CSIR NET Mathematical Science 2023: List of Most Important Topics

CSIR-NET Mathematical Science 2023: Most Important Topics

The test booklet for the CSIR-NET Mathematical Sciences paper will consist of 3 sections - A, B, and C. It will comprise multiple-choice questions type (MCQs). According to the latest exam pattern of the exam, there will be 120 questions in the CSIR NET Mathematical Science paper. Section A is of 30 marks, Section B is 75, and Section C is 95. The exam consists of 200 marks. Negative marking will also be applicable for each section.

Let’s now look at each section of the CSIR NET Mathematical Science exam comprises of:

Section A - This section is common for all subjects of the CSIR UGC NET paper. In this section, questions will be based on General Aptitude, emphasising analytical, logical reasoning, quantitative comparison, series formation, graphical analysis, numerical ability, puzzles, and general science etc.

Section B - This section is subject-based, i.e. Mathematical Science, and contains questions of 3 marks each generally covering the units given in the CSIR-NET syllabus. Each correct answer to the given problem will be awarded 3 marks, while 0.75 marks will be deducted as a negative marking.

Section C - This section is a critical, scoring and most important area in the CSIR NET Mathematical Science paper. Subject-based questions contain a high value, i.e. 4.75 marks that may test the candidate’s scientific knowledge of concepts and/or applying the scientific concepts. In addition, the nature of the questions is generally logical based and here, a candidate is expected to use scientific knowledge to write the solution for the given scientific problem.

Sections	No. of Qs.	No. of Qs. to be attempted	Total Marks	Negative marking for each Q.	Duration
SECTION A	20	15	30	0.5	3 hrs
SECTION B	40	25	75	0.75
SECTION C	60	20	95	0

List of Most Important Topics for CSIR-NET Mathematical Science 2023

We have provided below the most important topics for the Mathematical Science paper that our subject-matter experts meticulously designed to give you the most standard set of study materials to be focused upon.

Unit 1: Analysis and Linear Algebra

Analysis:

Real number system as a complete ordered field
Archimedean property, supremum, infimum
Sequences and series, convergence
Bolzano Weierstrass theorem
Heine Borel theorem.
Continuity & Differentiability

Linear Algebra:

Algebra of matrices
Cayley-Hamilton theorem
Matrix representation of linear transformations
Diagonal forms, triangular forms, Jordan forms. Quadratic forms, reduction and classification of quadratic forms

Unit 2: Complex Analysis, Algebra and Topology

Complex Analysis:

Algebra of complex numbers
Polynomials
Analytic functions
Cauchy-Riemann equations. Contour integral, Cauchy’s theorem
Cauchy’s integral formula, Liouville’s theorem,
Taylor series, Laurent series, calculus of residues.

Algebra:

Permutations & Combinations,
Chinese Remainder Theorem
Euler’s Ø- function
Cayley’s theorem
Sylow theorems.
Fields, finite fields, field extensions, Galois Theory

Topology:

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

Unit 3: ODEs, PDEs and Classical Mechanics

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

Classical Mechanics:

Generalized coordinates, Lagrange’s equations, Hamilton’s canonical equations
Hamilton’s principle and the principle of least action
The 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: Probability and statistics

Probability:

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.

Data Reduction Techniques:

Principle component analysis, Discriminant analysis, Cluster analysis, Canonical correlation.
Simple random sampling, stratified sampling and systematic sampling. Probability is proportional to size sampling.

How to Prepare for CSIR NET Mathematical Science?

CSIR NET exam is considered a difficult exam to crack, but you can definitely qualify for this exam if you prepare with a well-focused mind without getting confused. We are providing here some useful tips for your CSIR NET Mathematical Science preparation: -

1. Syllabus Plays A Crucial Role:

Before you start preparing for the CSIR-NET mathematical science exam, ensure you have accurate knowledge of the topics and units covered under the syllabus.

2. Good Study Material:

You should always refer to the good quality CSIR NET Mathematics Study Material that will help you to prepare, revise, and clear your doubts. So, choose it carefully.

3. Make A Proper Time Table:

Before beginning your CSIR-NET Mathematical Science paper preparation, you need to set a defined and comprehensive timetable. Make a timetable at your own convenience. If you manage your preparations with good time management, you will definitely find the accurate time to study each and every important topic.

4. Study Notes:

While studying, make a habit of creating paper notes side by side. It will be beneficial for you in learning quickly and revise before the examination. Also, it will benefit you in memorizing the topics.

5. Previous Year Question Papers:

Practising more and more previous year's question papers is the only key to success in any competitive exam. Therefore, you should solve as many previous year question papers before an exam to have a good command of your speed and accuracy.

6. Complete Revision:

As we stated earlier, revision is a must and a crucial part to crack the exam. Therefore, make a habit of revising the concepts as much as you can before appearing for the exam.

FAQs

How many sections does CSIR NET Mathematical Science 2022 contains?

The question paper for the CSIR-NET Mathematical Sciences paper will consist of 3 sections - A, B, and C. It will comprise multiple-choice questions type (MCQs). According to the latest exam pattern of the exam, there will be 120 questions in the CSIR NET Mathematical Science paper. Section A is of 30 marks, Section B is 75, and Section C is 95. The exam consists of 200 marks. Negative marking will also be applicable for each section.

How will making study notes be helpful in preparing for the CSIR NET Mathematical Science 2022 exam?

Preparing a detailed study note will be beneficial for you in learning quickly and revise before the examination. Also, it will benefit you in memorizing the topics.

What kind of questions are there in part A of CSIR NET Mathematical science exam 2022?

This section is common for all subjects of the CSIR UGC NET paper. In this section, questions will be based on General Aptitude, emphasising analytical, logical reasoning, quantitative comparison, series formation, graphical analysis, numerical ability, puzzles, and general science etc

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