CSIR NET Mathematical Science 2023: List of Most Important Topics – Check Here!

By BYJU'S Exam Prep

Updated on: September 13th, 2023

CSIR NET Mathematical Science 2023: CSIR NET Mathematical Science exam is a National level exam that CSIR conducts every year to select eligible science graduates for JRF and Lecturership. If you want to make your career as a Maths Lecturer at the university and college level or as a teaching faculty or want to get a fellowship as JRF in a reputed institute to do further studies, then you have come to a perfect place!

The CSIR NET Exam is a gateway for those aspiring candidates seeking admission to make their career as Junior Research Fellowship (JRF) and Associate Professor in Mathematical Science or any other field. If you are preparing for the CSIR NET Mathematical science 2023 exam, you must check the most important topics explained here to avoid missing any 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 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, emphasizing analytical, logical reasoning, quantitative comparison, series formation, graphical analysis, numerical ability, puzzles, 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 logically 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


  • Real number system as a completely 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. 


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


  • 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


  • 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?

THE 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 exam, ensure you have accurate knowledge of the topics and units covered under the CSIR-NET Mathematical Science 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 TimeTable:

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: 

Practicing more and more previous year’s question papers is the only key to success in any competitive exam. Therefore, you should solve as many mathematical science 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. 


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