Strategy for Mathematics « Kashish Mittal

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Strategy for Mathematics May 28, 2011 by Kashish Mittal I chose Mathematics and Physics as optional subjects as I had a considerable exposure to the topics in their syllabi from my study since classes +1, +2 upto college level. The books I referred for Mathematics are as follows: Paper I 1. Linear Algebra: Linear Algebra by Vasishtha and Sharma (Krishna Series) Matrices by Vasishtha and Vasishtha (Krishna Series) 2. Calculus: Differential Calculus by Shanti Narayan (S. Chand) Integral Calculus by Shanti Narayan (S. Chand) A Course of Mathematical Analysis by Shanti Narayan (S. Chand) 3. Analytic Geometry: Analytical Solid Geometry by Shanti Narayan (S. Chand) 4. Ordinary Differential Equations: Ordinary and Partial Differential Equations by M.D. Raisinghania (S. Chand) Laplace Transforms: Brilliant Tutorials Advanced Engineering Mathematics by Erwin Kreyszig 5. Statics: Statics (Krishna Series) Dynamics: Dynamics (Krishna Series) 6. Vector Analysis: kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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Vector Calculus (Krishna Series) Curves in Space: Calculus by Thomas & Finney Paper II 1. Algebra: Abstract Algebra by Khanna and Bhambri Topics in Algebra by I. N. Herstein 2. Real Analysis: Elements of Real Analysis by MD Raisinghania (S. Chand) 3. Complex Analysis: Functions of a Complex Variable (Krishna Series) 4. Linear Programming: Linear Programming (Krishna Series) 5. Partial Differential Equations: Ordinary and Partial Differential Equations by M.D. Raisinghania (S. Chand) Boundary Value Problems: Advanced Engineering Mathematics by Erwin Kreyszig 6. Numerical Analysis and Computer Programming: Numerical Methods by Jain, Jain and Iynger 7. Mechanics: Rigid Dynamics Volume I & II (Krishna Series) Fluid Dynamics: M.D. Raisinghania (S. Chand) [Due to some time constraint, I studied Abstract Algebra and Real Analysis mostly from 12 markers point of view. However, looking back, I think I could (& should) have done them thoroughly as well.] While studying these books I basically attempted the solved examples. In the first cycle of my study, I read selective solved examples and tried to register them in my mind, and solved some of them on my own. In the second cycle of the syllabus I properly attempted the solved examples on paper, trying my best to maintain the quality and language of the answers as close to the solutions in the books. The way of writing a solution is very important in the Mathematics paper, and can be best learnt from the solved examples themselves. After that I also attempted questions from the past 15-20 years’ papers. The answers/solutions can be verified from the Brilliant Tutorials and the books mentioned above. This exercise helps in giving an idea as to what is the kind and level of questions asked in the exam, and may also prove beneficial in case some questions in the exam come on similar lines as in the past. Finally, I also made summary sheets for every unit/topic (~ 2 pages per unit) in which I listed the important results/formulae/theorems/tips which can be gone through a day before the exam. This is helpful as it can give you a holistic & quick revision of the entire syllabus before the exam. In the exam, my correct attempt was ~ 258 in Paper I and ~ 260 in Paper II. My score in the exam kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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was 207 in Paper I and 198in Paper II. I think the accuracy in the Mathematics paper is extremely necessary, as candidates are penalised heavily for any errors in the solution/answer.

Posted in Uncategorized | 104 Comments

104 Responses

1. on May 29, 2011 at 3:57 am | Reply ankit hey congrats..i read in newspaper that you started preparing in the last year itself and cracked in your first attempt.can you please tell how much time is required for serious preparation for an average guy?

2. on May 30, 2011 at 8:17 am | Reply Sunny Any coaching you undertook for Mathematics? When did you start preparing this optional and how much time did you put in for Mathematics every day? I will be appearing for CSE 2012 and yet to start my preparations for this optional. Thank You

3. on May 31, 2011 at 8:08 am | Reply Hi, I have two questions:

Sunny

1) From where all these books can be easily available? I am not able to find these books even at flipkart. kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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2) If possible, can you mention the approximate prices of these books. I just checked ‘Abstract Algebra’ by Khanna and Bhambri online and the fact that it costs Rs. 890 put me into doubt if it is the same book that you have mentioned. Please check this link: http://www.flipkart.com/b/books/course-abstract-algebra-vijay-khannabook-0706983025?_l=CJHVEqJO3veuHytbACc9dw–&_r=shpuTL8%20JmwfVfTLqGuK2w– &ref=157fcb45-c9be-493e-8ab1-77e76e9425ee&pid=k4w3fbfyfe Thanks

4. on May 31, 2011 at 11:28 am | Reply Kashish Mittal @ankit: I started preparing in the beginning of my last year of college, i.e. one year before prelims. During this time I had to manage my college curriculum as well. However, after prelims, I devoted the next available 5-6 months fully for mains study ( ~ 10 hours everyday) as I had finished my degree in May,2010. In general, I think that if a person starts full fledged preparation around 1 year before prelims, it should be good enough to clear the exam.

5. on May 31, 2011 at 11:54 am | Reply Kashish Mittal @Sunny: I used to take up some elective courses of Mathematics at IIT, which helped me eventually in covering up the syllabus fast. Also, I took coaching for selected topics in Aug-Sept, 2010 (Complex Numbers, Calculus, Differential Equations) from DIAS Institute, Jia Sarai. I started the basic content of my Maths preparation on my own after prelims, using the above mentioned books. Regarding books, I bought them from Jawahar Book Depot, Ber Sarai (Behind IIT Delhi), Delhi [You can get their contact details at http://www.jawahar-book-centre.com/%5D. It may be difficult to order these books online, so I would suggest buying from any good shop. Also, the link you gave for Khanna and Bhambari is perhaps a different version/edition. The book i am referring to is available at http://www.flipkart.com/b/books/course-abstract-algebrakhanna-vijay-book-8125919112?_l=TD6zlqyt5zvAWw1GJEtIqA– &_r=oluRoWbXdQxMkcyDwKkIVQ–

6. on May 31, 2011 at 10:57 pm | Reply was the coaching at DIAS good. kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

nitish

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Also can we join there for only selected topics in maths?? did you complete all the topics entirely or selectively thank you nitish

7. on May 31, 2011 at 11:04 pm | Reply nitish Statistical analysis of CSE 2010 result can be found here: https://docs.google.com/document/d/1JsSCzPGbyqDgM7zNppdVMQoD0steVFciT2GZ8TRPJk/edit?hl=en&pli=1#

8. on May 31, 2011 at 11:35 pm | Reply ankit @kashish: thanks Hey some people do say that if one is not prepared for mains before prelims then they should not give the attempt that year. How far you agree?

9. on June 2, 2011 at 5:13 am | Reply Raj Congrats Kashish ………I have a few questions 1)Do we require coaching(from DIAS particularly). 2)Please write strategy for Physics also. 3)Elaborate more on how to write answers(particularly in Maths and Physics). Whats the basic difference when writing a University exam and IAS in terms of answering a question(Maths and Physics).

10. on June 2, 2011 at 11:11 am | Reply Kashish Mittal @nitish: You can go for selected topics at DIAS. The coaching for the topics I did was helpful, but I did not have time for doing more topics. Anyways, if you do not have time, you can manage all topics on your own itself, as the books are quite helpful and sufficient. I did all topics completely, except for Abstract Algebra and Real Analysis, which I did from 12 markers point of view. But as I have mentioned, even they can be done completely.

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Thanks for the statistical optionals data for CSE, 2010.

11. on June 2, 2011 at 11:12 am | Reply Kashish Mittal @ankit: If one has not even completed one Optional once before Prelims, I think it is better to appear next time.

12. on June 2, 2011 at 11:26 am | Reply Kashish Mittal @Raj: Coaching of those topics did help me, but if you put in enough time, you can cover the syllabus yourself just by studying the books mentioned above thoroughly. I will write strategy for Physics shortly. While attempting an answer in Maths, I used to directly solve the problem, without writing any information/details which were not asked. However, care must be taken to mention all steps and give the necessary explanation for the steps (as is given in the solved examples). It is also helpful if you label the equations by equation numbers and use these equation numbers whenever you have to operate on these equations (e.g., dividing eq. 2 by eq. 4, or differentiating equation 3 w.r.t x, etc.). The answer must be technically complete, but there is no need to write any unnecessary detail. I think if you keep above in mind, you will do well in both University exams and the UPSC exam.

13. on June 3, 2011 at 7:28 am | Reply nitish do you know how is IMS coaching center (by venkanna k) for maths as DIAS is far from rajendra nagar. Also are there any better coaching for maths in rajendra nagar area. As I am from south india,i dont know much about delhi,please guide me Thank you nitish k

14. on June 3, 2011 at 10:04 am | Reply Barnava Sir, is solving the solved examples from Shanti Narayan’s Analytical Solid Geometry enough to attempt the questions set from geometry? Can I follow B.S. Grewal’s Engg. Maths for Laplace transformation? I have’nt followed Kreyszig. kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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15. on June 4, 2011 at 2:48 am | Reply Kashish Mittal @nitish: I don’t know about any other coaching centers for maths in Delhi or elsewhere. However, even if you are not accessible to a good coaching center but do your books thoroughly, you can still score very well in the exam.

on June 4, 2011 at 3:16 am | Reply Kashish Mittal @Barnava: Yes, Shanti Narayan’s Analytical Solid Geometry is enough to attempt any question of Analytic Geometry. I haven’t been through B.S.Grewal’s book. Though Kreyszig + Brilliant Tutorials are good for Laplace Transformations, any book which contains the required theory and enough problems should be sufficient.

16. on June 10, 2011 at 10:36 am | Reply Sunny Hi, Can you tell me how did you attempt the following question in this years mains paper 2 section B. The question is : Determine whether the set S={e1-e2,e2-e3,e3-e4,………….,en-e1} is a set of linearly independent vectors or not. I just want to know the way of writing. Thank You

17. on June 10, 2011 at 3:40 pm | Reply Kashish Mittal @Sunny: In order to prove that a given set of vectors say a_1, a_2, ….a_n are linearly dependent, we just have to show the existence of scalars c_i (1<= i <= n), not all zero, such that the sum c_1.a_1 + c_2.a_2 + ….+c_n.a_n equals zero. So I wrote the above statement and showed the existence of c_i's which make the above sum zero, i.e. c_1 = c_2 = c_3 = … = c_n = 1

18. on June 11, 2011 at 5:26 am | Reply Sunny Let S={e1-e2,e2-e3,e3-e4,……………,en-e1} be a subset of a vector space V3(R). kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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and let c1,c2,c3……cn be the n scalars belonging to R. Clearly we have, e1-e2+e2-e3+e3-e4+………………….+en-e1=0 (as positives and negatives are cancelling down) which implies (e1-e2)+(e2-e3)+………………..+(en-e1)=0 which implies 1.(e1-e2)+1.(e2-e3)+ ………….. +1.(en-e1)=0 which implies c1.(e1-e2)+c2.(e2-e3)+ ………….. +cn.(en-e1)=0 where c1=c2=c3========cn=1 Hence, there exist scalars not all zero but making the linear combination of the given vectors zero. So, the given set of vectors is not linearly independent. Is this solution correct? I have doubt regarding what should we assume the e’s i.e. e1,e2 etc. to be. Can we say that e_i, i belongs to [1,n] ?? or shall we approach via a lengthier method by assuming e_i’s as basis vectors which are linearly independent. e,g, e1=(1,0,0,0,……. ), e2= (0,1,0,0,0,…….) ….. and so on and then getting the following equations on using the linear combination equation with constants c_i’s: c1-cn=0 c2-c1=0…………………….. c(n-2)-c(n-1)=0 Since we have n variables but n-1 equations so infinite non zero solutions exist. Hence linearly dependent. Given that the question was of 20 marks which approach should have been followed. Although it is difficult for one to proceed via 2nd method under examination conditions. Thanks a lot

19. on June 11, 2011 at 5:29 am | Reply Sunny Few mistakes that i have committed above are : 1) It is Vn(R) and not V3(R) 2) I meant to say that can we assume e_i’s as real numbers, so that we can approach via 1st method.

20. on June 11, 2011 at 6:50 am | Reply Kashish Mittal @Sunny: Your first solution above is correct (with the Vn(R) correction). You do not need to assume anything else about the e_i’s. Also, this question was for 10 and not 20 marks (as it was one out of two sub parts of the 20 marker). kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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21. on June 18, 2011 at 3:38 am | Reply raj Where Can we get Last 10 year solved papers of maths and physics(mains)?

22. on June 21, 2011 at 6:31 am | Reply Kashish Mittal @raj: I got the UNSOLVED papers from a shop in Rajendra Nagar. I think any good shop which deals with books on civil services have these papers. To get the solutions, I referred to Brilliant Tutorials which I received through correspondence.

23. on June 22, 2011 at 7:10 am | Reply Akanshu Govil Hi Kashish, Congrats on your success and thanks a lot for this blog of yours. I want to know what exactly you mean when you say that you did a particular topic from 12 marker point of view ? And how much do you think is sufficient for the complete preparation of Mathematics course and how will you rate the Brilliants’ material in relevance to the examination ? Thanks.

24. on June 26, 2011 at 1:39 am | Reply @Akanshu: Thank you.

Kashish Mittal

Doing a topic from 12 marker point of view meant that I left some subsections which I found very time consuming (Certain theorems/theorem proofs/etc.) The 12 marks questions are generally not very lengthy and usually test the basics of a topic. You can get a better idea if you go through the past 10-15 year papers and have a look at the 12 markers and the 20/30 marker questions. The sufficient time for complete prep of Mathematics depends from person to person. I basically started the prep after Prelims, but I did have background knowledge of some topics beforehand. I used Brilliant material only to check past year papers’ answers, and to cover a few topics which were not available in books.


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25. on June 28, 2011 at 2:27 am | Reply vinay tiwari Respected sir, kudos to ur success……..i just want to know the link to UPSC website frm where i can get the whole detailed syllabus of mathematics as it ll b more authentic………and d link to preliminry knwldge which calculator allow,,,which chart allow?????

26. on June 28, 2011 at 8:17 am | Reply Raj Thanks a lot again…………………I just wanted to ask what should be revise from +1,+2 which can be helpful to us in corroborating to your above mentioned strategy(also mention books if required)

27. on June 29, 2011 at 9:29 am | Reply Raj Just give a brief outline as to which derivations we have to do and which we have to leave…………..(maths and physics)

28. on June 29, 2011 at 12:08 pm | Reply @vinay: http://www.upsc.gov.in

Kashish Mittal

You can go to the examination section and thereafter in notifications. All syllabi, instructions are available there.

29. on June 29, 2011 at 12:17 pm | Reply Kashish Mittal @Raj: There is no need to go through +1,+2 books in general. The ones I have mentioned above are sufficient for UPSC and have all necessary background from scratch. Regarding derivations, you can best judge that by going through the past year papers of any particular topic and that can give you a good idea.

30. on June 29, 2011 at 1:00 pm | Reply vinay tiwari Sir….i attended the brief session by you held at prof vajpayee class….this is my final year at ITBHU(civil engg)…..before seeing the statistical analysis of CSE 2010…i was choosing maths & civil engg…as i have also done quite a bit exercises in both subjects…..but after going through kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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the analysis i got to know this year only a single person make to CSE taking civil engg as an optional….now i m in a great deadlock..taking civil engg (huge syllabus) will b just beneficial to me frm IES (point of view)……if so otherwise i m also comfortable with physics…..guide me accordingly….sir is it like this that it is predecided to select how many students taking particular optional….or after the complete process they thought of only 1 civil engg worthy of civil services??

31. on July 2, 2011 at 11:42 pm | Reply Hi Kashish, congrats on your success…

rahul

I am unable to find some books u mentiond in my town, so on searching flipkart found these links. Can u plzz verify are these the same books u mentiond…. (Linear Algebra) http://www.flipkart.com/books/rbkcy94t6nyzy25z? _l=CJHVEqJO3veuHytbACc9dw–&_r=Tv13xWKKedDxaNZRQqnx3g–&ref=fafe5d22-35c34f26-86de-a668ee3e748f&pid=rbkcy94t6nyzy25z (Vector Calculus) http://www.flipkart.com/books/8182830893 (Matrices) http://www.flipkart.com/books/rbkcy94typtvqthv (Linear Programming) http://www.flipkart.com/books/rbkcy94t3b4kee7y

on July 14, 2011 at 4:41 am | Reply prajwal hi rahul, can u plz upload the flipkart sites of the krishna series books like, Statics, Dynamics.

32. on July 5, 2011 at 2:34 am | Reply prajwal sir…is it sufficient to prepare only till 8 chapters for O.D.E in the mentioned book(M.D.Raisinghania)??

33. on July 6, 2011 at 3:54 am | Reply Kashish Mittal @vinay: Physics is a scoring subject and is also neither very lengthy nor very difficult to prepare. On the other hand, as far as I have heard, Civil engg. is a lengthy subject and preparing it along with Maths may be tough. Also, if you want to prepare for the CSE, then you should focus only on this exam and not think too much about others (IES, etc.) as that may divert your CSE kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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preparation. However, this is just my opinion – if you are confident about civil engg., you may carry on and take it up. I don’t think it is pre-decided on how many students to take in an optional, though the approximate percentage of selected students of each optional (w.r.t total students who took the optional) is roughly the same. Also, you should remember that the fact that a particular candidate is selected or not doesn’t depend on only one optional but his/her complete performance in all subjects.

34. on July 6, 2011 at 3:57 am | Reply @rahul: Thank you.

Kashish Mittal

The four books of which you have given the links are the same as I mentioned. However for the first book, you may do only the linear algebra part and skip abstract algebra (which is to be covered from Khanna and Bhambri).

35. on July 6, 2011 at 4:00 am | Reply Kashish Mittal @prajwal: Yes, as far as I remember. As I don’t have access to the book for now, can you let me know what are chapter names after chapter 8 in ODE section?

36. on July 6, 2011 at 11:34 am | Reply sir…the chapter names are: 9.exact D.Es and eqns of special forms 10.linear D.Es of second order 11.applications of D.Es

prajwal

37. on July 6, 2011 at 7:26 pm | Reply Kapil Do we need to cover Quadratic Forms under the Matrices Unit ? Although the topic had been removed from the syllabus since 2009 onwards yet the UPSC has been putting up questions from the same old syllabus. This year they had asked a question on conformal mapping/bilinear transformations in the complex analysis section which had been deleted from the latest syllabus. Similarly they had asked the method of undetermined coefficient in ODE which is not explicitly mentioned in the syllabus. How to tackle such problems ? kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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38. on July 7, 2011 at 12:38 am | Reply Nitish Kumar Congrats sir for your success…… Sir i m also having same optionals Physics and Maths…….sir i have purchased brilliant tutorial material (xerox) for maths from Jawahar book centre (ber sarai)……is it the same material which you have got through correspondence…..i mean both r same or not…….and can you pls post some of your sample answers for maths and physics………….and how can i contact kunal silku sir….actually i want some inputs regarding answer writing for physics……. Thanks in advance

39. on July 12, 2011 at 1:48 pm | Reply hello sir… congrates on your huge success!!!!

nandan

1. Is it necessary to study “plane sections of conicoid and confocal conicoid” in analytic geometry?? 2. How much time it should take to complete “abstract algebra” if some one is studying it for the first time?? thank you in advance

40. on July 12, 2011 at 9:03 pm | Reply Vinay Gowda Many congratulations for your stupendous success. Can you list the chapters in statics of krishna series which is there in syllabus? Specifically the last two, the attraction and potential? Also, one more humble request, if you could spare some time, it would be a lot helpful it you mention the chapters name also in the books mentioned.

41. on July 15, 2011 at 3:27 pm | Reply vinay tiwari @ALL—–anyone here, please tell me the chapters of partial differential equations to be covered from raisinghania…as it is little confusing for me……

42. on July 17, 2011 at 2:46 pm | Reply Jagadamba Hi Kashish………..again hearty congratulations for your achievement and thanks for providing key guidance to all.Please tell me how much should I read complex integration and calculus of kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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residues in Complex Analysis?As I am reading from Krishna Series and earlier in my graduation I read from Schaum Series,that has few variety of problems.Do I need to learn abc of conformal mappings(not mentioned in syllabus)? Thank you very much

43. on July 20, 2011 at 1:15 am | Reply Kashish Mittal @prajwal: You have to do chapter 10. Linear DEs of second order.

44. on July 20, 2011 at 1:21 am | Reply Kashish Mittal @Kapil: Though ideally such questions should not be asked (whose topics have been removed from syllabus), but you are right – every year one or two such questions do crop up. I personally did not cover Quadratic forms/conformal mappings/undetermined coefficients, so I could not attempt the questions on conformal mappings and undetermined coefficients. I would advise you to cover the present syllabus fully first. Then in your second cycle you may go through such topics which were there in the old syllabus if you have time. But basically if you have prepared the present syllabus well, there is enough choice in the exam for you to attempt fully.

45. on July 20, 2011 at 1:26 am | Reply Kashish Mittal @Nitish: The brilliant material available in Ber Sarai is basically the same, but it may be just a couple of years older. So it may not have answers to the latest UPSC papers. I will try to post answers of Maths/Physics but cannot give my word for that presently. But basically the way of writing for Maths/Physics is on the lines of the derivations/solved examples in books and Vajpayee Sir’s notes (Physics). You can contact Kunal Silku over facebook at: https://www.facebook.com/kunal.silku

46. on July 20, 2011 at 1:33 am | Reply @Nandan: Thanks for your wishes.

Kashish Mittal

I do not have access to my books as of now, but as far as I remember, you do have to cover some sections (refer syllabus and past year papers) of the chapter on “Plane sections of conicoids and confocal conicoids”. kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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It depends on person to person on how much time he/she takes on a topic, e.g. abstract algebra. I had studied it in college before so I gave the first cycle of this topic in 3-4 days (I skipped some tougher portions on Rings in the first cycle). For a person studying abstract algebra for the first time, it may take longer (a week or so), but I would advise skipping tougher portions in the first go.

47. on July 20, 2011 at 1:38 am | Reply Kashish Mittal @Vinay Gowda, Vinay Tiwari: I am sorry, I don’t have access to my books as of now. But I remember that for Statics in particular, no chapter in the book has to be done fully in the book. However some portions have to be done from almost all the chapters – the best way to make sure is to go through the syllabus and past year problems + Brilliant series to make sure what portion of a chapter needs to be done. This technique is useful for all topics – be it statics, PDE, or any other topic.

48. on July 20, 2011 at 1:42 am | Reply Kashish Mittal @Jagdamba: The solved problems of Krishna Series for Complex Integration and Calculus of Residues are enough. However if you have been using Schaum Series before, you can cover that too, side by side. Conformal mappings had been removed from syllabus, but a question on it was asked this time. So I would suggest that you may go through this section if you have some time to spare.

49. on July 24, 2011 at 4:43 am | Reply SriNarayanan Thanganadar Hi Kashish, Can you confirm if the [Complex Analysis: Functions of a Complex Variable (Krishna Series)] book belongs to Krishna series or S Chand . Only this book http://www.flipkart.com/books/8121906393?_l=CJHVEqJO3veuHytbACc9dw– &_r=NvY0X%20JQLxIe8Y84Gf4vFg–&ref=3dbfd7cb-4e42-4a69-ae3a22cc23bf5afd&pid=ju23fp94eb is available , but it is from S-Chand and not Kirshna.

on July 27, 2011 at 7:20 pm | Reply Kashish Mittal The book I studied was by Krishna Series.


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50. on July 26, 2011 at 6:09 am | Reply Hi,

sunny

Do we need to remember the proofs of almost all the theorems in Real Analysis or can we just concentrate on the problems ?? e.g. The proof of Bolzano – Weierstrass theorem was once asked in UPSC mains. Thank You

on July 27, 2011 at 7:30 pm | Reply Kashish Mittal There are some proofs which you do need to remember in Real Analysis. For this, I had consulted the blog by Prakash Rajpurohit (AIR-2, CSE 2009). Here’s the link to that particular page: http://prakashrajpurohit.wordpress.com/2010/06/13/mathematics-part-2/

51. on July 27, 2011 at 3:58 am | Reply vinay tiwari HIIIII Sir…… sir,recently i have completed the ODE & partial DE…as it is my self study during the last topic method of characteristics i was feeling quiet uncomfortable from the point of view of getting feel of theory like what is characteristics strip? elementary cone? bt still i am able to solve the examples as well last years problems….should we write the physical interpretation in this method and also in solutions of laplace eqns?….should i still work on the topics else jump to new one? also the link http://thinking-alike.blogspot.com/2008/11/strategy-for-mathematics-as-optional-in.html little confused me the authenticity of raisinghania as this guy talked about some Schaum series books by M R Spiegel saying the importance of applied approach to differential eqns. and also it will be time saving for me if you or any one here will tell me the chapters to be covered from course of mathematical analysis (shanti narayan) and elements of real analysis (RAIsinghania) as i am going to start either of the two. thanking you vinay tiwari part IV (civil) ITBHU


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on July 27, 2011 at 7:43 pm | Reply Kashish Mittal I read the physical interpretation and derivation of method of characteristics, but found it too involved – so i just structured the steps in my mind to solve a given question by this method (Just as you have written, I solved the examples/past problems on my own, and this is pretty much what you need to do). There is no need to remember or write the physical interpretation of method of characteristics. You just need to solve the question fully and get the correct answer. For solutions of laplace eqns the physical interpretation is relatively easy, so u can read it. However you don’t need to mention it in an answer unless it is asked. Raisinghania’s book for Diff Eqns. is very good and you will be able to do every question in the exam from this topic if you do the book well. I am sorry, I don’t have access to my books as of now but you can consult the syllabus plus past year papers & Brilliants to see what chapters you need to do from a particular book. For the books you have mentioned (Calculus & Real Analysis), Prakash Rajpurohit (AIR-2, CSE 2009) has mentioned the chapters in his blog at this particular page: http://prakashrajpurohit.wordpress.com/2010/06/13/mathematics-part-2/

52. on July 27, 2011 at 11:55 am | Reply Hi Kashish,

Sashi Kanth

Congrats on your success! I wanted to ask you how much of a time constraint is there in the exam? Do you get time to think on the questions?

on July 27, 2011 at 7:03 pm | Reply Kashish Mittal Thanks. You can get a good idea of the time constraint by taking a good look at a previous year paper. In particular, mathematics paper is generally lengthy. For example for a 20 marks question, you have (20/300)x180 = 12 mins. So ideally one should complete the question in about 8-9 mins (including thinking time) and give 3-4 mins to revise the answer.

53. on July 29, 2011 at 10:41 am | Reply vinay tiwari sir can i do vector analysis from erwin kreyszig engg mathematics…………bt it seems that it doesnt have sufficient practise problems?? kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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because krishna series is not available at flipkart…..

on July 31, 2011 at 9:00 pm | Reply Kashish Mittal You can go to some good book store and try to get the book from there. Otherwise, you can use Briliant’s material or the past year papers to get more questions.

54. on August 1, 2011 at 12:07 am | Reply vinay tiwari same with shanti narayan sir….it also has very few solved examples…..but conceptual knowledge is good…..so i am referring to BT for examples…..thank you…

55. on August 1, 2011 at 12:47 am | Reply Hi Kashish,

Sashi Kanth

I wanted to get some practise problems to solve in test like conditions. The problems in the books immediately follow the relevant chapters so I was looking for some test papers etc. I called up Jawahar book store and they said that they don’t keep any xeroxes of test papers. Do you know any place in Delhi where I could get test series / tutorial papers of maths of DIAS / DIPS? Thanks a lot for all the help!

on August 11, 2011 at 8:18 pm | Reply Kashish Mittal I used to solve basically the past year papers only to do problems in test like conditions. Otherwise I didn’t get any coaching test papers. In case you do want them, you can consult any student of DIAS/DIPS from Jia Sarai, Delhi, and get them xeroxed.

56. on August 3, 2011 at 12:15 am | Reply vinay tiwari sir during the final year of the college have you kept yourself completely isolated from the placement programs…….or have tried the least possible… because since i came college in last month 25june to 23 july days i have done quiet good job…..ODE & PDE….as well some NCERT……. but now as the placement session begins..since last week…..i am not able to devote that much of time…


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on August 11, 2011 at 8:20 pm | Reply Kashish Mittal I did not sit for the placement session as it was quite time consuming and required extra preparation. Also, if you really want to write the UPSC exam dedicatedly, it is better that you do it with full focus and do not have extra burdens at hand.

57. on August 3, 2011 at 12:02 pm | Reply MR can you explain the how to write the solution to question no 1(d) of paper 2 of mains maths 2010.

on August 11, 2011 at 8:31 pm | Reply Kashish Mittal It is a standard question of monotonic sequences. First you show that the sequence is bounded below ( as x_n is a positive square root therefore x_n > 0 for all n) Then you prove by Mathematical Induction that the sequence is monotonically decreasing. (ix_(n+1) < x_n for all n) From the above two, you get that the sequence converges to a finite limit, say l. Taking limit both sides in the equation, you get the answer.

on August 12, 2011 at 10:33 am MR I thought the last step(taking limits) was sufficient to show what is asked. But it is necessary to prove the first two statements also; because what is asked is only to show that the sequence converge to ….. Please suggest

on August 12, 2011 at 11:17 am Kashish Mittal The last step is not sufficient to show what is asked. The first two statements are necessary. This is because in the last step you cannot assume that the sequence x_n converges. You first have to show that it converges, to some finite limit (say, l) and only then can you take limits both sides.


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58. on August 5, 2011 at 12:40 pm | Reply Hi,

Sunny

Could you please tell me if ‘Infinite Product of Series’ – Real Analysis, is there in the syllabus? This topic is not covered in the Real Analysis book i.e. ‘Elements of Real Analysis by M.D. Raisinghania’. What is given in the book is only ‘Cauchy’s Product of Infinite Series’ but at my maths coaching class, i was taught a number of other things regarding infinite products which i feel are not there in the syllabus. Thank You

on August 11, 2011 at 8:59 pm | Reply Kashish Mittal Infinite Product of Series is not mentioned directly in the syllabus, so I wouldn’t recommend spending a lot of time on that. If you do find time, then you can go through those coaching notes but only after you have done all the topics which are there in the syllabus. (You can leave such doubtful topics for the end – do them if there’s time left.)

59. on August 6, 2011 at 1:12 am | Reply ajay Hello Kashish, could you please mention the chapter we need to do in Rigid Dynamics Vol 1 and 2, Krishna publication. I am new in preparation and could not make out the relevent portion of the book from the syylabus. the chapters are Rigid Dynamics Vol1: chapter 0: Moment of Inertia Chapter 1: D’Alembert Principle Chapter 2: Motion about a fixed axis Chapter 3: Motion in two Dimensions (under finite forces) Chapter 4: Motion in two Dimensions (under impulsive forces) Chapter 5: Conservation of Momentum and Energy Chapter 6: Initial Motion Chapter 7: Lagrange’s equations of motion, small oscillation, normal coordinate Chapter 8: Euler Dynamical equations Chapter 9: Hamiltonian Formation and Variational Principles Chapter 10: Motion of Top Please mention which chapter needs to be covered fully. thank you


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60. on August 6, 2011 at 1:17 am | Reply ajay For Rigid Dynamics Vol 2: Chapter 1: Mechanics of a particle Chapter 2: Motion of a system of particles Chapter 3: Lagrangian Dynamics Chapter 4: Rigid body motion (including motion in three dimension) Chapter 5: Theory of small oscillation Chapter 6: Hamiltonian formulation, transformation and haimilton-jacobi theory Chapter 7: Motion of spinning tops and gyroscope Chapter 8: Mechanics of Continuous media thanks

61. on August 6, 2011 at 8:09 am | Reply snoopy namaskara sir, i am planning to write IFos too next year.i heard there is no scaling in that exam because all are science optionals and so by default there is a level playing field.is it true?also i am not from an IIT/NIT and from an ordinary engineering college in karnataka.most kannadigas prefer the arts optionals and very few take maths/physics.do guys from the local institutes stand a chance?

on August 11, 2011 at 9:35 pm | Reply Kashish Mittal There are many candidates from engg. colleges other than IITs/NITs who clear the UPSC Civil Services and IFoS exams. The only thing that is required is full dedication and a desire to succeed. Also, as IFoS subjects are mostly science based, so definitely there is a more level playing field than Civil Services exam. Having said that, even in Civil Services exam it is given extreme care that there is a level playing field across all subjects.

62. on August 6, 2011 at 2:06 pm | Reply snoopy are books by western authors good for indian exams?herstein and kreyzig may have great theory but for the kind of exams we have aren’t the books by indian authors better?beyond krishna/s chand is there no other series around?

on August 11, 2011 at 9:38 pm | Reply Kashish Mittal This depends from topic to topic and book to book. The books I have mentioned above are kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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very good in terms of theory and problem coverage as far as the UPSC exam is concerned. Therefore, in my opinion you do not need to go beyond and look for other books and series.

on August 11, 2011 at 10:06 pm snoopy thanks a lot mate.i gather that you are 21-22 and this is your first attempt.thanks for the encouragement and good luck to you!

on August 12, 2011 at 11:15 am Thanks for your wishes.

Kashish Mittal

63. on August 9, 2011 at 5:18 am | Reply Aswini Kumar Dear Sir Hope u r fine by his grace.is there any scaling for maths optional in mains exam.

on August 11, 2011 at 9:15 pm | Reply Kashish Mittal If you are one of the top scorers in Maths then the scaling is quite low. However, it is generally seen that if you don’t do that well, then you are more affected by scaling. Having said that, Maths is still a good optional to take and one can score really well in Maths (compared to other subjects) if you have prepared it sufficiently.

64. on August 11, 2011 at 8:25 am | Reply sameer does anyone know how to solve the very first question of paper 1 in 2010 maths paper (ias) . . the problem regarding eigen values . . . problem 1(a) . .i.e. ??

65. on August 13, 2011 at 6:48 am | Reply ajay hello kashish, could u plz answer my question regarding what to read in rigid dynamics books of krishna publication i already mentioned the name of the chapter in my previous post thanks


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66. on August 17, 2011 at 1:21 am | Reply Archana Aggarwal Can u please tell me as to which of the following chapters are to be prepared from S.Chand’s Analytical Solid Geometry book : 1. Conicoids 2. Plane sections of conicoids 3. Generating lines of conicoids 4. General equation of the second degree 5. Confocal Conicoids I will be thankful for ur reply and guidance.


K. Dinesh Kumar

Congrates for ur superb success. Can u pls provide a breif solution for the question 1(a) in Maths 2010 paper – I ? Thanks in advance.


Aravinda HS

I would be appearing for 2011 UPSC mains & have maths as one of my optionals. Given that there is hardly 2 months, I request your advice on which coaching institute’s material would be able to provide me – complete course material & also questions & answers for previous year papers (previous 5 years atleast) & also provide me enough solved examples & also practice questions/test series? Sorry, I am here asking one single source for everything on maths but due to serious time constraints, I definitely would not be able to go through multiple books in this short time, hence requesting your advice. Some of the coaching institutes I came across on net are 1) http://www.ims4maths.com 2) Analog 3) Brilliant tutorials Please advice which of these could give me best material for maths? Incase any other institute is better, please recommend. I plan to go for corresponding course. kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

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My sincere thanks to you in advance! - Aravind

69. on September 2, 2011 at 1:27 pm | Reply heavenlyniceguy hi Kashish…i know u must be very busy…but i would be extremely grateful to you if you could remove some of my fears about Mathematics as an optional.. I asked Prakash Rajpurohit on his blog, but got no repsonse, and as i have no guidance, you are my final hope. Please help me buddy. I am 28 years old and CSE 2012 would be my first and last attempt. I really like Mathematics and i am taking Math and Physics as my optionals. I am reading I.N.Herstein as suggested by you.I have no problems following the book, but i am not able to solve most of the unsolved exercises , as solving them is extremely time consuming. There are simply too many unsolved problems, and too little time. Is it necessary/helpful /important to solve the unsolved exercises?? Did you do them ?? Also, given the time constraint i have, which topics should i give priority to while preparing as im starting from scratch,and for the past 15 days i have been doing nothing but reading I.N.Herstein, as u suggested that newbies should read it thoroughly at least 2-3 times. Do the books suggested by you need to be read from cover to cover? Am i doing the right thing or should i prepare from herstein later do other easier, shorter topics first? When should i start preparation for prelims GS> Kashish, i’d be highly highly obliged if you could allay my fears regarding Math as an optional..coz …the only problem i face in Math are the UNSOLVED problems(The unsolved exercises) ..are they necessary?

70. on September 6, 2011 at 1:32 am | Reply koustav hello: i am a student of iit kgp .I took maths as my first optional.While going through the book u suggested for abstract/modern algebra “khanna and bhambri” ,i found out quite a number of mistakes(proofs that were either too arbitrary or illogical) in solved examples as well as in theorems .What should i do in this respects????

71. on September 6, 2011 at 9:12 am | Reply kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

vinay tiwari 24/28

hiiii bhaiya…..one thing to ask….i have done solid geometry frm shanti narayan till conicoids…….should i also do next 2 chapters plane sections of conicoids & generating lines of conicoids…..as i have not seen any question from these topics in exam………..they are also not explicitly mentioned in the syllabus too…..

on September 12, 2011 at 8:30 am | Reply dilip those chapters have questions based on hyperboloids on which question was asked , i guess in 09 or 10. 72. on September 20, 2011 at 5:03 am | Reply Strategy for Maths from toppers' blogs [...] [...]

73. on September 20, 2011 at 8:37 pm | Reply Hi Kashish,

abhish agarwal

Please tell me if they allow use of calculator in the exam. Becasue iin maths paper numerical methods have transcendental equations to solve. So how will be do that? Please tell me it is very urgent you know it very well.

on January 10, 2012 at 10:31 am | Reply Hi Abhish

Ashish Modi

I guess Kashish isnt replying because he might be busy with training. If you havent figured out yet, Calc is allowed in the exam. Regards Ashish

74. on October 5, 2011 at 5:08 am | Reply MANINDER SINGH congrats for ur stupendous achievement…..sir i m taking maths and chemistry as optionals……i hv done btech in electrical from PEC Chandigarh……plz guide me the right coaching inst. for maths and chems…….for maths can i join IMS …… plz refer me the blog of who has cleared ias with chemistry as optional


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75. on October 10, 2011 at 12:14 am | Reply Not much of a understanding concept

Faith Ananthy Sundraraj

76. on February 4, 2012 at 10:44 pm | Reply Hi,

Santhosh

Please let me know whether book in the below mentioned link is the right book for Statics and Dynamics. http://www.flipkart.com/books/rbkcy94tdtebyc4v?_l=gWxQa0snNjHUHKJhnj_y0w– &_r=dVs56y2V%20FecwEVoIgmEJA–&ref=546e24de-f877-4cf5-a5c2-c1624b6648ba Regards, Santhosh

77. on May 5, 2012 at 8:02 am | Reply Swappy Sir, I am pursuing Civil Engineering at IIT Delhi and am about to complete my second year. I am thinking about maths as one of my optionals. I was good at maths during my JEE days and enjoyed it. The level of maths, however in the IAS exam is of university level and I have not taken up any math courses at IIT Delhi (except the introductory ones). Please advise whether I should consider maths as my optional or not. Thanks.

78. on May 17, 2012 at 11:32 pm | Reply Naveen Hi sir, Congrats on getting such a good rank in IAS. I am having economics and statistics as optionals. Can you name a few blogs of previous year toppers who have taken these as optionals. Regards Naveen IIT Kharagpur

79. on May 20, 2012 at 1:01 am | Reply kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/

Naveen 26/28

check out which university has the highest success rate in UPSC civil services exam and more only on http://iasstudycircle.forumotion.in/t34p15-interesting-upsc-statistics

80. on May 20, 2012 at 9:37 pm | Reply Hi Kashish,

Soham Das

I am an Engineer, and have used Erwin Kreyszig extensively during my engineering days. Can you tell me, how good is Erwin Kreyszig for topics like Matrix, Calculus etc… As you can see, I am biased towards EK as I have done most of it, during Year 1 and Year 2 of Engineering. Soham

81. on July 23, 2012 at 10:04 am | Reply Neetu Tomar sir congratulations 4 ur success I really want to become an ias officer n want to crack it in 2013 with maths as an optional i can not afford for coaching so u r requested to plz plz plz help me out. I want to ask whether the books mentioned by u r sufficient n helpful in gud scoring without any coasching.

82. on August 2, 2012 at 7:39 am | Reply shruti gupta hellloooo…..i m currently doing btech from computer science in 2nd year. i want to opt maths as my subject in ias mains so how can i star my prep for it…???? will wait for ur reply..!!!


Rahul

I am an ECE engineer and confused whether to take Physics or Maths as an optional. Which would be more marks fetching ? As I have to give exam on 2013, accordingly I have to take coaching from Oct session. Rahul


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Rohit Jain

can you please tell me the title of Thomas and Finney book?

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Strategy for Mathematics « Kashish Mittal

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