**CSIR UGC NET/JRF MATHEMATICS COACHING**

*CSIR UGC NET MATHS COACHING* :- CSR Mathematics Have Constantly Been Producing* Top Ranker And Scholarship Holders* In

*CSIR UGC NET/JRF Mathematics, GATE Maths And Ph.D Exams.*

**CSIR NET Cut off Marks – 17th Dec 2017 [Declared]**

**CSIR NET Cutoff for JRF**

### SUBJECT – MATHEMATICAL SCIENCES

### UNRESERVED – 48.38%

### OBC – 40.75%

### SC – 31.25%

### ST – 25%

### PWD – 25.13%

**CSIR NET Cutoff For NET**

### SUBJECT – MATHEMATICAL SCIENCES

### UNRESERVED – 43.54%

### OBC – 36.68%

### SC – 28.13%

### ST – 25%

### PWD – 25%

**CSIR UGC NET MATHS COACHING**

CSIR-NET Exam is mandatory for candidates aspiring to teach in various degree colleges/ universities in all over India. CSIR-UGC conducts JRF/NET exam twice a year in the month of June and December. The exam will be conducted in different subjects like Mathematical Sciences, Physical Sciences & Life Sciences etc.

Recent changes in CSIR-UGC:

⦁ Observing that “the courts should not venture into academic field, Delhi High Court has upheld the mandatory requirement of clearing the NET or SLET for appointment to the post of Lecturer.

⦁ The University Grants Commission (UGC) framed the Rule & Regulations – 2009 in July. Which says that NET or SLET is mandatory for appointment of Lecturers.

⦁ Atleast 55% marks or equivalent grade is required in master degree for NET qualification.

⦁ Atleast one Professor in each Dept. in P.G. College is a requirement.

⦁ The new regulations have also created an additional post senior professor. Accordingly, the new hierarchy in ascending order is assistant professor, associate professor, professor and senior professor.

⦁ One post of a professor in each department of the postgraduate college, and of 10% posts in an undergraduate college shall be of those from professors only.

*CSIR UGC NET MATHS COACHING:-*

**CSIR-UGC (NET) EXAM FOR AWARD OF JUNIOR RESEARCH FELLOWSHIP AND ELIGIBILITY FOR LECTURERSHIP**

__MATHEMATICAL SCIENCES__

__MATHEMATICAL SCIENCES__

**EXAM SCHEME**

**T****IME****: 3 H****OURS**** M****AXIMUM ****M****ARKS: ****200**

CSIR-UGC (NET) Exam for Award of Junior Research Fellowship and Eligibility for Lecturership shall be a Single Paper Test having Multiple Choice Questions (MCQs). The question paper shall be divided in three parts.

## Part ‘A’

This part shall carry 20 questions pertaining to General Science, Quantitative Reasoning & Analysis and Research Aptitude. 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’.

**(Age Limit & Relaxation)**

**(Age Limit & Relaxation)**

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).

### *CSIR UGC NET MATHS COACHING:-*

**CSIR NET Cutoff Marks – 18th June 2017**

**CSIR NET Cutoff Marks – 18th June 2017**#### Selected: JRF (NET) CSIR: 1858 candidates

#### JRF (NET) UGC: 1500 candidates

#### JRF (NET): 95 candidates

#### Lecturership (NET): 3597 candidates

This year, the examination is tentatively scheduled to be held on June 18. The results are available on csirhrdg.res.in. How to check CSIR UGC NET June 2017 results: Go to csirhrdg.res.in

**CSIR NET Dec. for JRF & Lect.-18th December 2016**

**CSIR NET Dec. for JRF & Lect.-18th December 2016**

### **For Junior Research Fellowship-**

SUBJECT | GEN | OBC | SC | ST | PH |

Mathematics |
59.50 | 50.00 | 39.25 | 27.63 | 26.00 |

**For Lectureship**

SUBJECT |
GEN | OBC | SC | ST | PH |

Mathematical |
53.55 | 45.00 | 35.33 | 25.00 | 25.00 |

*CSIR UGC NET MATHS COACHING:-*

**CSIR Net June 2016 Result & Cut Off – 19th June 2016**

**CSIR Net June 2016 Result & Cut Off – 19th June 2016**

**For Junior Research Fellowship**

SUBJECT |
GEN | OBC | SC | ST | PH |

Mathematical |
54.88 | 47.38 | 37.63 | 25.00 | 25.75 |

**For Lectureship**

SUBJECT |
GEN | OBC | SC | ST | PH |

Mathematics |
49.39 | 42.64 | 33.87 | 25.00 | 25.00 |

### **CSIR Net Result Dec 2015 & Cut Offs – 20th December 2015**

**CSIR Net Result Dec 2015 & Cut Offs – 20th December 2015**

**For Junior Research Fellowship**

SUBJECT |
GEN | OBC | SC | ST | PH |

Mathematics |
54.88 | 47.75 | 38.63 | 25.63 | 32.00 |

**For Lectureship**

SUBJECT | GEN | OBC | SC | ST | PH |

Mathematics |
49.39 | 42.98 | 34.77 | 25.00 | 25.54 |

* CSIR UGC NET MATHS COACHING:-*

**CSIR Net June 2015 Result & Cut Off – 21st June 2015**

**CSIR Net June 2015 Result & Cut Off – 21st June 2015**

**For Junior Research Fellowship**

SUBJECT | GEN | OBC | SC | ST | PV |

Mathematics |
53.13 | 45.25 | 36.13 | 25.50 | 38.63 |

**For Lectureship**

SUBJECT |
GEN | OBC | SC | ST | PH |

Mathematics |
47.82 | 40.73 | 32.52 | 25.00 | 34.77 |

### CSIR UGC NET MATHS COACHING:-

**EXAM SCHEME**

**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.

**(CLICK HERE)**

**FOR MODEL QUESTION PAPER FOR CSIR UGC NET MATHEMATICS 2017**

**CSIR UGC NET MATHS COACHING**

CSIR-UGC holds a national eligibility test twice a year in the month of June and December for JRF and Lectureship (LS). Approximately 12000 students appear from Maths stream and among them approximately two hundred students awarded eligibility certificate from CSIR/UGC, which make them eligible for teaching in various degree institutions all over India.

**CSIR NET qualified candidates given below are also eligible for lecturer-ship.**

**CSIR NET qualified candidates given below are also eligible for lecturer-ship.**

1. |
GEN | 834 + 730 = 1564 |

2. |
OBC | 457 + 397 = 854 |

3. |
SC | 264 + 230 = 494 |

4. |
ST | 123 + 107 = 230 |

5. |
PWD | 45 + 36 = 81 |

Total |
1723 + 1500 = 3223 |

**SYLLABUS FOR MATHEMATICAL SCIENCES**

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

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

**(Common Syllabus for Part ‘B & C’)**

### CSIR UGC NET MATHS COACHING:-

**UNIT – 1**

**Analysis**

**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, 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. Metric spaces, compactness, connectedness. Normed Linear Spaces. Spaces of Continuous functions as examples.

**CSR RECOMMENDED BOOKS**

Principle of Mathematical Analysis -S.L.Gupta,N.R.Gupta (Pearson Publication).S.L.Gupta, N.R. Gupta (Pearson Publication)Real Analysis -Robert G Bartle (Wiley Publication) Real Analysis -M.D. Raisinghania (S. Chand Publication)

**Linear Algebra**

**Linear Algebra**

Vector spaces, subspace, 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.

**CSR RECOMMENDED BOOKS**

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**

**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.

**CSR RECOMMENDED BOOKS**

Complex Variables -H.S. Kasana(PHI Publication )Complex Analysis -S Ponnusamy(Narosa Publication)Complex Analysis -R.V. Churchill (Tata McGraw – Hill Publication)

**Algebra**

**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, homeomorphisms, cyclic groups, permutation groups, Cayley’s theorem, classequations, 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.

**CSR RECOMMENDED BOOKS**

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)

# UNIT – 3

**Ordinary Differential Equations**

**Ordinary Differential Equations**

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.

**CSR RECOMMENDED BOOKS**

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) **

**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.

**CSR RECOMMENDED BOOKS**

Partial Differential Equations -T. Amaranath (Narosa Publication) Introduction To Partial Differential Equations -K. Sankara Rao (PHI Publication )

**Numerical Analysis**

**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.

### CSR RECOMMENDED BOOKS

Numerical Analysis -R.K. Jain, S.R.K. Iyengar (New Age Publication )

**Calculus of Variations**

**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.

**CSR RECOMMENDED BOOKS**

Calculus of Variations -A. S. GUPTA (Narosa Publication

**Linear Integral 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.

**CSR RECOMMENDED BOOKS**

Linear Integral Equations -M D Raisinghania (S.Chand Publication)

**Classical Mechanics**

**Classical Mechanics**

Generalised 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.

**CSR RECOMMENDED BOOKS**

Classical Mechanics -J. 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.

⦁ 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, tests for linear hypotheses and confidence intervals. 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 randomised designs , randomised blocks and Latin-square designs. Connectedness, and orthogonal block designs, BIBD. 2K factorial experiments: confounding and construction. Series and parallel systems, hazard function and failure rates, censoring and life testing. ⦁ Linear programming problem. 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.

**CSR RECOMMENDED BOOKS**

Probability and statistics -S. C. Gupta and V. K. Kapoor(S.Chand Publication)

**Syllabus of Part – C**

**Syllabus of Part – C**

Mathematics: This section shall carry questions from Unit I, II and III. Statistics: Apart from Unit IV, this section shall also carry questions from the following areas. Sequences and series, convergence, continuity, uniform continuity, differentibility. Remann integeral, improper integrals, algebra of matrices, rank and determinant of matrices, linear equations, eigenvalues and eigenvectors, quadratic forms.

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