A. How to prepare for CSIR NET Mathematical Science? I don't have any idea of how to prepare for that.
I. It is always better to know the syllabus from which you would be tested/examined about. This pdf file has the syllabus for your exams (http://www.csirhrdg.res.in/mcs_ma_sylbs.pdf)
II. The next step would be to understand the exam format which will help you in smart and relevant preparation.
This CSIR NET exam has MCQs that can be grouped under 3 divisions
A- (General Science, Quantitative Reasoning & Analysis and Research Aptitude) . You have to answer any 15 questions that carry 2 marks each.
B - Includes all the topics in the syllabus. You have to answer any 25 questions that carry 3 marks
C- this section tests your grasp of the concepts and its applications. You have to answer any 20 question and each carries 4.75 marks.
Parts A (-0.5 marks) and B (-0.75 marks) have negative marking. C section - No negative marking. Please remember the negative marking while you prepare and answer the actual paper
III. Once you are aware of the above, then is it wise to have a glance at the previous questions papers so that you have a idea of how the exam is going to be. I have enclosed the sample ones.
For section A (http://www.csirhrdg.res.in/gp.pdf)
For section B & C (http://www.csirhrdg.res.in/ms_mp.pdf)
IV. Now list your existing knowledge, the time in hand, your strengths and weakness so that you can do justice to all the subjects. Make a rough plan for your studies and review every couple of weeks to ensure that you are on track or need to make adjustments with time.
V. Studying for such difficult exams can be made easy when you have a group of friends for group study and revisions. If you are alone and need support, consider joining a SIR-NET coaching center.
VI. Writing the real exam. When faced with a tough exam, with MCQs and negative marking, you should be clear about the total time in hand, your difficult areas and the marks in each section. Here, this exam has 3 hours,
section A has 30 marks, section B has 75 marks and section C has 95 marks. So, allocate about 1 1/2 hours for section C, one hour for section B and half an hour for section A. Remember the chance of losing marks in A and B, hence do not just blindly guess.
B.What Books need to be used in order to clear the exam?
Books are just guides to help you to prepare to be successful in exams. Some of these books will be voluminous, it is a common tendency for students to revise the subjects they know well and find that they have actually little time for the areas they are weak in.
1. Real analysis
Apostol, Mathematical analysis.
Real Analysis by H.L. Royden
Bartley and Sherbert, Introduction to analysis.
Mathematical Analysis by S.C. Malik and Savitha Arora
Linear algebra by Seymour Lipschutz and Marc Lipson Schaum series
S. Axler, Linear Algebra Done Right
Linear algebra by Vasishtha and Sharm
J. B. Conway, Functions of One Complex Variable
Foundation of Complex Analysis by S. Ponnusamy
Churchill and Brown, Complex Variables and Applications
Joseph A Gallian, Contemporary abstract algebra
A Course in Abstract Algebra by Vijay K.Khanna and S.K. Bhambri
I. N Herstein, Topics in algebra.
Topology by James Munkres.
Schaum's outline of general topology by Seymour Lipschutz
6.Numerical Analysis etc
I. N. Sneddon, Elements of Partial Differential Equations
K. E. Atkinson, Introduction to Numerical Analysis
S. L. Ross, Differential Equations
Numerical methods for scientific and engineering computation M. K. Jain, S. R. K. Iyengar and R.K. Jain