**CSIR UGC NET Mathematics Coaching in Chandigarh**

Statesman Academy is known as best CSIR UGC NET coaching institute that provide best** CSIR UGC NET Mathematics coaching in Chandigarh.** Our objective is to prepare candidate to score best in this exam. STATESMAN ACADEMY relies on hard work and sincere efforts on the part of teachers as well as on the part of students. We work with honesty, integrity and transparency to accomplish best outcomes in UGC-NET Mathematics Coaching Programme.

For more than 10 years, STATESMAN ACADEMY, has been indomitably and persistently producing top ranks in the field of **csir net Mathematics coaching**. This endeavour is still in progress with every successive year with more top positions at all India levels. All the credit for this immense success goes to our dedicated faculty who with their painstaking efforts guides our students with utmost care and commitment.

### Introduction

- The main objective of CSIR NET exam is to determine the eligibility of the Indian National candidates for the award of Junior Research Fellowships (JRF) NET and also to determine their eligibility for appointment of Lecturers (NET) in subjects that fall under the faculty of Science & Technology. CSIR holds the Joint CSIR-UGC NET twice a year usually in the month of June and December.

## EDUCATIONAL QUALIFICATION

**JRF**: BS – 4 Years program / BE / B.Tech / B.Pharma / MBBS / Integrated BS-MS / M.Sc or equivalent degree with at least 55% marks for general and OBC (50% for SC/ST candidates, physically and Visually Handicapped candidates).**LECTURESHIP:**Ph.D Degree holders who have passed Master’s Degree prior to 19th September 1991, with at least 50% marks are eligible for Lectureship only.

### Age Limit & Relaxation:

**The age limit for admission to the Test is as under:**

- For JRF (NET): Maximum 28 years (upper age limit may be relaxed up to 5 years in case of candidates belonging to SC/ST/OBC (As per GOI central list), Physically handicapped/Visually handicapped and female applicants).
**For Lectureship (NET): No upper age limit.**

### CSIR New Pattern of Examination

- MATHEMATICAL SCIENCES
**TIME: 3 HOURS****MAXIMUM MARKS: 200**- From June, 2011 CSIR-UGC (NET) Exam for Award of Junior Research Fellowship and Eligibility for Lectureship shall be a Single Paper Test having Multiple Choice Question (MCQs). The question paper shall be divided in three parts.

### Part ‘A’

- This part shall carry 20 questions pertaining to General Aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzle etc. The candidates shall be required to answer any 15 questions. Each question shall be of two marks. The total marks allocated to this section shall be 30 out of 200.

### Part ‘B’

- This part shall contain 40 Multiple Choice Questions (MCQs) generally covering the topics given in the syllabus. A candidate shall be required to answer any 25 questions. Each question shall be of three marks. The total marks allocated to this section shall be 75 out of 200.

### Part ‘C’

- This part shall contain 60 questions that are designed to test a candidate’s knowledge of scientific concepts and or application of the scientific concepts. The questions shall be of analytical nature where a candidate is expected to apply the scientific knowledge to arrive at the solution to the given scientific problem. The questions in this part shall have multiple correct options. Credit in a question shall be given only on identification of all the correct options. No credit shall be allowed in a question if any incorrect option is marked as correct answer. No partial credit is allowed. A candidate shall be required to answer any 20 questions. Each question shall be of 4.75 marks. The total marks allocated to this section shall be 95 out of 200.
- For Part ‘A’ and ‘B’ there will be Negative marking @25% for each wrong answer. No Negative marking for Part ‘C’.
- To enable the candidates to go through the questions, the question paper booklet shall be distributed 15 minutes before the scheduled time of the exam.
- On completion of the exam i.e. at the scheduled closing time of the exam, the candidates shall be allowed to carry the question Paper Booklet. No candidate is allowed to carry the Question Paper Booklet in case he/she chooses to leave the test before the scheduled closing time.

### SYLLABUS AND RECOMMENDED BOOKS

General Aptitude (GA): Common to All Papers of Part A

**Logical reasoning,graphical analysis, analytical and numerical ability, quantitative comparison, series formation, puzzle etc.**

### 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 of real numbers and their convergence. limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.

Principle of Mathematical Analysis –S.L. Gupta, N.R. Gupta*(Pearson Publication)*Real Analysis –Robert G Bartle

- Elementary set theory, finite, countable and uncountable sets. Real number system as a complete ordered field. Archimedean property, supremum, infimum. Sequences and series of real numbers and their convergence. limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, uniform continuity, differentiability, mean value theorem. Sequences and series of functions, uniform convergence. Riemann sums and Riemann integral, Improper Integrals. Monotonic functions, types of discontinuity, functions of bounded variation, Lebesgue measure, Lebesgue integral. Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems. Metric spaces, compactness, connectedness. Normed linear Spaces. Spaces of continuous functions as examples.

*(Wiley Publication)*

Real Analysis –

M.D. Raisinghania

*(S. Chand Publication)*

### LINEAR ALGEBRA

- Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations. Algebra of matrices, rank and 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. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification of quadratic forms.

Linear Algebra Schaum’s Series –*(Tata McGraw-Hill Publication)*Linear Algebra –Kenneth M Hoffman, Ray Kunze*(PHI Publication)*

Linear Algebra –

Vivek Sahai, Vikas Bist

*(Narosa Publication)*

### 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.

Complex Variables –H.S. Kasana*(PHI Publication )*Complex Analysis –S Ponnusamy

- 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.

*(Narosa Publication)*

Complex Analysis –

R.V. Churchill

*(Tata McGraw – Hill Publication)*

### ALGEBRA

- Permutations, combinations, pigeon-hole principle, inclusion-exclusion principle, derangements. Fundamental theorem of arithmetic, divisibility in Z, congruences, Chinese Remainder Theorem, Euler’s Ø- function, primitive roots. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley’s theorem, class equations, Sylow theorems. Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domain, principal ideal domain, Euclidean domain. Polynomial rings and irreducibility criteria. Fields, finite fields, field extensions, Galois Theory.

Contemporary Abstract Algebra –Joseph A. Gallian*(Narosa Publication )*Modren Algebra –Surjeet Singh and Qazi Zameeruddin

*(Vikas Publication)*

Abstract Algebra –

David S. Dummit, Richard M. Foote

*( Wiley Publication)*

### TOPOLOGY

- Basis, dense sets, subspace and product topology, separation axioms, connectedness and compactness.

Topology –

- D. Joshi

*(New Age International Publication)*

### 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, system of first order ODEs. General theory of homogenous and non-homogeneous linear ODEs, variation of parameters, Sturm-Liouville boundary value problem, Green’s function.

Ordinary Differential Equations –MD Rai Singhania*( S.Chand Publication )*Differential Equations –Shepley L. Ross

*(Wiley Publication )*

Differential Equations –

Earl Codington

*(PHI Publication )*

**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.

Partial Differential Equations –Amaranath*(Narosa Publication )*Introduction To Partial Differential Equations –Sankara Rao

*(PHI Publication )*

### NUMERICAL ANALYSIS

- Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Gauss elimination and Gauss-Seidel methods, Finite differences, Lagrange, Hermite and spline interpolation, Numerical differentiation and integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and Runge-Kutta methods.

Numerical Analysis –R.K. Jain, ?S.R.K. Iyengar*(New Age Publication )*

### 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.Calculus of Variations –S. GUPTA
*(Narosa Publication )*

### 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.

Linear Integral Equations –

M D Raisinghania

*(S.Chand Publication )*

### CLASSICAL MECHANICS

- Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations, Hamilton’s principle and principle of least action, Two-dimensional motion of rigid bodies, Euler’s dynamical equations for the motion of a rigid body about an axis, theory of small oscillations.

Classical Mechanics –

- C. Upadhyaya

*(Himalaya Publication )*

### 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. Characteristic functions. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case). Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes. 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: most powerful and uniformly most powerful tests, likelihood ratio tests. Analysis of discrete data and chi-square test of goodness of fit. Large sample tests. Simple nonparametric tests for one and two sample problems, rank correlation and test for independence. Elementary Bayesian inference. Gauss-Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses. Analysis of variance and covariance. Fixed, random and mixed effects models.

Simple and multiple linear regression. Elementary regression diagnostics. Logistic regression. Multivariate normal distribution, Wishart distribution and their properties. Distribution of quadratic forms. Inference for parameters, partial and multiple correlation coefficients and related tests. 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. Ratio and regression methods. Completely randomized designs, randomized block designs and Latin-square designs. Connectedness and orthogonality of block designs, BIBD. 2K factorial experiments: confounding and construction. Hazard function and failure rates, censoring and life testing, series and parallel systems.

Probablity and statistics –

C. Gupta and ?V. K. Kapoor

*(S.Chand Publication )*

### LINEAR PROGRAMMING PROBLEM AND OPERATIONS RESEARCH

- Simplex methods, duality. Elementary queuing and inventory models. Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1.

Operations Research –

Prem Kumar Gupta, D. S. Hira

*(S.Chand Publication )*

CSIR-UGC-NET Coaching In Chandigarh

Statesman Academy, SCO 54-55, 2nd Floor,

Sector 34A, Chandigarh (UT), Punjab

160022