- Introduction: Maths as an optional subject
- General tips for preparation:
- General tips while attempting the paper:
- Paper 1: Topicwise Booklist
- Paper 2: Topicwise Booklist
- Model Answers for UPSC Maths Paper
I’m merely copy pasting the article of Prakash Rajpurohit (AIR 2/ CSE 2010).
Before starting with the strategy I would like to answer a common question: What is the final score vis-à-vis correct attempt? It is true that there is heavy moderation of marks in science subjects especially in mathematics. But despite that it is possible to score very high. My final score and correct attempt paper wise is:
|Paper||Paper I||II||Paper I||Paper II|
|Correct Attempt (out of 300)||261||250||300||285|
|Marks Received (after scaling)||184||206||209||218|
In the correct attempt I have counted only those answers which are absolutely correct. Paper I is relatively easy so the reduction is huge. Also do not confuse the term scaling down as only multiplication by a constant factor (some says scaling is 0.6 or 0.7). The statistical formulas are more complex and the subtraction part has larger weightage I guess (seeing the mark trends of all the students in last 2 years).
competition in maths is very tough, most of the candidates are from iit or from math background. scoring here is different from school/college as there is heavy moderation of marks.
- Need of coaching is a subjective matter. I did not take any.
- For maths practice is appropriate word instead of revision.
- While preparing one should not be bothered about the moderation/scaling. Target should be to score maximum possible marks.
- study only those topics which are mentioned in the syllabus.
- In Paper I try to cover all the topics. If time does not permit then cover dynamics and statics from 12 markers point of view.
- In Paper II focus on the topics: Complex Analysis, Linear Programming, Partial Differential Equations and Numerical Analysis. Rest of the topics should be covered from 12 markers point of view.
- it is not possible that you come across all the question before exam. what i do is try to finish the paper quickly and keep some time to think over them. for mechanics and dynamics see all the 12 markers which have come in last 10 years. try to cover the theory required to solve them. and practice few more examples related to that.
- Make a fair copy and practice all the previous year questions in it.
- Practice with pen and paper(Many aspirants take this point casually and just read the solved examples)
- Do at least 3-4 papers in exam like conditions.
- Ordering of questions does not matter. Attempt the questions which you know the best at the start.
- Try to finish each question in the 75-80% of the allotted time. For example, a 15 marks question has allotted time of 9 minutes. Try to finish it in 7 minutes. Rest 2 minutes must be spent on revising the answer. Rechecking entire paper at the end may not be possible. Try to work out the answer quickly in rough space. All this is important because wrong answer may carry heavy penalty.
- i did not write any theory, not even explained the terms in lagarange interpolation formula.. focus should be on getting the correct answer and that too quickly.
- All the trivial calculations (like simple integration, algebraic and trigonometric manipulations) can be done in rough space to save time (I believe that showing them in answer might not carry any weightage).
- I will also upload some of the answers which I wrote in the paper. In the next articles I will be sharing the detailed strategy for both the papers.
A major question that comes in the mind of an aspirant is whether she should go for selective or exhaustive preparation. I went for the exhaustive preparation, as most part of the syllabus was part of my graduation curriculum. But if time does not permit one can leave some topics from point of view of full 60 marks question. In this post I am giving topic wise preparation strategy.
- Calculus – Shanti Narayan – Course on Mathematical Analysis (S. Chand)
- Analytic Geometry – Shanti Narayan (S. Chand)
- Ordinary Differential Equations – M.D. Raisinghania (S. Chand)
- Statics – Krishna Series
- Dynamics – Krishna Series
Paper I Topics
- Linear Algebra Focus should on understanding the definition of various terms mentioned in the syllabus (like vector spaces, subspaces, linear dependence and so on). While answering questions explain all the steps.
- Calculus Single variable calculus is not a problem for candidates. Refer to chapters (book I mentioned in the booklist) that deal with continuity and differentiability for 2 variables. For double and triple integration also refer to that book. The solved examples from that book are sufficient. The relevant chapters are:12,13,15,16,17,18. Theory is not important , just understand the techniques through solved examples.
- Analytic Geometry Refer book by PN Chaterjee(Rajhans Publications). This book contains solved examples and all the questions are taken from this book.
- Ordinary Differential Equations In this topic it is better to make a sheet of all the formulas and techniques. Practice all the solved questions of the book I have mentioned.
- Dynamics and Statics Completing the Krishna Series books(do only topics mentioned in the syllabus) will be sufficient for attempting 60 marks question. Common Catenary, central orbits, constrained motion should be covered in depth(that is do all the solved examples). For rest of the topics covering only few examples is sufficient.
- Vector Analysis In this topic make the formula sheet. And practice previous year questions. Regularly practice the derivations asked in the exam.
- Algebra Khanna and Bhambri
- Algebra- I. N. Herstein
- Elements of Real Analysis -MD. Raisinghania(S. Chand)
- Complex Analysis – Krishna Series
- Linear Programming - Krishna Series
- Partial Differential Equations- M.D. Raisinghania + (Some portion of book on Boundary Value Problem by S. Chand)
- Numerical Analysis – Jain and Iynger
- Fluid Dynamics – M.D. Raisinghania
- Mechanics – Krishna Series (Rigid Dynamics vol.-1 and Vo.-II)
- For Linear Algebra and Vector Analysis, I could not find any books relevant to the exam. So I referred to Brilliant Tutorials material to practice questions.
Paper 2: Topics and Tips
- Algebra For the people who are totally new to this topic i would suggest that read the books i have mentioned 2-3 times. Then practice all the theorems and questions yourself 2-3 times.
- Real Analysis Cover chapters: 2- The Real Numbers(till page 24), 3-Neighbourhoods and Limit Point of a set(till page 11), 4 Countability of Sets(first 12 theorems and examples given at the end) 5,6,7(Regarding Sequence and series) 8. Real Functions. Limit and Continuity, 9,10,11,12,13,15,16. For the topics underlined cover the theorems also. For rest of the chapters solved examples are enough.
- Complex Analysis Cover this topic from any book. Practice this topic thoroughly.
- Linear Programming Practice is important. Improve upon the speed and accuracy for this topic.
- Partial Differential Equations Same as Ordinary Differential Equations.
- Numerical Analysis and Computer Programming Make the formula sheet for all the methods. Cover error analysis for newton raphson, lagrange interpolation, numerical integration. Draw flow chart and algorithm for all the numerical methods. Practice them regularly. For other topics i had M Morris Mano(this is digital electronics book). One can refer to the internet if she does not find the leftover topics in book.
- Mechanics and Fluid Dynamics For Mechanics focus on chapters of Lagrangian(cover it from Vol-II, Rigid Dyanamics-Krishna Series), Hamiltonian, Moment Of Inertia, D’Alembert’s principle. For Fluid Dynamics cover topics mentioned in the syllabus. The book of MD Raisinghania covers syllabus from IAS exam perspective also.
My methodology was to first cover the topic from the books. Then practice previous year questions from that topic. I covered the topics in the order mentioned in the syllabus. However it does not matter much. After covering the entire syllabus I practiced last 3-4 year papers in exam like conditions.
I have uploaded solutions to Q 1(a) and Q 7(a) of CSE-2009 paper-II attempted by me. Here they’re: