Mathematics Preparation Tips for CSIR UGC NET 2020

Updated On -

Jun 22, 2020

Sudeshna Bhar

Exams Prepmaster

CSIR NET Exam is taken to identify deserving candidates for research fellowship or lectureship jobs out of thousands of candidates. A well planned and determined approach will provide you with the desired achievement. Starting self-preparation would be a challenging job especially for such a difficult exam.

Why take CSIR NET Mathematical Sciences?

After Post-graduation, it is the open path you can where you can make your career. Choosing CSIR NET is one of the wisest decisions. As qualifying, this prestigious exam would be a milestone in your life and you will have many options opening up in front of you and you get to choose according to your passion and merit.

After clearing the exam for JRF will be eligible to in many sectors who prefer especially CSIR NET Candidate such as:

• Research in any of the CSIR Laboratories.
• Applying for Assistant Professor.
• Applying for Professorship.
• Research and a Ph.D. degree in India and Abroad.

To know more about the career opportunities, Check Career Scope after Qualifying CSIR NET

CSIR NET Mathematics Syllabus and Important Topics

When a candidate has decided to crack exams like CSIR NET, the first step is to have a detailed syllabus and exam pattern in your hand. A proper syllabus will make your preparation journey a lot easier and you will what should be prepared and what should be omitted. Here is the syllabus:

Units Syllabus of Mathematics
Unit 1 Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Differentiability, Mean value theorem, Sequences, and series. Functions of several variables, Metric spaces, compactness, connectedness. Normed Linear Spaces.
Linear Algebra: Vector spaces, algebra of linear transformations. Algebra of matrices, determinant of matrices, linear equations. Eigenvalues and eigenvectors, Cayley-Hamilton theorem. Matrix representation of linear transformations. Change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms.Quadratic forms, reduction, and classification of quadratic forms
Unit 2 Complex Analysis: Algebra of complex numbers, the complex plane, polynomials, power series, transcendental functions such as exponential, trigonometric, and hyperbolic functions. Analytic functions, Cauchy-Riemann equations. Contour integral, Cauchy’s theorem, Cauchy’s integral formula, Liouville’s theorem, Maximum modulus principle, Schwarz lemma, Open mapping theorem. Taylor series, Laurent series, calculus of residues. Conformal mappings, Mobius transformations.
Algebra: Permutations, combinations, Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots, Cayley’s theorem, Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, Polynomial rings, and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory.
Topology: basis, dense sets, subspace and product topology, separation axioms, connectedness, and compactness.
Unit 3 Ordinary Differential Equations (ODEs): Existence and uniqueness of solutions of initial value problems for first-order ordinary differential equations, singular solutions of first-order ODEs, the system of first-order ODEs.
Partial Differential Equations (PDEs): Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first-order PDEs. Classification of second-order PDEs, General solution of higher-order PDEs with constant coefficients, Method of separation of variables for Laplace, Heat and Wave equations.
Numerical Analysis: Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence,
Calculus of Variations: Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations.
Linear Integral Equations: Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel.
Classical Mechanics: Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and the principle of least action, Two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, the theory of small oscillations.
Unit 4 Descriptive statistics, exploratory data analysis, Sample space, discrete probability, independent events, Bayes theorem. Random variables and distribution functions (univariate and multivariate); expectation and moments. Independent random variables, marginal and conditional distributions.
Standard discrete and continuous univariate distributions. Sampling distributions, standard errors and asymptotic distributions, distribution of order statistics, and range.
Methods of estimation, properties of estimators, confidence intervals. Tests of hypotheses, Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance. Simple and multiple linear regression, Multivariate normal distribution, Distribution of quadratic forms.
Data Reduction Techniques: Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation. Simple random sampling, stratified sampling, and systematic sampling. Probability proportional to size sampling.

By looking at the tabular any mathematics CSIR NET candidate would agree that it is quite huge to cover. Since through UGC board is identifying candidates for research and professorship, it is obvious to make the syllabus and the exam pattern difficult to understand and cover-up. To know more the exam pattern and syllabus of CSIR NET Mathematics

Importance of Previous Years papers

The syllabus of UGC CSIR NET Mathematics is so vast because as we know that these papers are designed for the candidates who age going to be research scholars and professors. the complexity level of the papers is also high. Therefore candidates are advised to rely on previous years’ papers and sample papers to exercise their study and make themselves prepare for the exam.

• Attempt mock test and test series to know the format and environment of the exam. To practice and test yourself, Click for the Test Series of CSIR NET.
• Practice Previous years’ papers to build an understanding and develop the predictability of the types of questions that are going to be asked. To get the Previous years’ papers and download them, Click Here.
• Sample papers are equally important due to having the nature of presenting the probable question papers of CSIR NET 2021 Mathematics.

Best Books and Study Material for CSIR NET Mathematics

Choosing proper study material and books for preparation is the second most important. There are so many many books on different topics in mathematics. but for just one exam you cannot read all these books. And not all the topics included in CSIR NET Mathematics is important, so there is no need to focus on all the topics at once. Here in this section, we are going to provide you with the list of books according to the important topics and sections.

Topics Name of Books Author/ Publisher
Real Analysis Introduction to Real Analysis Donald R. Sherbert Robert G. Bartle
Introduction to Real Analysis Sadhan Kumar Mapa
Principles of Mathematical Analysis Walter Rudin
Fundamental Real Analysis S.L. Gupta and Nisha Rani
Mathematical Analysis  S C Malik
Calculus Thomas' Calculus  George B. Thomas, Joel Hass , et al.
Linear Algebra:  Linear Algebra By Pearson Kenneth M Hoffman
Schaum's Outline of Linear Algebra, Sixth Edition (Schaum's Outlines) Seymour Lipschutz and Marc Lipson
Theory and Problems of Linear Algebra Ritu Jain R.D. Sharma
Modern Algebra:  Contemporary Abstract Algebra Joseph A Gallian
A Course in Abstract Algebra Vijay K Khanna and S K Bhambri
Algebra: Abstract and Modern Swamy and Murthy
Complex Analysis: Complex Variables and Applications Ruel Churchill and James Brown
Foundations of complex analysis S. Ponnusamy
Ordinary differential equations Ordinary and Partial Differential Equations Dr. M.D. Raisinghania
Differential Equations Ross Shepley L.
Integral equations: Integral Equations and Boundary Value Problems M D Raisinghania
Numerical analysis Introductory Methods of Numerical Analysis Sastry S.S
Metric spaces Metric Spaces Third Edition Pawan K. Jain
Metric Spaces P. K. Jain and K. Ahmad
Topology Topology Munkres
Introduction To Topology And Modern Analysis George Simmons
Functional Analysis  Functional Analysis 3 edition P.K. Jain
Measure theory Lebesgue Measure and Integration P.K. Jain
Classical Mechanics Classical Mechanics H. Goldstein
Statics Statics S. C. Gupta

Preparation Strategy for CSIR UGC NET - Mathematics

• Maintain a study schedule

It is very important for the candidates to prepare a study schedule according to their daily lifestyle and comfort zone and maintain the schedule unless the candidate would wake up in the morning and think what will be the topic he/she is going to cover this day. Many candidates make timetables wherein they divide time for their daily work and study hours.

So, you also need to have a strong determination to keep up with your daily study hours which will give you the motivation to keep it and constancy to complete the syllabus without much difficulty. All those who do not will have to undergo severe pressure and eventually will end up leaving out many valuable topics unprepared. Your plan should include each day record and you also can maintain a spreadsheet for your study plan.

• Divide chapters/topics

All the topics of CSIR NET Mathematics Syllabus should be divided according to the time you have left before the exam. Suppose if the candidates have 6 months in hand for preparation then the time they give in studies must be 7 to 8 hours a day. If the candidates are left with 2 months, then they must give more time to study, say 9 to 11 hours a day with proper strategy and study planning.

Only then, it will be possible for the candidates to complete their syllabus on time. Not completing the syllabus will cause unnecessary stress and depression in the mind of candidates no matter how talented the candidates are. Another thing that should be in mind is saving time for revision. This way candidates will have enough time for revision after completing the syllabus of CSIR UGC NET 2020 on time

Candidates must start their preparation from the subject they are good at. By doing this, candidates will be able to polish the subject in which they are already good at.

Candidates often make a mistake of neglecting their strength. Starting your preparation with what you are already good at - will not just enhance your strength, will also help you to understand the related topics and find other topics within your control.

In case you start your preparation with the subject he/she weak at, then more time will be spent in order to prepare for it. Thus, wasting more time on one topic/subject will be risky for preparation strategy especially when the time is less in hand.

This would leave them with very little time to prepare the rest of the topics that will be asked in the CSIR UGC NET exam. Lack of time might lead the candidates in a state of confusion. Last-minute preparation might also lead them to forget important theories and formulas that they have learned.

• Dos and Don’ts for CSIR NET Preparation

Apart from studying and practising, you must also take special care of themselves both mentally and physically while preparing for the CSIR UGC NET 2021 exam. They can include the following activities in their routine to remain absolutely stress-free while preparing:

• Make sure you wake up early in the morning and sleep on time at night.
• Drink water properly and never skip your meal.
• Spare at least half an hour to listen to some good music or follow your hobby for refreshing your mind.
• Do not confine yourself to your room, go out and refresh your mind like take breaks for 5 minutes after 1 hour of study.
• Do some yoga or jogging or exercise to maintain your health.
• Give yourself at least 6-7 hours of sleep.
• Lastly, Meditate to develop your concentration power and mental health.
• LastMinute Preparation tips

Exam time is the most crucial time in your life, especially when you are going for a competitive exam CSIR NET exam. You have worked hard enough yet thinking about the exam makes you nervous. In such a position, follow the below-mentioned strategies to give a better performance in the exam:

• Don’t victimize yourself with the exam stress which will make you lose focus on the processes of raising the topics as last-minute preparation.
• Avoid getting pressurized due to a lack of motivation or words from the people from your atmosphere.
• Don’t get distracted by mobile phones, TV, music, social media, games, etc. at the time you start studying.
• Take short breaks in every one hour. If feeling tired, have a nap for 1-2 hours if needed.
• Don’t panic when the exam starts.
• Be confident to avoid committing mistakes. Read the questions carefully before answering.

CSIR NET Exam is the perfect field for the aspirant who is attracted to the lectureship and Research program. You can prepare for the exam if you will carry a positive attitude towards it

Start your preparations early and try to understand the concepts. We wish you the very best for your forthcoming CSIR NET Exam.

FAQs

Ques. Can we crack CSIR NET without coaching?

Ans. Yes, one can 'crack' CSIR-NET without coaching, if one believes. If you are not ready to put in efforts and think coaching will do the trick, you have got it figured all wrong. Coaching allows one to be disciplined and complete the required syllabus on time. Still is you are determined, Read the above article carefully.

Ques. How many attempts can one give in CSIR NET?

Ans. Candidates can appear several times for the CSIR NET Exam. There is no restriction upon the number of attempts. If they are appearing for JRF they have to remember the upper age limit i.e. 28 years. For Assistant Professor, there is no upper age limit.

*The article might have information for the previous academic years, please refer the official website of the exam.