Maths paper 2 - Pointers + book list

Paper 2

(updated with chapter details)

Points to ponder : 

1. The syllabus of Paper 2 of Mathematics is slightly tricky when compared to Paper 1, especially due to presence of topics like Algebra and Fluid Dynamics.
2. A general trend in recent times has been the mixing of questions of different topics in all the optional questions. This means that one has to have some degree of acquaintance with all the topics of the paper.
3. For those not very conversant with fluid dynamics, it would pay more to focus more on Algebra and Real Analysis so as to avoid having to select two optional questions from Section II of this paper.
• I adopted this strategy, having more or less pre-decided to prefer selecting two questions from section 1, giving more emphasis on modern algebra and real analysis.
• This did not work for me in CSE-2016 though, as questions out of CSE syllabus were asked then - this is also a reason why a basic coverage of all the topics is essential.
• I had tried to practise this strategy in the various various mock tests I had attempted before the exam
4. My strategy in Paper 2 was to minimise my efforts for topics like Fluid Dynamics, Mechanics and focus more on Algebra, Real Analysis.
5. Topics like Numerical methods, Linear programming, PDE are easier to handle and one needs to ensure no calculation mistakes are made while attempting questions from these topics (I did one while solving the simplex question in CSE-2017)

The following are my topic wise sources and strategy for covering the topics of Paper 2 :
(Chapters of the books mentioned are on the lines suggested by Prakash Rajpurohit sir on his blog... to be updated once I get access to my books within the next 3-4 days)

1. Algebra :
   

   • Sources : 
   • Topics in Algebra by I.N. Herstein 
   • Chapter details : Chapter 2 (till 2.11), Chapter 3
   • Previous years questions
   • Strategy : 
   • Algebra is seen to be one of the most difficult topics in the syllabus. Unlike topics like ODE, linear algebra where a single read of the text book allows one to have a decent grasp of the topic, this may not be true in case of algebra especially for those reading it the first time.
   • I gave multiple (read 2-3) readings of the book 'Topics in Algebra' before I started getting some idea of the topic and what it is about.
   • One advantage of the above book is that it has fewer pages to cover (around 100 in total), which allows one to have seemingly small targets in a day. I would typically set myself a target of 15-20 pages of reading per day (on some days even less). This resulted in me paying greater attention to details of each topic.
   • I supplemented this with youtube videos whenever necessary to gain a better understanding.
   • I also focussed on solving questions of exercises given in the Topics in Algebra  (some solutions are available online by an IISc professor)
   • Link : http://www.math.iisc.ac.in/~rakesh13/solutions.html
   • Solutions of Previous years questions were obtained from Dips Academy booklet and https://sites.google.com/site/sunderlalchd/
   • I prepared a notebook for Algebra listing down important/difficult questions and theorems for revision in final days before the examination which helped me immensely
   • I tried books like Khanna and Bhambhri (was too bulky, could not complete even 1 chapter), Gallian (good book but had a very different structure, I did not find it very suitable for CSE purposes)

   
   
2. Real Analysis :
• Sources : 
• Elements of Real Analysis by Shanti Narayan
• Principles of Real Analysis by Malik and Arora (partly done by me)
• Both cover the syllabus well, one can choose either
• Chapter details : 
• Malik and Arora : mentioned under Calculus sources for Paper 1
• Shanti Narayan : Chapter 1-13, 15, 16 (Focus on proofs from 2,3,4,8,13)
• Strategy : 
• I prepared Real Analysis and Calculus together due to significant overlap between the 2 topics.
• These topics require a high degree of practise and may even need some rote-learning for difficult problems








Complex Analysis :


• Sources : 
• Functions of a complex variable by Krishna publication
• Chapter details : 
• Chapters 1-3, 6 (left analytic continuation, reflection principle), 7 (left integration of multi-valued fucntions and beyond)
• Strategy : 
• Solved all the examples of the book of relevant chapters
• Did not do contour integration of rectangular contours and beyond
• Ignored most of the proofs as they are generally quite complex - except those found in previous years papers








Linear Programming :


• Sources : 
• Linear Programming book by Krishna publications
• Chapter details : 
• Did duality, dual simplex method, primal to dual tableau conversion and vice-versa
• Left chapters on resolution of degeneracy, revised simplex methods
• Strategy : 
• Solved a few examples from the textbook to get a hang of topics
• Solved all the previous years questions for practise (last 20 years approx)
• Did not do proofs except those asked previously
• In some books the notation used in simplex tableau is different…I do not think there is an issue there..as I have never used the method/format of Krishna series book







Partial Differential Equations (PDE) :


• Sources : 
• ODE & PDE by M.D. Raisinghania
• Higher Engineering Mathematics by B.S. Grewal (only for Boundary value problems) - great coverage of topics in a concise manner
• Chapter details : 
• M.D. Raisinghania : Chapters 1,2, 3 ( only charpit's method and cauchy's method of characteristics), 4-6,8 (only reduction to normal forms)
• B S Grewal : Chapter on Application of PDE
• Strategy : 
• Solved all the examples from the textbooks







Numerical Methods and Computer programming :


• Sources : 
• Numerical Methods : Numerical Analysis by Burden and Faires
• I referred to it only as it was covered in one of my college courses - not good for proofs, convergence type of questions
• B S Grewal seems a good alternative
• Computer programming : Googled various topics, Digital Logic by Morris Mano (only one chapter is required, buying the whole book would be a waste)
• Strategy : 
• Practised previous years questions and all the questions asked in the test series
• Off late, there is a need to lay more emphasis on proofs, convergence, order of convergence, error calculcations of the methods listed in the syllabus due to rising frequency of questions asked from these domains








Mechanics and Fluid dynamics :


• Sources : 
• Fluid Dynamics by M.D. Raisinghania 
• Chapter details : 
• For selective/ minimal coverage of this topic : 
• Chapters 2, 3, 5, 11 - again was selective in these chapters - left out portions of impulsive motion 
• Chapter 3 is the trickiest of them all which requires quite a bit of memorisation - I relied more on the energy method to work in the exam
• I adopted this approach in my first 2 attempts, would have covered other chapters as well in the subsequent attempt
• For comprehensive coverage :  (i.e. chapters in syllabus)
• Chapters 2,3,5,7,10,11,14 
• Rigid Dynamics Vol. 1 by Krishna publications
• Chapter details : 
• Chapters on Moment of inertia, D'Alembert's principle, Lagrangian (excluding portions on small oscillations), Hamiltonian, Conservation of energy
• No proofs, only solved examples
• Again it was found that after a point questions got too difficult in chapters like Lagrangian, even some in Moment of inertia. I simply noted some of them down in my notebook but I could not rote-learn them before the exam and would have tried to avoid those questions in the exam
• One can refer to Rigid dynamics Vol. 2 for more examples on Lagrangian, Hamiltonian
• Strategy : 
• Was very selective in what I did from these topics, tried to do the bare minimum
• Prepared them to enable me to get past the compulsory question and maybe 1-2 easier questions





Coverage of all the topics of paper-2 and having a sense of confidence in each of them before the exam is very difficult in my opinion. 

One needs to develop an idea of when to stop while doing a particular topic and not delve too much on one section. One should be familiar with the basics of all the topics but try to focus more on certain sections which one can prepare better. 

So in Paper -2, there is a greater need of setting priorities among topics, based on one's comfort level and develop strengths accordingly. 





Any doubts which one may have after reading this may be put in the comments section below.  I will try to answer them as much as I can.