CSIR NET Mathematical Sciences Syllabus 2019  Study Materials & Question Papers
CSIR NET Mathematical Sciences Syllabus 2019: Are you preparing for the CSIR NET exam 2019? Do you have the latest syllabus and study materials?
Don’t worry! Here in this article, we are covering a detailed guide on CSIR NET Mathematical Sciences Syllabus 2019.
CSIR NET Mathematical Sciences
If you are dreaming of building your career in the Mathematics Field, then you must appear in the CSIR NET Mathematical Science Exam. It is conducted twice a year. After qualifying CSIR NET Mathematical Science, you will get tremendous chances for job and research opportunities across India.
 Official website: csirnet.nta.nic.in
The next CSIR NET Mathematical Sciences Exam for 2019 is going to be held on 15th December 2019 (tentatively).
CSIR NET Mathematics Eligibility Criteria
Before applying for the exam, you should be very well aware of the CSIR NET Mathematics eligibility criteria. Without fulfilling the eligibility criteria, you cannot appear in the exam.
 You must have an MSc or equivalent degree/Integrated BSMS/BS4 years/BE/BTech/BPharma/MBBS degree or B.Sc (Hons) or equivalent degree or students enrolled in Integrated MSPhD program with an aggregate marks of 55% for General and OBC categories and 50% for SC/ST/PwD candidates.
 You should have a Bachelor’s Degree. Then you will be eligible for the Fellowship only if you have enrolled for a Ph.D./Integrated Ph.D. program within the validity period of two years.
Age Limit: The upper age limit to appear for the exam is 28 years. The age relaxation is applicable as per government rule.
CSIR NET Maths Syllabus and Exam Pattern
You should know the CSIR NET Syllabus for Mathematics to start solid exam preparation. You should have adequate knowledge about the topics to cover from the CSIR NET Syllabus Mathematics PDF.
It is tough to cover the vast syllabus for CSIR NET Mathematical Sciences in a short span of time. You should start preparing for the exam as soon as possible.
Here you can find some important topics for the preparation.
 Linear Algebra
 Real Analysis
 Ordinary and Partial differential equation
 Modern Algebra
 Complex Analysis
CSIR NET Syllabus for Mathematical Sciences
You can see that in CSIR NET Mathematical Sciences Syllabus has four units.
Here you can check Unitwise syllabus of CSIR NET Mathematical Sciences is tabulated below:
Units 
CSIR NET Mathematical Sciences Syllabus 
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, limsup, liminf. 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, CayleyHamilton 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, CauchyRiemann 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 firstorder ordinary differential equations, singular solutions of firstorder ODEs, the system of firstorder ODEs.
Partial Differential Equations (PDEs): Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for firstorder PDEs. Classification of secondorder PDEs, General solution of higherorder 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 NewtonRaphson method, Rate of convergence, Calculus of Variations: Variation of a functional, EulerLagrange 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, Twodimensional 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, GaussMarkov 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. 
Download Mathematical Sciences Syllabus PDF
CSIR NET Mathematical Science Exam Pattern
You create a better strategic plan for the CSIR NET Mathematics exam. You should be aware of the latest exam pattern.
You have to know the marks distribution for various unites to understand the paper format in a very well. An exam pattern will let you know the time duration and number of questions asked in the exam.
Please check the CSIR NET Mathematics Exam pattern given below.
S.No. 
Sections 
No. of Ques. Given 
No. of Ques. to be Attempted 
Marks 
Neg. Marking 
Duration of Exam 
1 
PARTA 
20 
15 
30 
0.5 
3 Hours 
2 
PARTB 
40 
20 
75 
0.75 

3 
PARTC 
60 
20 
95 
0 

TOTAL MARKS 
200 
CSIR NET Previous Years Question Papers For Mathematics
Along with the study of every section, you should start solving previous year question papers. It will give you the brief idea of the exam and time management.
It will also boost up your speed and accuracy while solving the CSIR NET Mathematics Questions. You will have an exact idea about the format of the questions and marking scheme as well.
CSIR NET Mathematical Science Books and Study Material
You will find the huge number of books for CSIR NET Mathematical Sciences. But you have to choose wisely the best study materials for CSIR NET Mathematical Science to clear your concept. By picking any random book, you will be losing the chance to crack the exam.
Some best books are as given below.
CSIR NET Mathematical Sciences Reference Books 

Topics 
Authors 
Real Analysis 
H.L. Royden 
Linear Algebra 
Hoffman and Kunze 
Complex Analysis 
R.V.Churchill 
Algebra 
Joseph A. Gallian 
Topology 
G .F. Simmons 
Ordinary & Partial Differential Equations 
M.D. Rai Singhania 
Numerical Analysis 
Jain and lyenger 
Calculus of Variations 
A. S. Gupta 
Linear Integral Equations 
Shanti Swarup 
Classical Mechanics 
H. Goldstein 
Statics 
S. C. Gupta 
Kopykitab’s Special Study Package To Boost Your Preparation
To boost your preparation, we are also providing the best . With the package, you will get,
 Latest Syllabus
 Topicwise Online Tests
 Study Material eBooks
 Previous Year Papers 20122019
Career Scope After Qualifying CSIR NET Mathematical Sciences
You will get tremendous career opportunities after passing the CSIR NET Mathematical Sciences 2019.
You will get the main opportunities after passing the exam.
 For JRF exam: You will be eligible to perform research in any of the CSIR Laboratories.
 For Assistant Professor exam: You will be recruited as a lecturer to teach University level students.
Apart from the above, you will also get a chance to work in various private and government organizations.