitish K Rank – 8 and Maths Topper CSE – 2014

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STRATEGY FOR MATHEMATICS OPTIONAL (UPSC CSE MAINS)

Nitish K, IAS (Rank – 8, CSE – 2014) 

His Blog

 

Who can take Mathematics as an optional?

A large number of aspirants called or messaged me saying that they have decided to or wanted to take Maths and asked me to share my strategy. When I asked them why they wanted to choose Maths, most of them told that it was because of good performance of Maths in recent years.

Is Mathematics really performing well in recent years?

On the surface it might look that Maths is doing well. This time around 25-30 candidates have got in the range 290-310. But the problem with Maths optional is scaling. Due to scaling (I don’t know how UPSC does it), a very few number of candidates get high and remaining ones get very low. The ones who get high would have obviously done better than the rest. But due to scaling, difference in marks between the highest and the lowest increases drastically. If the difference in correct attempts is say 60-70, then after scaling the difference becomes 110-120. Thus in Maths, marks are binary. Either you get high or you get low. There are no average marks in Maths, unlike humanities optional. Therefore one should not get attracted to Maths by marks obtained by a few successful candidates. A huge majority would have got very low marks in Maths. Thus Maths is performing well for say around 10% and poor for 90%.

Who are the ones who usually take Maths as an optional?

A large number of those who take Maths as optional come from reputed institutions like IITs, BITS and NITs etc. Due to this the competition is very high.

So back to first question, who can take Maths as an optional?

I feel only those who are very strong in Maths and have genuine interest should take Maths. Unlike humanities optional which can be taken by anybody, Mathematics requires aptitude. As there is huge competition, unless one is at the topmost part of the pyramid, Maths would result in low marks. I have seen many people who take Maths in haste, waste attempts and later change optional.

I was not from any IIT, BITS or NIT. I still went for Maths because I felt I am good in Maths. Mine previous performance in Maths boosted my confidence. I had got 99/100 in 10th (CBSE), 100/100 in both 11th and 12th, 10/10 grade in all four semesters in Engineering Maths. This is not to boast about myself, but to press the point that Maths should be taken only if you have good track record in Maths.

Also given the complexity of topics and huge syllabus, I don’t think any coaching institute will be able to fully cover all the topics. I feel coaching has a limited role and own effort matters more.

 

Paper I

Booklist and Strategy                                                      

Book List 

Paper I

  1. Linear Algebra :
  2. Schaum’s outline on Linear Algebra: this book has explained linear algebra in a far better and simpler manner than Krishna Series. Due to its clarity, it can be read quickly also.
  3. Krishna Series on Matrices
  4. Calculus :
  5. Krishna Series on Differential calculus
  6. Krishna Series on Integral calculus
  7. Mathematical Analysis by Malik and Arora : a must read book for both Paper I and II
  8. Analytical Geometry :
  9. Krishna Series on Analytical Geometry : this book is better than Shantinarayan and has many solved examples
  10. Krishna Series on Analytical Solid Geometry : for Conicoids, Generating Lines
  11. Ordinary Differential Equations:
  12. Ordinary and Partial Differential Equations by MD Raisinghania
  13. Advanced Differential Equations by MD Raisinghania : required for Laplace Transforms (Paper-I) and Boundary value problems (Paper-II)
  14. Dynamics and Statics
  15. Krishna Series on Statics
  16. Krishna Series on Dynamics
  17. Vector Analysis
  18. Krishna Series on Vector Calculus (~ 330 pages)
  19. Schaum’s outline on Vector Analysis

 

                                                            

                                                               Strategy for Paper I:

  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 above mentioned books. Regularly revise particularly skew lines, sphere, cone and conicoids. 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 formula sheet for every chapter and revise it regularly. Otherwise you might forget many formulas in exam.
  6. Practice makes perfect. Try solving problems with pen and paper with book closed, instead of just reading.

 

Paper II :

Booklist and Strategy

Booklist

Paper II

  1. Abstract Algebra: This being my favourite topic, I had referred many books. But as many candidates find this topic tough, I would suggest referring to following books.
  2. Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications)
  3. Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)
  4. Abstract Algebra by Joseph Gallian (optional)
  5. Real Analysis:
  6. Mathematical Analysis by Malik and Arora
  7. Real Analysis by MD Raisinghania
  8. Complex Analysis:
  9. Krishna Series
  10. Linear Programming:
  11. Operations Research by JK Sharma or Kanti Swarup or Krishna Series
  12. Partial Differential Equations:
  13. ODE and PDE by MD Raisinghania
  14. Engineering Maths by Grewal : for boundary value problems
  15. Advanced Differential Equations by M.D Raisinghania (for boundary value problems)
  16. Numerical Analysis and Computer programming:
  17. Numerical Methods by Jain and Iyengar (but questions are not coming from this book from past few years)
  18. Numerical Analysis chapter from Grewal, Engineering Mathematics
  19. For Algorithms and flowcharts, I am having soft copy of a book which I will share.
  20. Mechanics and Fluid Dynamics:
  21. Fluid Dynamics by MD Raisinghania
  22. Krishna Series, Dynamics for Moment of Inertia and D Alembert’s Principle
  23. Krishna Series, Rigid Dynamics for Lagrangian and Hamiltonian. (Unfortunately this is a poorly written book with lot of mistakes. Will try to upload material for these topics)

Strategy for Paper – 2:

  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 is a unique topic. Either you like the topic or you don’t. In first case it will be easy otherwise very tough. I loved the topic and did not read it from exam point of view. If you are finding it tough, I would suggest you to do it from 10 markers point of view. There is no point in spending a lot of time on Abstract Algebra as you won’t be rewarded proportionately. The same time could be used for studying other topics of Maths or GS, which would fetch much more marks. For 10 markers point of view, read books (a) and (b) mentioned above. Memorize all the theorems. Skip proofs of theorems which 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, Malik and Arora is the best. You can supplement it by MD Raisinghania. I felt it is better to leave the proofs. 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. PDE: Even though not mentioned in syllabus, Charpit’s method has to be covered as questions are regularly asked. For Boundary Value problems (heat equation etc.) first read from Grewal. For more types of problems you should refer to book (c) mentioned above in the booklist.
  6. Mechanics and Fluid Dynamics: From last year UPSC has started mixing questions from PDE, Numerical Analysis and Fluid & Rigid Dynamics. Therefore to score high it has become imperative to cover this topic. But the problem is the syllabus has been vaguely defined and there is confusion about which topics are there in syllabus. By analyzing past years question papers. I covered only the following topics. In 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 booklist above.

 

GENERAL OBSERVATIONS:

  1. The fixed space for each question in Mathematics causes lot of disadvantage vis-à-vis other optional, particularly humanities. If you made a mistake while solving a problem and have consumed most of the available space, then despite knowing the correct method you would not have space to rectify your mistake. To tackle this, practice solving problems and write many mock tests. By greater practice you will be able to reduce unforced errors. Also if the problem is new or unfamiliar, I used to briefly solve it in the last page with pencil, later transferring it to main page.
  2. A lot of aspirants face the dilemma of how much time to give for Maths compared to GS. There is no hard and fast rule. I used to give 50% of my time (say around 5 hrs per day) for Maths and 50% for GS. Owing to huge syllabus of Maths, candidates generally tend to neglect GS and Essay. This has to be avoided.
  3. It is very important to complete at least 80% of syllabus before prelims. Also between prelims and mains, try to do both Maths and GS everyday. Don’t lose touch of Maths. The last one month before Mains is very important. During this period keep on revising formulas and practicing problems.
  4. Join Test Series programme between Prelims and Mains. This helps you to complete the syllabus in time, gives you practice, improve your speed and accuracy etc. I had joined Venkanna’s (IMS) test series 4 times (2011,12,13,14) and found them very helpful. I did not attend their classroom coaching and went only for test series programme.

 

My Sample Answer-scripts:

Scan 07-Nov-26014 9.19 pm

Scan 11-Nov-2014 9.26 pm

Scan 20-Oct-2014 9.20 pm

Scan 25-Oct-2014 9.54 pm

Scan 31-Oct-2014 10.22 am

Scan 28-Oct-2014 9.23 pm

I wrote above tests during last year online test series at IMS.

 

Related Article:

My Overall Strategy for Essay, GS, Interview

PS: Mathematics Marks in CSE Mains 2014: Paper – 1 – 173; Paper – 2 – 173

Note from Insights: 

Please visit His Blog (CLICK HERE) for any queries. and ask him there your doubts. Thank you.

 

 

 

 

  • Sri charan Das Goswami

    Thank you Nitish sir….it was really helpful

  • satyajit

    Are bhai itna score 346 great congratulate

    Dear insightsonindia team try to put strategy of Sanskrit Lit

  • anu

    thankyou so much sir for sharing detailed strategy…

  • rautela

    Bro how di u get such score and thank your for posting yr.

  • Shahid Ahmed

    Pls provide law optional book list

  • Patil123

    Hi Nitish,

    Thank you so much!!!!

  • Neelima thandra

    sir can u plzz provide the strategy for sociology optional….?

  • Anand Rai

    pl provide strategy for geography optional

  • Aman Gupta

    i have one query regarding preparation for maths optional.
    As you said that for ODE, prefer MD Raisinghania book, so will i have to read the whole book or read some selected chapters?

  • Jaskaran Singh

    Thanks a lot Nitish sir. As you would be knowing better during your prep that there’s least resources/help available on web for mathematics optional aspirants. This article of yours will be of immense benefit to all us..

  • Santosh Kumar

    Schaum’s outline on Linear Algebra:

    Two books are available
    1.Third edition
    2.Fifth edition
    Which one to buy

    • Any one you can purchase

      • LBSNAA, I’m Coming in 2018

        Hi Ramanasri,

        Are you preparing with maths optional???

  • Fast Track

    hello anna,
    having confusion in buying books.In website of http://krishnaprakashan.com/ for some books there is an abbreviation at the end as (GEN),(U.P.Unified),(Unified).which books are we supposed to buy.

    for eg :

    **Krishna Series on Matrices :
    http://www.krishnaprakashan.com/indetails.asp?id=26

    http://www.krishnaprakashan.com/indetails.asp?id=340

    Please help

    • Balaaji Mahadevan

      Same doubt here. Did someone clarify which of those(Gen/Unified/UP Unified) to buy?

      • Fast Track

        Gen..

  • shiva051

    Hi..
    I have complete set of books for maths optionals. Please let me know if anyone is in need. I can give it in reasonable price.

    • Fast Track

      Hello sir,
      I am interested in buying the same.here is my mob no : 8082388908.pls give a miss call so that I can call you back again.

    • Raghavendra Gbtv

      I need books.my number is 9990362315.
      Pls Give me ur number.

  • Bhaskar

    Show that 1+i is prime element in the ring R of Gaussian integers
    http://thesolutionslab.blogspot.com/2016/02/show-that-1i-is-prime-element-in-ring-r.html

  • It’s really great that you were able to share this kind of information for those people who might really need to practice their skills in mathematics. Thus, they could potentially promote another reason to learn that would satisfy their learning and gain another knowledge about math.

  • Ramanasri Mula

    For more information visit website mathematicsoptional.com

  • Kayana Devi K

    Hello Friends ,
    I’m from North-earth,and i’m done M.Sc in Maths.
    I Want to Prepare for ias with Maths Optional.
    some person told me DIAS & IMS is proving for this.
    But i confused for this which is better for me.
    Please Suggest me where can i join.

    One of my friend join DIAS,and he told me Vajpayee sir is good teacher,
    he taught Fluid,Dynamics,Mechanics,etc. is just like a megic.

    Now I’m Very Confused,where can i Join.
    Please tell me………..Please
    thanks …………Kayana
    [email protected].

    • Priyatam bolisetty

      DIAS is good but don’t expect them to complete the portion.
      or pay them in installments which is better and the best decision i’ve made considering how they turned out.
      they don’t have any coaching staff for maths except Vajpayee so the topics which he won’t be teaching he brings someone else who had been preparing for more than 2-3years or someone from DU.
      but IMS is plain worse but the student atmosphere there is good which is not available in DIAS as my batch had only 10 students and 5 are regular and the rest module wise joiners.

      so choose at your own descretion.

  • kalom lego

    hello i m from northeast india,,,,,,,im confusing that is coaching is benefit for upsc maths optinal,,or it will better in self study,,,,,