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**Dips Academy, MATHEMATICS study material for , Gate, Net etc. pdf **| **CSIR NET / JRF Mathematics Volume – 1 (A Perfect book for your revision plan)** book pdf

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**DIPS ACADEMY STUDY MATERIAL*** is enough to crack IITJAM 2023, NET 2023, GATE 2023 and many more entraces. In this post you will get the MATHEMATICS DIPS ACADEMY STUDY MATERIALS, this study material enhanced your knowledge , concepts and thinking ability through which you can easily crack the exam for which you are preparing for.*

Here, we provided to CSIR NET/JRF Mathematics Volume-1. Mathematics includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature.

Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences. Applied mathematics has led to entirely new

mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Mathematics studies numbers, structure, and change and draws its origins from early philosophy. This ancient discipline is commonly used for calculations, counting, and

measurements. However, mathematics is a complex field that also involves theories, the discovery of patterns, development of law, nicknamed “The queen of sciences”. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Throughout history, a significant amount of mathematicians such as Galileo Galilei, Albert Einstein, Pythagoras, Archimedes, and many others brought innovations in mathematics and gave birth to new theories and solutions to analytical problems. Mathematical principles can also be found in disciplines such as medicine, natural sciences, engineering, finance, and social sciences. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Students who hold a Bachelor’s degree in mathematics can turn to applied mathematics, statistics, physics, or engineering if they wish to continue their studies. Such a program develops skills such as knowledge of arithmetic, algebra, trigonometry, and strong deductive reasoning. After graduating from a Master’s degree in mathematics, students have the choice to be employed as operational researchers,

statisticians, aerospace engineers, accountants, software testers, or teachers. Free download PDF CSIR NET/JRF Mathematics Volume-1.

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The University Grants Commission (UGC) conducts the National Eligibility Test (NET) twice a year to determine eligibility for lectureship and for the award of Junior Research Fellowship (JRF) to Indian nationals to ensure minimum standards for the entrants in the teaching profession and research. UGC NET Tutor Mathematical Sciences has been revised as per the new syllabi and examination pattern issued by the UGC for Mathematical Sciences. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Mathematics is very helpful for the aspirants of CSIR UGC NET Mathematics, IIT JAM Mathematics, GATE mathematics, NBHM, TIFR, and all different tests with a similar syllabus. Mathematics is designed for the students who are making ready for numerous national degree aggressive examinations and additionally evokes to go into Ph. D. Applications by using manner of qualifying the numerous the front examination. Free download PDF CSIR NET/JRF Mathematics Volume-1.

Being a CSIR NET aspirant, you all might be wishing to get success in CSIR NET Exam in your very first attempt, and getting the “key” that will transform your preparation into

success is, to practice more and more. Free download PDF CSIR NET/JRF Mathematics Volume-1.

After applying for CSIR NET Exam, you might be planning forthe strategies to prepare for the exam and trying to arrange the relevant study material. As an important part of CSIR Study Material, you wish to include CSIR NET Question Paper of previous years for practicing, because every practice is a learning process that will lead you to get success in exams. Free download PDF CSIR NET/JRF Mathematics Volume-1.

CSIR NET Syllabus For Mathematics:

The CSIR NET Syllabus for Mathematical Sciences is as

under:

- Analysis
- Complex Analysis
- Linear Algebra
- Algebra
- Topology
- Ordinary Differential Equations
- Partial Differential Equations
- Numerical Analysis
- Linear Integral Equations
- Calculus of Variations
- Classical Mechanics
- Exploratory Data Analysis
- Descriptive Statistics

CSIR NET Exam Pattern 2020 :

NTA has released the CSIR NET Exam Pattern for all the five subjects. Candidates will have to pick any one subject and apply for the same. The CSIR UGC NET exam pattern and marking scheme are different for all the subjects. However, Part A syllabus is the same for all subjects.

- CSIR NET question paper for each subject is divided into three parts namely, Part A, Part B, Part C.
- All three sections are compulsory.
- There will be no break between the three sections.
- All 3 parts will have only Multiple Choice Questions
- (MCQs).
- The CSIR NET 2020 will be conducted for a total of
- 200 marks.
- The exam will be held for a duration of 3 hours.

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## CSIR UGC NET 2023 Exam Pattern – Mathematical Sciences

CSIR NET Mathematical Sciences exam will have 20, 40 and 60 questions, however, candidates have to attempt only 15, 25 and 20 questions in Part-A, Part-B and Part-C respectively.

**Each question will have 4 alternatives, Questions in Part A and Part B will have only one correct answer whereas Part-C questions may have one or more correct answers.**- Credit will be given only when exact number of correct answers are marked.
- There will be a negative marking of 25% in Part A and Part B. However, no negative marking is applicable in Part-C.

CSIR NET Mathematical Science Paper Parts | Number of Questions in CSIR NET Mathematical Science Paper | CSIR NET Mathematical Science Paper Marks |
---|---|---|

A | 20 (Questions to be attempted: 15) | 30 |

B | 40 (Questions to be attempted: 25) | 75 |

C | 60 (Questions to be attempted: 20) | 95 |

Total | 120 (Questions to be attempted: 60) | 200 |

**Marking scheme**: Each question in Part A carries two marks weightage. On the other hand, each question in Part B and C carries weightage of three and 4.75 marks, respectively. There is negative marking of 0.5 and 0.75 marks in Part A and B. However, there is no negative marking for questions in Part C of the exam.

CSIR NET Mathematical Science Paper Parts | Marks Allotted for Each Question | Marks Deducted for Each Question |
---|---|---|

A | +2 | -0.5 |

B | +3 | -0.75 |

C | +4.75 | 0 |

### CSIR NET Syllabus for Mathematical Sciences

There are four units in CSIR NET Mathematical Sciences Syllabus. All students are supposed to answer Unit 1 questions, students with mathematics background may attempt additional questions from Unit 2 and 3 whereas students with statistics background are expected to solve problems of Unit 4. Unit-wise syllabus of CSIR NET Mathematical Sciences is tabulated below:

- Unit 1: Analysis Linear Algebra
- Unit 2: Complex Analysis, Algebra, Topology
- Unit 3: Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), Numerical Analysis, Calculus of Variations, Linear Integral Equations, Classical Mechanics
- Unit 4: Statistics, Exploratory Data Analysis

**CSIR – UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship**

**COMMON SYLLABUS FOR PART ‘B’ AND ‘C’ MATHEMATICAL SCIENCES**

**》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, 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.

**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

**》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, 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.

**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, 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.

**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, 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 andRunge-Kutta methods.

**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 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.

**》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.

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.

All students are expected to answer questions from Unit I. Students in mathematics are expected to answer additional question from Unit II and III. Students with in

statistics are expected to answer additional question from Unit IV.

## Advantages of Solving CSIR – NET / JRF MATHEMATICS PREVIOUS YEARS QUESTIONS PAPERS

• By practicing the CSIR – NET / JRF papers of last years, you’ll be able to understand the IIT JAM Exam Syllabus and Pattern.

• By solving the last years CSIR – NET / JRF papers, you’ll find an idea about the questions that what kind of questions were asked and what kind of questions can be asked.

*• Also By continuous practicing of theCSIR – NET / JRF last years papers, you’ll be able to rectify your sharpness, accuracy, capacity and also time management skills.*

**How can I start preparing for CSIR – NET / JRF for Mathematics ?**

**Step-wise CSIR – NET / JRF Maths 2023 Preparation Plan**

Aspirants should check the following steps to start with the preparation process of CSIR – NET / JRF 2023.

**Step 1:** Know the CSIR – NET / JRF syllabus thoroughly.

**Step 2:** Understand the CSIR – NET / JRF exam pattern and marking scheme.

**Step 3:** Get the best books to study for CSIR – NET / JRF and other study material.

**Step 4:** Make a monthly time-table, a weekly time-table, and a daily time-table.

**Step 5:** Solve past years’ question papers, sample papers, and mock tests.

**CSIR NET / JRF Mathematics Volume – 1 (A Perfect book for your revision plan)**

### 》 **BOOK DETAILS **《

Book name | CSIR NET / JRF Mathematics Volume – 1(A Perfect book for your revision plan) |

Authors | Rajendra Dubey |

Publication | Dips Academy |

Language | English |

Subject | Mathematics |

Format | Pdf |

File size ( in MB) | MB |

NOTE : – If you need anything else more like ebooks, video lectures, syllabus etc regarding your Preperation / Examination then do 📌 mention in the Comment Section below. |

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