Mathematics optional is
one of the favorite subject preferred by Engineers and Math graduates. Syllabus
and difficulty level of Math paper is quite similar to what it is at graduate
level but this optional has been punished by UPSC via scaling/moderation in the
last decade. However we are seeing the revival of this subject in last 2-3
years. This year also Mathematics result has been good with 5-6 people getting
400+ score, top score being of Himanshu Gupta at 430.
However to get such a
good score, one must go for exhaustive study with proper revision plan. Some
useful tips for each module is as follow:
Paper 1
1. Linear Algebra and
Matrices: For linear Algebra, I followed Schuam's outline series "Linear
Algebra" by 'Seymour Lipschutz' and 'Marc Lipson'. For Matrices Krishna
Publication book "Matrices" by Vashishtha is good.
In Linear Algebra, one
must do all the important derivation. Also be sure of what a specific term
means e.g. difference between a space and a subspaces. Matrices part is more
date intensive and one must be fast in calculation and use of calculator
advance features.
In my opinion, this
module can be mastered easily and one must attempt question from this module.
2. Calculus: for calculus either buy Krishna Publication
or the S. Chand publication book.
3. Analytic Geometry:
Book by P.N. Chaterjee of Rajhans Publications is must. UPSC has taken direct
examples from this book in last few years.
4. ODE: book by M.D. Raisinghania of S. Chand
publication is best book for this part. Differential equations is an important
topic in this preparation and must be done thoroughly. It find useful
application in many other subject like in vectors, fluid dynamics, partial
differential, numerical analysis etc. Students should complete this module
before moving to these above topics.
5. Dynamics and Statics:
Follow Krishna Publication book for both. There are lots of solved example
given. If you have less time, then you can selectively choose the questions of
each type and do it. Although UPSC asks solved example of these books.
6. Vector Analysis:
Krishna Publication book; easy topic and one must target full attempt from this
module.
Paper 2
1. Modern Algebra:
Achilles heel for many of the aspirants esp engineers. This is a pure
mathematics subject and would need patience and hard work. It is a very
important module in point of view of scoring in the exam and one must try to
get mastery of this subject.
For theory part one can
consult book by 'I. N. Herstein' or alternatively by 'John B. Fraleigh'.
Also Krishna series book
is good in view of solved examples.
2. Real Analysis: "
Elements of Real Analysis" by M.D. Raisinghania and Shanti Narayan is the
best book for this module. Do it thoroughly.
3. Complex Analysis:
Krishna series book is very good book.
4. Linear Programming:
Engineering students will find it a cakewalk however other student must
practice a lot in this topic. Speed and accuracy is of prime importance here.
5. PDE: 'Advance
Differential Equation" by M.D. Raisinghania is the book to be referred
here. Special focus should be on Wave and Heat problem.
6. Numerical Analysis: I
did it via "advanced engineering mathematics' book by Grewal. This book
has some excellent solved examples and must be followed for other modules as
well.
7. Fluid Dynamics: book
by M.D. Raisinghania is sufficient. Questions are numerical and directly taken
from this book.
One very important
advice to all aspirants is that please give proper respect to this optional.
You must practice a lot using pen and paper; Casual reading of question and
answer is of no use. Also coaching is not necessary at all for this optional
but one must join a good test series for self evaluation.
Twp useful blog for
Mathematics preparation is
http://prakashrajpurohit.wordpress.com/2010/06/05/mathematics-part-1/
http://kashishmittal.wordpress.com/2011/05/28/strategy-for-mathematics/
Wishing you best of luck
for your preparation.
Ajay Tomer ( Rank 88)
