# Mathematics preparation by Nitish K (AIR 8)

I have been preparing Maths for the last 5 years and have scored highest or one of the highest marks in Maths in all my 3 attempts. At the outset, I would like to thank Prakash Rajpurohit (AIR 2, CSE-2009) for his excellent blog, which formed the basis for my preparation.

Below I have written down booklist and strategy for Paper I and II.

Booklist and strategy for Paper I :

Book List

Linear Algebra:

a) 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.

b) Krishna Series on Matrices

Calculus:

a) Krishna Series on Differential calculus

b) Krishna Series on Integral calculus

c) Mathematical Analysis by Malik and Arora : a must read book for both Paper I and II

Analytical Geometry:

a) Krishna Series on Analytical Geometry : this book is better than Shantinarayan and has many solved examples

b) Krishna Series on Analytical Solid Geometry : for Conicoids, Generating Lines

Ordinary Differential Equations:

a) Ordinary and Partial Differential Equations by MD Raisinghania

b) Advanced Differential Equations by MD Raisinghania : required for Laplace Transforms (Paper-I) and Boundary value problems (Paper-II)

Dynamics and Statics:

a) Krishna Series on Statics

b) Krishna Series on Dynamics

Vector Analysis:

a) Krishna Series on Vector Calculus (~ 330 pages)

b) 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.

Booklist and strategy for Paper II :

Booklist :

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.

a) Abstract Algebra, Group Theory by R Kumar (Vardhaman Publications)

b) Abstract Algebra, Ring Theory by R Kumar (Vardhaman Publications)

c) Abstract Algebra by Joseph Gallian (optional)

Real Analysis:

a) Mathematical Analysis by Malik and Arora

b) Real Analysis by MD Raisinghania

Complex Analysis:

a) Krishna Series

Linear Programming:

a) Operations Research by JK Sharma or Kanti Swarup or Krishna Series

Partial Differential Equations:

a) ODE and PDE by MD Raisinghania

b) Engineering Maths by Grewal : for boundary value problems

c) Advanced Differential Equations by M.D Raisinghania (for boundary value problems)

Numerical Analysis and Computer programming:

a) Numerical Methods by Jain and Iyengar (but questions are not coming from this book from past few years)

b) Numerical Analysis chapter from Grewal, Engineering Mathematics

c) For Algorithms and flowcharts, I am having soft copy of a book which I will share.

Mechanics and Fluid Dynamics:

a) Fluid Dynamics by MD Raisinghania

b) Krishna Series, Dynamics for Moment of Inertia and D Alembert’s Principle

c) 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:

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.

Also I have uploaded my sample test papers, collection of solved problems, self-study guide for Lagrangian and Hamiltonian in my blog, which you can download.