{"id":3760,"date":"2025-11-22T13:08:30","date_gmt":"2025-11-22T13:08:30","guid":{"rendered":"https:\/\/vedprep.com\/exams\/?p=3760"},"modified":"2026-03-20T11:01:30","modified_gmt":"2026-03-20T11:01:30","slug":"csir-net-mathematics-sciences-syllabus-2026","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/csir-net\/csir-net-mathematics-sciences-syllabus-2026\/","title":{"rendered":"CSIR NET Mathematics Sciences Syllabus 2026 : Download Pdf"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">CSIR NET Mathematics Sciences syllabus aims to strengthen understanding of mathematical principles and their applications. It emphasizes problem-solving, logical reasoning, and analytical skills across areas such as real analysis, complex analysis, algebra, and statistics. <\/span><b>CSIR NET Mathematics preparation<\/b><span style=\"font-weight: 400;\"> is a question many aspirants ask. The key lies in <\/span><b>understanding the syllabus thoroughly<\/b><span style=\"font-weight: 400;\">, covering all important topics like Algebra, Analysis, Mathematical Methods, and Applied Mathematics. Effective preparation involves <\/span><b>consistent practice of previous years\u2019 papers and mock tests<\/b><span style=\"font-weight: 400;\">, maintaining conceptual clarity, and managing time efficiently. By following a <\/span><b>structured study plan<\/b><span style=\"font-weight: 400;\"> and focusing on both theory and problem-solving, candidates can systematically prepare for the exam and increase their chances of success.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is a high-level academic framework divided into four distinct units. It encompasses core subjects like Real Analysis, Linear Algebra, and Complex Analysis, alongside applied topics such as Differential Equations and Numerical Analysis. Mastery of this syllabus is essential for securing a Junior Research Fellowship (JRF) or Assistant Professorship in Indian universities.<\/span><\/p>\n<h2><b>CSIR NET Mathematics Sciences Exam Overview\u00a0<\/b><\/h2>\n<p><b>CSIR NET exam<\/b><span style=\"font-weight: 400;\"> is a prestigious national-level examination conducted twice a year by the <\/span><b>NTA (National Testing Agency)<\/b><span style=\"font-weight: 400;\">. It covers five subjects: Life Sciences, Physical Sciences, Chemical Sciences, Earth, Atmospheric, Ocean and Planetary Sciences, and <\/span><a href=\"https:\/\/drive.google.com\/file\/d\/1MLD7G3YvPuiZnBZK3rl3jrj4tf-Hpgdv\/view\" target=\"_blank\" rel=\"noopener nofollow\"><b>Mathematical <\/b><\/a><b>Sciences<\/b><span style=\"font-weight: 400;\">. For candidates aspiring to pursue a career as a <\/span><b>Junior Research Fellow (JRF) or Assistant Professor in Mathematical Sciences<\/b><span style=\"font-weight: 400;\">, understanding <\/span><b>how to prepare for CSIR NET Mathematics preparation<\/b><span style=\"font-weight: 400;\"> is crucial.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">This national-level exam can be effectively cracked with a clear <\/span><b>preparation strategy<\/b><span style=\"font-weight: 400;\">, access to the right <\/span><b>study materials<\/b><span style=\"font-weight: 400;\">, and consistent practice. Candidates must be aware of the <\/span><b>best study resources<\/b><span style=\"font-weight: 400;\">, including<\/span><a href=\"https:\/\/www.vedprep.com\/\"><span style=\"font-weight: 400;\">\u00a0 vedprep<\/span><\/a><span style=\"font-weight: 400;\"> online references, and <\/span><b>previous years\u2019 question papers<\/b><span style=\"font-weight: 400;\">, and know how to use them efficiently.<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\" wp-image-3640 aligncenter\" src=\"https:\/\/vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003-300x166.png\" alt=\"\" width=\"501\" height=\"277\" srcset=\"https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003-300x166.png 300w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003-1024x567.png 1024w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003-768x425.png 768w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003-1536x850.png 1536w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-17-215003.png 1675w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<h2><b>CSIR NET Mathematics Sciences Exam Preparation Tips<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The <\/span><b>CSIR NET Mathematical Sciences exam<\/b><span style=\"font-weight: 400;\"> is one of the most competitive national-level exams, conducted by the <\/span><b>NTA<\/b><span style=\"font-weight: 400;\"> to select candidates for the roles of <\/span><b>Junior Research Fellow (JRF)<\/b><span style=\"font-weight: 400;\"> and <\/span><b>Assistant Professor<\/b><span style=\"font-weight: 400;\">. The exam is divided into <\/span><b>three parts \u2013 Part A, Part B, and Part C<\/b><span style=\"font-weight: 400;\">, with a total of <\/span><b>120 questions<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Some of the <\/span><b>key topics<\/b><span style=\"font-weight: 400;\"> in the CSIR NET Mathematical Sciences syllabus include:<\/span><\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Linear Algebra<\/b><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Complex Analysis<\/b><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Ordinary Differential Equations (ODEs)<\/b><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Partial Differential Equations (PDEs)<\/b><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Classical Mechanics<\/b><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li aria-level=\"1\"><b>And other core areas of mathematical sciences<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Success in this exam depends not only on understanding the concepts but also on <\/span><b>strategic preparation<\/b><span style=\"font-weight: 400;\">. Here, we share some of the <\/span><b>best CSIR NET Mathematical Sciences preparation tips<\/b><span style=\"font-weight: 400;\"> that can help candidates plan their study schedule, strengthen problem-solving skills, and increase their chances of cracking the exam.\u00a0\u00a0<\/span><\/p>\n<p><b>CSIR NET Mathematics Sciences Exam Pattern<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Understanding the <\/span><b>exam pattern<\/b><span style=\"font-weight: 400;\"> is a critical step in effective preparation. The <\/span><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/csir-net-application-form-2026\/\" rel=\"nofollow noopener\" target=\"_blank\"><span style=\"font-weight: 400;\">CSIR NET <\/span><\/a><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-mathematics-2025\/\" target=\"_blank\" rel=\"noopener nofollow\"><span style=\"font-weight: 400;\">Mathematical Sciences <\/span><\/a><span style=\"font-weight: 400;\">exam may seem challenging initially, but with proper analysis,\u00a0<\/span><\/p>\n<table style=\"width: 83.2499%;\">\n<tbody>\n<tr>\n<td style=\"width: 47.25%;\"><b>Particulars<\/b><\/td>\n<td style=\"width: 239.25%;\"><b>Details<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 47.25%;\"><span style=\"font-weight: 400;\">Duration of examination<\/span><\/td>\n<td style=\"width: 239.25%;\"><span style=\"font-weight: 400;\">3 hours (180 minutes)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 47.25%;\"><span style=\"font-weight: 400;\">Total number of questions<\/span><\/td>\n<td style=\"width: 239.25%;\"><span style=\"font-weight: 400;\">120<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 47.25%;\"><span style=\"font-weight: 400;\">Total marks<\/span><\/td>\n<td style=\"width: 239.25%;\"><span style=\"font-weight: 400;\">200<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 47.25%;\"><span style=\"font-weight: 400;\">Type of questions<\/span><\/td>\n<td style=\"width: 239.25%;\"><span style=\"font-weight: 400;\">Objective Type Questions<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 47.25%;\"><span style=\"font-weight: 400;\">Negative marking<\/span><\/td>\n<td style=\"width: 239.25%;\"><span style=\"font-weight: 400;\">Part A &amp; B: 25%<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Part C: No negative marking<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: center;\"><iframe src=\"\/\/www.youtube.com\/embed\/qY9pbn5ZF8M\" width=\"720\" height=\"404\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/h2>\n<h2><b>CSIR NET <\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-mathematics-2025\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>Mathematics<\/b><\/a><b> Sciences Syllabus preparation<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Before starting preparation, the first and foremost step is to thoroughly go through the CSIR NET Mathematics\u00a0 syllabus and exam pattern. Understanding the exam structure, marking scheme, and type of questions helps candidates plan their preparation effectively and know what to expect on the actual exam day.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Unit<\/b><\/td>\n<td><b>Topics<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Unit 1<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Analysis, Linear Algebra<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Unit 2<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Complex Analysis, Algebra, topology<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Unit 3<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), Numerical Analysis, Calculus of Variations, Linear Integral Equations, Classical Mechanics<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Unit 4<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Descriptive Statistics, Exploratory Data Analysis<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Part B and Part C focus on <\/span><b>conceptual understanding and problem-solving<\/b><span style=\"font-weight: 400;\"> in the above topics.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Candidates must prioritize <\/span><b>core areas<\/b><span style=\"font-weight: 400;\"> like Linear Algebra, ODEs, PDEs, and Classical Mechanics as they are frequently asked in previous papers.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Reviewing the syllabus before planning your study schedule ensures <\/span><b>efficient and targeted preparation<\/b><span style=\"font-weight: 400;\">.<\/span><\/li>\n<\/ul>\n<p><b>Also read &#8211;<\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-physical-science\/\" target=\"_blank\" rel=\"noopener nofollow\"><b> Important Topics for CSIR NET Physical Science: Syllabus, Best Books, Revision Strategy, PYQs<\/b><\/a><\/p>\n<h2><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/csir-net-application-form-2026\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>CSIR NET Mathematical Science Syllabus Unit-wise\u00a0<\/b><\/a><\/h2>\n<p><span style=\"font-weight: 400;\">The CSIR NET Mathematical Sciences syllabus includes Unit 1, Unit 2, Unit 3 and Unit 4: for complete exam preparation.<\/span><\/p>\n<p><img decoding=\"async\" class=\" wp-image-3761 aligncenter\" src=\"https:\/\/vedprep.com\/exams\/wp-content\/uploads\/CSIR-NET-Mathematical-Science-Syllabus-2025-Unit-wise-Topics-\u200b\u200b-200x300.jpeg\" alt=\"\" width=\"481\" height=\"722\" srcset=\"https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/CSIR-NET-Mathematical-Science-Syllabus-2025-Unit-wise-Topics-\u200b\u200b-200x300.jpeg 200w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/CSIR-NET-Mathematical-Science-Syllabus-2025-Unit-wise-Topics-\u200b\u200b-683x1024.jpeg 683w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/CSIR-NET-Mathematical-Science-Syllabus-2025-Unit-wise-Topics-\u200b\u200b-768x1152.jpeg 768w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/CSIR-NET-Mathematical-Science-Syllabus-2025-Unit-wise-Topics-\u200b\u200b.jpeg 1024w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<h2><b>CSIR NET Mathematics Sciences Syllabus PDF<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Mathematical Sciences <\/span><b>Syllabus pdf <\/b><span style=\"font-weight: 400;\">can be downloaded directly from the link given below or the NTA or CSIR HRDG websites.<\/span><\/p>\n<table style=\"width: 81.657%;\">\n<tbody>\n<tr>\n<td style=\"width: 234.576%;\" colspan=\"2\"><b>CSIR NET Mathematical Sciences Syllabus PDF<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.6356%;\"><b>Subjects<\/b><\/td>\n<td style=\"width: 162.94%;\"><b>Download Link<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.6356%;\"><b>CSIR NET Syllabus Mathematical Sciences<\/b><\/td>\n<td style=\"width: 162.94%;\"><a href=\"https:\/\/csirhrdg.res.in\/SiteContent\/ManagedContent\/ContentFiles\/20201221140054469mathmeticascience_syllbus.pdf\" target=\"_blank\" rel=\"noopener nofollow\"><b>Download PDF<\/b><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><b>CSIR NET All Syllabus PDF<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The official CSIR NET 2025 syllabus PDF for all subjects (including General Aptitude \u2013 Part A, Life Sciences, Chemical Sciences, Physical Sciences, and Earth Sciences) can be downloaded directly from the link given below or the NTA or CSIR HRDG websites.<\/span><\/p>\n<table style=\"width: 92.0884%;\">\n<tbody>\n<tr>\n<td style=\"width: 275.439%;\" colspan=\"2\">\n<p style=\"text-align: center;\"><b>CSIR NET Syllabus PDF<\/b><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.5175%;\"><b>Subjects<\/b><\/td>\n<td style=\"width: 205.921%;\"><b>Download Link<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.5175%;\"><b>CSIR NET Syllabus Life Sciences<\/b><\/td>\n<td style=\"width: 205.921%;\"><a href=\"https:\/\/csirhrdg.res.in\/SiteContent\/ManagedContent\/ContentFiles\/20201221135946325lifescience_syllbus.pdf\" target=\"_blank\" rel=\"noopener nofollow\"><b>Download PDF<\/b><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.5175%;\"><b>CSIR NET Syllabus Chemical Sciences<\/b><\/td>\n<td style=\"width: 205.921%;\"><a href=\"https:\/\/csirhrdg.res.in\/SiteContent\/ManagedContent\/ContentFiles\/20201221135711180chemical_science_syllabus.pdf\" target=\"_blank\" rel=\"noopener nofollow\"><b>Download PDF<\/b><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.5175%;\"><b>CSIR NET Syllabus Physical Sciences<\/b><\/td>\n<td style=\"width: 205.921%;\"><a href=\"https:\/\/csirhrdg.res.in\/SiteContent\/ManagedContent\/ContentFiles\/20201221140202824physicalscience_syllbus.pdf\" target=\"_blank\" rel=\"noopener nofollow\"><b>Download PDF<\/b><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.5175%;\"><b>CSIR NET Syllabus Earth Sciences<\/b><\/td>\n<td style=\"width: 205.921%;\"><a href=\"https:\/\/csirhrdg.res.in\/SiteContent\/ManagedContent\/ContentFiles\/20201221135834347earth_science_syllabus.pdf\" target=\"_blank\" rel=\"noopener nofollow\"><b>Download PDF<\/b><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><b>How to Download CSIR NET Syllabus PDF\u00a0<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">To download the CSIR NET Syllabus PDF:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Visit the official National Testing Agency (NTA) CSIR NET <\/span><a href=\"http:\/\/csirnet.nta.ac.in\" rel=\"nofollow noopener\" target=\"_blank\"><span style=\"font-weight: 400;\">website: csirnet.nta.ac.in.<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Look for the \u201cSyllabus\u201d or \u201cInformation Bulletin\u201d section on the homepage.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Download the syllabus PDF for your chosen subject (Life Sciences, Physical Sciences, Chemical Sciences, Earth Sciences, or Mathematical Sciences) from the provided links.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The downloaded PDF will contain the detailed, topic-wise syllabus for Part A (General Aptitude) and Parts B\/C (subject-specific).<\/span><\/li>\n<\/ol>\n<p><b>Also read &#8211;<\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/csir-net-application-form-2026\/\" target=\"_blank\" rel=\"noopener nofollow\"><b> CSIR NET Application Form 2026 : Age Limit, Eligibility Criteria, Process, Fee, Exam Dates, Exam Centres<\/b><\/a><\/p>\n<h2><img decoding=\"async\" class=\" wp-image-3764 aligncenter\" src=\"https:\/\/vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033-300x141.png\" alt=\"\" width=\"711\" height=\"334\" srcset=\"https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033-300x141.png 300w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033-1024x481.png 1024w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033-768x361.png 768w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033-1536x722.png 1536w, https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/Screenshot-2025-11-22-111033.png 1869w\" sizes=\"(max-width: 711px) 100vw, 711px\" \/><\/h2>\n<h2><b>CSIR NET Mathematics Science Syllabus 2025 Unit-wise Topics \u200b\u200b<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Explore the complete CSIR NET Mathematical Science Syllabus 2025 with detailed unit-wise topics, including Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics for effective exam preparation.<\/span><\/p>\n<h3><b>Unit 1: Analysis CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Set Theory &amp; Real Numbers<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Elementary Set Theory<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Basics of sets, operations, relations, Cartesian product<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Finite, Countable, Uncountable Sets<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Classification of sets by cardinality<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Real Number System<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Complete ordered field; supremum and infimum<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Archimedean Property<\/span><\/td>\n<td><span style=\"font-weight: 400;\">For any real numbers x,y&gt;0x, y &gt; 0x,y&gt;0, \u2203 n\u2208Nn \\in \\mathbb{N}n\u2208N s.t. nx&gt;ynx &gt; ynx&gt;y<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Sequences &amp; Series<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Convergence of Sequences<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definition of limit; monotone and bounded sequences<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">limsup &amp; liminf<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Upper and lower limits of sequences<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Series<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Convergence tests, absolute and conditional convergence<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Theorems in Analysis<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Bolzano-Weierstrass Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Every bounded sequence has a convergent subsequence<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Heine-Borel Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Closed and bounded subsets of Rn\\mathbb{R}^nRn are compact<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Continuity &amp; Differentiability<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Continuity &amp; Uniform Continuity<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definitions and properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Differentiability<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Derivative at a point; linear approximation<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Mean Value Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Relates derivative to function increments<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Sequences &amp; Series of Functions<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Pointwise &amp; Uniform Convergence<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definitions; uniform convergence preserves continuity<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Integration<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Riemann Sums &amp; Riemann Integral<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definition of integral using partitions<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Improper Integrals<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Integrals over infinite intervals or with unbounded integrand<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Advanced Function Properties<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Monotonic Functions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Increasing, decreasing, and their limits<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Types of Discontinuity<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Removable, jump, essential<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Bounded Variation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Functions whose total variation is finite<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Lebesgue Measure &amp; Integral<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Generalization of length and integral for more functions<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Functions of Several Variables<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Directional &amp; Partial Derivatives<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Rate of change in a direction or along coordinate axes<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Derivative as Linear Transformation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Total derivative as a linear map approximating function<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Inverse &amp; Implicit Function Theorems<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Conditions for existence of local inverse or implicit functions<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Metric Spaces &amp; Topology<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Metric Spaces<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definition, open\/closed sets, convergence<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Compactness &amp; Connectedness<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Fundamental topological properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Normed Linear Spaces &amp; Functional Analysis<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Normed Spaces<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Vector spaces with norm; convergence and completeness<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Spaces of Continuous Functions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Examples of normed spaces; sup norm, C[a,b]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 1: Linear Algebra CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Vector Spaces<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Vector Spaces &amp; Subspaces<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definition, examples, closure under addition and scalar multiplication<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Linear Dependence &amp; Independence<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Linear combination of vectors; dependence criteria<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Basis &amp; Dimension<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Minimal generating set; dimension as number of basis vectors<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Algebra of Linear Transformations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Addition, scalar multiplication, composition of linear maps<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Matrices &amp; Linear Equations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Algebra of Matrices<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Matrix addition, multiplication, transpose, inverse<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Rank &amp; Determinant<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Rank: dimension of row\/column space; determinant properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Linear Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Systems of equations; solutions via matrix methods<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Eigenvalues &amp; Eigenvectors<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Eigenvalues &amp; Eigenvectors<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Av=\u03bbvAv = \\lambda vAv=\u03bbv; spectral properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cayley-Hamilton Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Every square matrix satisfies its characteristic equation<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Matrix Representation<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Linear Transformations as Matrices<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Representation depends on choice of basis<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Change of Basis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Similarity transformations; coordinate changes<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Canonical Forms<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Diagonal, triangular, Jordan forms; simplification of matrices<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Inner Product Spaces<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Inner Product &amp; Orthonormal Basis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Length, angle, orthogonality, Gram-Schmidt process<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Quadratic Forms<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Quadratic Forms<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Expression Q(x)=xTAxQ(x) = x^T A xQ(x)=xTAx; symmetric matrices<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Reduction &amp; Classification<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Diagonalization; positive definite, negative definite, indefinite forms<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>You can also check &#8211; <\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/how-to-prepare-for-csir-net-mathematics-preparation\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>How to prepare for CSIR NET Mathematics preparation : Syllabus,Tips Preparation strategy, Books<\/b><\/a><\/p>\n<h3><b>Unit 2: Complex Analysis CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Complex Numbers &amp; Functions<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Algebra of Complex Numbers<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Addition, multiplication, modulus, conjugate, polar form<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Complex Plane<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Representation of complex numbers; Argand diagram<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Polynomials &amp; Power Series<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Roots of polynomials, radius of convergence, analytic properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Transcendental Functions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Exponential, logarithmic, trigonometric, hyperbolic functions in complex domain<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Analytic Functions<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Analyticity<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Function differentiable in complex sense; Cauchy-Riemann equations<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cauchy-Riemann Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Necessary condition for differentiability of complex functions<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Complex Integration<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Contour Integrals<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Line integrals along paths in complex plane<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cauchy&#8217;s Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Integral over closed contour of analytic function is zero<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cauchy&#8217;s Integral Formula<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Value of analytic function inside contour in terms of integral over contour<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Liouville&#8217;s Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Bounded entire functions are constant<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Maximum Modulus Principle<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Maximum of modulus occurs on boundary of domain<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Schwarz Lemma<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Bounds analytic functions mapping unit disk to itself<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Open Mapping Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Non-constant analytic functions map open sets to open sets<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Series Expansion &amp; Residues<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Taylor Series<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Power series expansion around regular point<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Laurent Series<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Expansion with negative powers around singularity<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Calculus of Residues<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Residue theorem for evaluating integrals; poles, essential singularities<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Conformal Mappings<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Conformal Maps<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Angle-preserving maps; locally analytic and non-constant<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">M\u00f6bius Transformations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Linear fractional transformations; preserve circles and angles<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 2: Algebra CSIR NET <\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/how-to-prepare-for-csir-net-mathematics-preparation\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>Mathematical Sciences Syllabus<\/b><\/a><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Combinatorics<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Permutations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Arrangement of nnn objects in order; with\/without repetition<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Combinations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Selection of rrr objects from nnn without order; (nr)=n!r!(n\u2212r)!\\binom{n}{r} = \\frac{n!}{r!(n-r)!}(rn\u200b)=r!(n\u2212r)!n!\u200b<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Pigeonhole Principle<\/span><\/td>\n<td><span style=\"font-weight: 400;\">If nnn objects in mmm boxes with n&gt;mn&gt;mn&gt;m, at least one box contains &gt;1 object<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Inclusion-Exclusion Principle<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Counting union of overlapping sets: (<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Derangements<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Permutations where no element is in its original position; !n=n!\u2211k=0n(\u22121)kk!!n = n!\\sum_{k=0}^{n} \\frac{(-1)^k}{k!}!n=n!\u2211k=0n\u200bk!(\u22121)k\u200b<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Number Theory<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Fundamental Theorem of Arithmetic<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Every integer &gt;1 can be expressed uniquely as a product of primes<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Divisibility in Z\\mathbb{Z}Z<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(a<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Congruences<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(a \\equiv b \\ (\\text{mod } n) \\iff n<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Chinese Remainder Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">System of congruences with coprime moduli has a unique solution modulo the product<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Euler&#8217;s \u03d5\\phi\u03d5-function<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Counts integers \u2264 n coprime to n; \u03d5(pk)=pk\u2212pk\u22121\\phi(p^k) = p^k &#8211; p^{k-1}\u03d5(pk)=pk\u2212pk\u22121<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Primitive Roots<\/span><\/td>\n<td><span style=\"font-weight: 400;\">ggg is primitive root modulo n if all numbers coprime to n are powers of ggg<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Group Theory<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Groups &amp; Subgroups<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Definitions, examples, subgroup criteria<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Normal Subgroups &amp; Quotient Groups<\/span><\/td>\n<td><span style=\"font-weight: 400;\">N\u25c3GN \\triangleleft GN\u25c3G; cosets form quotient group G\/NG\/NG\/N<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Homomorphisms &amp; Cyclic Groups<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Structure-preserving maps; groups generated by single element<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Permutation Groups<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Groups of bijections under composition<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cayley&#8217;s Theorem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Every group is isomorphic to a subgroup of a symmetric group<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Class Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">(<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Sylow Theorems<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Existence, conjugacy, and number of subgroups of order pkp^kpk in finite groups<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Ring Theory<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Rings &amp; Ideals<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Set with two operations; ideals closed under addition and multiplication by ring elements<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Prime &amp; Maximal Ideals<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Prime: ab\u2208P\u2005\u200a\u27f9\u2005\u200aa\u2208Pab \\in P \\implies a \\in Pab\u2208P\u27f9a\u2208P or b\u2208Pb \\in Pb\u2208P; Maximal: no ideal strictly between MMM and RRR<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Quotient Rings<\/span><\/td>\n<td><span style=\"font-weight: 400;\">R\/IR\/IR\/I with addition and multiplication modulo I<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">UFD, PID, Euclidean Domain<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Unique factorization, principal ideal generation, division algorithm<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Polynomial Rings<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Polynomial Rings<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Rings of polynomials R[x]R[x]R[x]<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Irreducibility Criteria<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Eisenstein criterion, degree tests<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Field Theory &amp; Galois Theory<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Fields &amp; Finite Fields<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Commutative rings with inverses; GF(pn)GF(p^n)GF(pn)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Field Extensions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">F\u2286KF \\subseteq KF\u2286K, KKK extension of FFF<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Galois Theory<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Connection between field extensions and group theory; solvability of polynomials<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 2: Topology CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Topology<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Basis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Collection of open sets such that every open set can be expressed as a union of them<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Dense Sets<\/span><\/td>\n<td><span style=\"font-weight: 400;\">A subset DDD of XXX is dense if every point of XXX is either in DDD or is a limit point of DDD<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Subspace Topology<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Topology induced on a subset Y\u2286XY \\subseteq XY\u2286X from the parent space XXX<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Product Topology<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Topology on a product of spaces; open sets are products of open sets of component spaces<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Separation Axioms<\/span><\/td>\n<td><span style=\"font-weight: 400;\">T0, T1, T2 (Hausdorff), T3, T4: conditions that separate points and closed sets<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Connectedness<\/span><\/td>\n<td><span style=\"font-weight: 400;\">A space is connected if it cannot be represented as the union of two non-empty disjoint open sets<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Compactness<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Every open cover has a finite subcover; in metric spaces, equivalent to sequential compactness<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 3: Ordinary Differential Equations (ODEs) CSIR NET Mathematical Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>First-Order ODEs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Existence &amp; Uniqueness<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Conditions for solutions of initial value problems (IVPs); Picard-Lindel\u00f6f theorem<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Singular Solutions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solutions not obtained from general solution; often envelope of family of curves<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Systems of First-Order ODEs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Coupled first-order equations; can be written in matrix form<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Higher-Order Linear ODEs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Homogeneous Linear ODEs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solutions of form y\u2032\u2032+p(x)y\u2032+q(x)y=0y&#8221; + p(x)y&#8217; + q(x)y = 0y\u2032\u2032+p(x)y\u2032+q(x)y=0; superposition principle<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Non-Homogeneous Linear ODEs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">General solution = complementary function + particular solution<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Variation of Parameters<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Method to find particular solution for non-homogeneous ODEs<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Boundary Value Problems<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Sturm-Liouville Problems<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Eigenvalue problems; orthogonal eigenfunctions; arises in physics and engineering<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Green&#8217;s Function<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Integral kernel representing solution of linear differential equations with boundary conditions<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 3: Partial Differential Equations (PDEs) CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>First-Order PDEs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Lagrange Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solves linear first-order PDEs using characteristic equations<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Charpit Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solves nonlinear first-order PDEs; extends Lagrange method<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Cauchy Problem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Determining solution from initial curve or surface data<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Second-Order PDEs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Classification<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Elliptic, Parabolic, Hyperbolic types based on discriminant of second-order terms<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Higher-Order PDEs with Constant Coefficients<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solve using characteristic equation; general solution depends on roots<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Separation of Variables<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Laplace Equation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solution as product of functions of individual variables; boundary value problems<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Heat Equation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Diffusion equation; separation leads to Fourier series solutions<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Wave Equation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Hyperbolic PDE; solutions via separation or d\u2019Alembert formula<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Also read &#8211; <\/b><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/csir-net-mathematical-science-question-papers-2026-pdf\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>CSIR NET Mathematical Science Question Papers 2025 pdf<\/b><\/a><\/p>\n<h3><b>Unit 3: Integral Equations CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Linear Integral Equations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">First Kind<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Unknown function appears only under the integral; \u222babK(x,t)\u03d5(t)dt=f(x)\\int_a^b K(x,t) \\phi(t) dt = f(x)\u222bab\u200bK(x,t)\u03d5(t)dt=f(x)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Second Kind<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Unknown function appears inside and outside integral; \u03d5(x)\u2212\u03bb\u222babK(x,t)\u03d5(t)dt=f(x)\\phi(x) &#8211; \\lambda \\int_a^b K(x,t)\\phi(t)dt = f(x)\u03d5(x)\u2212\u03bb\u222bab\u200bK(x,t)\u03d5(t)dt=f(x)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Fredholm Type<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Limits of integration are fixed<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Volterra Type<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Upper limit of integration depends on variable; e.g., \u222baxK(x,t)\u03d5(t)dt\\int_a^x K(x,t) \\phi(t) dt\u222bax\u200bK(x,t)\u03d5(t)dt<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Solutions with Separable Kernels<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Separable Kernels<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Kernel K(x,t)=\u2211i=1nfi(x)gi(t)K(x,t) = \\sum_{i=1}^n f_i(x) g_i(t)K(x,t)=\u2211i=1n\u200bfi\u200b(x)gi\u200b(t); reduces integral equation to algebraic system<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Eigenvalues and Eigenfunctions<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Characteristic Numbers &amp; Eigenfunctions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Eigenvalues \u03bb\\lambda\u03bb for which homogeneous equation has non-trivial solution<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Resolvent Kernel<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Resolvent Kernel<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Kernel used to express solution of integral equation as series; helps solve Fredholm equations<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 3: Numerical Analysis CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Numerical Solutions of Algebraic Equations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Method of Iteration<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solve x=g(x)x = g(x)x=g(x) iteratively; convergence requires (<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Newton-Raphson Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Iterative formula: xn+1=xn\u2212f(xn)f\u2032(xn)x_{n+1} = x_n &#8211; \\frac{f(x_n)}{f'(x_n)}xn+1\u200b=xn\u200b\u2212f\u2032(xn\u200b)f(xn\u200b)\u200b; quadratic convergence<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Rate of Convergence<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Measures speed of convergence; linear, quadratic, cubic orders<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Systems of Linear Algebraic Equations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Gauss Elimination<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Direct method; reduces system to upper triangular form, then back substitution<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Gauss-Seidel Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Iterative method; updates solution component-wise using latest approximations<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Finite Differences<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Forward, Backward, Central Differences<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Approximates derivatives using differences of function values at discrete points<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Interpolation<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Lagrange Interpolation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Polynomial passing through given points; formula: P(x)=\u2211yi\u220fj\u2260ix\u2212xjxi\u2212xjP(x) = \\sum y_i \\prod_{j\\neq i} \\frac{x-x_j}{x_i-x_j}P(x)=\u2211yi\u200b\u220fj=i\u200bxi\u200b\u2212xj\u200bx\u2212xj\u200b\u200b<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Hermite Interpolation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Uses function values and derivatives at given points for approximation<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Spline Interpolation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Piecewise polynomials; cubic splines ensure smoothness at data points<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Numerical Differentiation &amp; Integration<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Numerical Differentiation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Approximate derivative using finite difference formulas<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Numerical Integration<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Approximate definite integrals using Trapezoidal rule, Simpson\u2019s rules, etc.<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Numerical Solutions of ODEs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Picard Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Successive approximations using integral form of differential equation<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Euler Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">First-order method: yn+1=yn+hf(xn,yn)y_{n+1} = y_n + h f(x_n, y_n)yn+1\u200b=yn\u200b+hf(xn\u200b,yn\u200b)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Modified Euler Method<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Improved Euler\/Heun\u2019s method; second-order accuracy<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Runge-Kutta Methods<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Higher-order methods (RK2, RK4) for accurate solutions<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 3: Calculus of Variations, CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Functionals &amp; Variations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Variation of a Functional<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Small change in a functional; \u03b4J[y]=0\\delta J[y] = 0\u03b4J[y]=0 for extremum<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Euler-Lagrange Equation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Necessary condition for a functional J[y]=\u222bF(x,y,y\u2032)dxJ[y] = \\int F(x, y, y&#8217;) dxJ[y]=\u222bF(x,y,y\u2032)dx to have an extremum: \u2202F\u2202y\u2212ddx\u2202F\u2202y\u2032=0\\frac{\\partial F}{\\partial y} &#8211; \\frac{d}{dx} \\frac{\\partial F}{\\partial y&#8217;} = 0\u2202y\u2202F\u200b\u2212dxd\u200b\u2202y\u2032\u2202F\u200b=0<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Necessary &amp; Sufficient Conditions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Conditions to identify maxima, minima, or saddle points of functionals<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Variational Methods for BVPs<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Ordinary Differential Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Solve boundary value problems by minimizing associated functional<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Partial Differential Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Extend variational principles to PDEs; e.g., energy methods, Ritz method<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 3: Classical Mechanics CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Generalized Coordinates<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Definition &amp; Examples<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Coordinates that uniquely define configuration of system; reduce degrees of freedom<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Lagrange&#8217;s Equations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Formulation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">ddt\u2202L\u2202q\u02d9i\u2212\u2202L\u2202qi=0\\frac{d}{dt} \\frac{\\partial L}{\\partial \\dot{q}_i} &#8211; \\frac{\\partial L}{\\partial q_i} = 0dtd\u200b\u2202q\u02d9\u200bi\u200b\u2202L\u200b\u2212\u2202qi\u200b\u2202L\u200b=0; Lagrangian L=T\u2212VL = T &#8211; VL=T\u2212V<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Hamiltonian Mechanics<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Hamilton\u2019s Canonical Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">q\u02d9i=\u2202H\u2202pi, p\u02d9i=\u2212\u2202H\u2202qi\\dot{q}_i = \\frac{\\partial H}{\\partial p_i}, \\ \\dot{p}_i = -\\frac{\\partial H}{\\partial q_i}q\u02d9\u200bi\u200b=\u2202pi\u200b\u2202H\u200b, p\u02d9\u200bi\u200b=\u2212\u2202qi\u200b\u2202H\u200b; phase space formulation<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Hamilton\u2019s Principle &amp; Principle of Least Action<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Action S=\u222bLdtS = \\int L dtS=\u222bLdt is stationary for true path; variational approach<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Rigid Body Dynamics<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Two-Dimensional Motion<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Motion in plane; translation + rotation about center of mass<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Euler\u2019s Dynamical Equations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">L\u02d9+\u03c9\u00d7L=N\\dot{\\mathbf{L}} + \\boldsymbol{\\omega} \\times \\mathbf{L} = \\mathbf{N}L\u02d9+\u03c9\u00d7L=N; motion about a fixed axis<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Small Oscillations<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Theory of Small Oscillations<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Linearization near equilibrium; normal modes and frequencies; application to coupled systems<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><b>Unit 4: Statistics CSIR NET Mathematics Sciences Syllabus<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>Main Topic<\/b><\/td>\n<td><b>Subtopics \/ Concepts<\/b><\/td>\n<td><b>Key Points \/ Notes<\/b><\/td>\n<\/tr>\n<tr>\n<td><b>Descriptive Statistics &amp; EDA<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Descriptive Statistics<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Measures of central tendency, dispersion, skewness, kurtosis<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Exploratory Data Analysis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Graphical and numerical methods to summarize data; boxplots, histograms<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Probability Theory<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Sample Space &amp; Discrete Probability<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Basic probability concepts; independent events; Bayes theorem<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Random Variables &amp; Distribution Functions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Univariate &amp; multivariate; cumulative distribution, probability mass\/density functions<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Expectation &amp; Moments<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Mean, variance, higher moments, covariance<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Characteristic Functions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Tool for studying distributions; moment generating properties<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Probability Inequalities<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Markov, Chebyshev, Jensen inequalities<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Modes of Convergence &amp; Limit Theorems<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Convergence in probability, almost surely; weak &amp; strong laws of large numbers; Central Limit Theorem (i.i.d.)<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Stochastic Processes<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Markov Chains<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Finite\/countable state space; classification of states; n-step transition probabilities; stationary distributions<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Poisson &amp; Birth-and-Death Processes<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Counting processes; transition rates; applications<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Standard Distributions &amp; Sampling<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Discrete &amp; Continuous Distributions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Binomial, Poisson, Geometric, Uniform, Normal, Exponential, etc.<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Sampling Distributions &amp; Standard Errors<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Distribution of sample mean, variance; asymptotic distributions<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Order Statistics<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Distribution of min, max, and other order statistics<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Estimation &amp; Hypothesis Testing<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Methods of Estimation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Method of moments, maximum likelihood; properties of estimators<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Confidence Intervals<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Interval estimation for parameters<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Tests of Hypotheses<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Most powerful, uniformly most powerful, likelihood ratio tests<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Chi-square &amp; Large Sample Tests<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Goodness-of-fit tests, asymptotic testing procedures<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Nonparametric Tests<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Sign test, Wilcoxon tests, rank correlation, independence tests<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Elementary Bayesian Inference<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Prior, posterior, Bayesian estimation<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Regression &amp; ANOVA<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Gauss-Markov Models<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Estimability, BLUE, linear hypotheses tests, confidence intervals<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Analysis of Variance &amp; Covariance<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Fixed, random, mixed effects models<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Regression Models<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Simple and multiple linear regression; diagnostics; logistic regression<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Multivariate Analysis<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Multivariate Normal &amp; Wishart Distributions<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Properties, quadratic forms<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Correlation &amp; Partial Correlation<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Inference for parameters, tests<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Data Reduction Techniques<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Principal Component Analysis, Discriminant Analysis, Cluster Analysis, Canonical Correlation<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Sampling Techniques<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Sampling Methods<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Simple random, stratified, systematic, PPS sampling; ratio &amp; regression methods<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Design of Experiments<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Experimental Designs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Completely randomized, randomized block, Latin-square designs<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Block Designs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Connectedness, orthogonality, BIBD<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Factorial Experiments<\/span><\/td>\n<td><span style=\"font-weight: 400;\">2K2^K2K factorial designs; confounding and construction<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Reliability &amp; Life Testing<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Hazard Function &amp; Failure Rates<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Reliability measures, censoring, life testing<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Series &amp; Parallel Systems<\/span><\/td>\n<td><span style=\"font-weight: 400;\">System reliability analysis<\/span><\/td>\n<\/tr>\n<tr>\n<td><b>Operations Research &amp; Queuing<\/b><\/td>\n<td><span style=\"font-weight: 400;\">Linear Programming Problem<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Formulation, simplex method, duality<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Queuing Models<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Steady-state solutions: M\/M\/1, M\/M\/1 with limited waiting, M\/M\/C, M\/M\/C with limited waiting, M\/G\/1<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span style=\"font-weight: 400;\">Inventory Models<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Elementary inventory control models<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><iframe src=\"\/\/www.youtube.com\/embed\/ivQwcJWFzXA\" width=\"720\" height=\"404\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/h2>\n<h2><b>CSIR NET Mathematics Sciences Topic-Wise Weightage\u00a0<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">A highly effective approach to excel in the CSIR NET Mathematical Sciences exam is to concentrate on topics that contribute the most marks. Knowing the weightage of each topic allows you to <\/span><b>plan your preparation strategically<\/b><span style=\"font-weight: 400;\">, <\/span><b>optimize your scoring potential<\/b><span style=\"font-weight: 400;\">, and <\/span><b>manage your study time efficiently<\/b><span style=\"font-weight: 400;\">. By analyzing trends from previous years\u2019 question papers, we can create a comprehensive <\/span><b>topic-wise weightage guide<\/b><span style=\"font-weight: 400;\"> for the CSIR NET Mathematical Sciences exam.<\/span><\/p>\n<table style=\"width: 91.7095%;\">\n<tbody>\n<tr>\n<td style=\"width: 32.9885%;\"><b>Subject Area<\/b><\/td>\n<td style=\"width: 18.046%;\"><b>Approx. Questions<\/b><\/td>\n<td style=\"width: 16.5517%;\"><b>Estimated Marks<\/b><\/td>\n<td style=\"width: 13.5632%;\"><b>Paper Section<\/b><\/td>\n<td style=\"width: 62.5287%;\"><b>Priority Level<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Linear Algebra<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">7\u20139<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">20\u201330<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Very High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Real Analysis<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">6\u20138<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">20\u201325<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Very High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Complex Analysis<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">5\u20136<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">15\u201320<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Ordinary Differential Equations (ODEs)<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">4\u20136<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">15\u201320<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Partial Differential Equations (PDEs)<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">4\u20135<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">12\u201318<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Abstract Algebra \/ Group Theory<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">4\u20135<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">12\u201318<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">High<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Topology<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">3\u20134<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">10\u201315<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Moderate<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Numerical Analysis<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">3\u20134<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">8\u201312<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Sections B &amp; C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Moderate<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Calculus of Variations<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">2\u20133<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">5\u201310<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Section C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Moderate<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Classical Mechanics<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">2\u20133<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">5\u201310<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Section C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Moderate<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Linear Integral Equations<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">1\u20132<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">3\u20135<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Section C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Low<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">Functional Analysis<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">1\u20132<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">3\u20135<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Section C<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Low<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 32.9885%;\"><span style=\"font-weight: 400;\">General Aptitude (Part A)<\/span><\/td>\n<td style=\"width: 18.046%;\"><span style=\"font-weight: 400;\">15<\/span><\/td>\n<td style=\"width: 16.5517%;\"><span style=\"font-weight: 400;\">30<\/span><\/td>\n<td style=\"width: 13.5632%;\"><span style=\"font-weight: 400;\">Section A<\/span><\/td>\n<td style=\"width: 62.5287%;\"><span style=\"font-weight: 400;\">Easy &amp; High Scoring<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Notes \/ Tips for Preparation:<\/b><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Very High Priority:<\/b><span style=\"font-weight: 400;\"> Linear Algebra and Real Analysis are must-prepare topics\u2014they appear most frequently.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>High Priority:<\/b><span style=\"font-weight: 400;\"> Complex Analysis, ODEs, PDEs, and Abstract Algebra are consistently tested.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Moderate Priority:<\/b><span style=\"font-weight: 400;\"> Topics like Topology, Numerical Analysis, Calculus of Variations, and Classical Mechanics can be attempted after focusing on high-priority areas.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Low Priority:<\/b><span style=\"font-weight: 400;\"> Linear Integral Equations and Functional Analysis appear less often but should not be ignored entirely.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>General Aptitude:<\/b><span style=\"font-weight: 400;\"> Easy to score; prepare thoroughly for quick marks in Section A.<\/span><\/li>\n<\/ul>\n<h2><b>How to Make the Most of the CSIR NET Mathematics Sciences Syllabus<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">CSIR NET Mathematical Sciences syllabus provides a clear pathway to organize your studies and focus on key concepts efficiently.<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Familiarize Yourself with the Complete Syllabus<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Begin by thoroughly going through the CSIR NET Mathematical Sciences syllabus. Break it down into individual topics to quickly identify your strengths and the areas that need more focus.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Give Priority to High-Weightage Topics<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Focus on topics that carry more marks in the exam, such as Linear Algebra, Real Analysis, and Complex Analysis. These subjects appear frequently and have a significant impact on your overall score.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Create a Weekly Study Schedule<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Plan your preparation week by week, ensuring that all topics of the syllabus are systematically covered. Include time for revision to consolidate learning.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Practice Previous Year Questions by Topic<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Solve past CSIR NET papers by linking each question to its corresponding syllabus topic. This approach reinforces your understanding and shows how concepts are tested in the actual exam.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Take Syllabus-Based Mock Tests<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Attempt regular mock tests that follow the structure of the syllabus. This practice improves speed, accuracy, and helps you manage exam pressure effectively.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Use Notes, Formula Sheets, and Flashcards<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Maintain concise notes, formula sheets, or flashcards for each topic. These tools are extremely useful for quick revisions just before the exam.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Include General Aptitude in Your Routine<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\"> Don\u2019t overlook the General Aptitude section. Practicing it weekly can help you gain additional marks with minimal effort, boosting your overall score.<\/span><\/li>\n<\/ol>\n<h2><b>Recommended Books for CSIR NET General Aptitude<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">A strong foundation in <\/span><b>General Aptitude<\/b><span style=\"font-weight: 400;\"> is crucial for scoring well in the CSIR NET examination. Several books are available to help aspirants build concepts, practice problems, and prepare effectively. Here are some highly recommended titles:<\/span><\/p>\n<table style=\"width: 98.6047%;\">\n<tbody>\n<tr>\n<td style=\"width: 71.7391%;\"><b>Book Name<\/b><\/td>\n<td style=\"width: 172.283%;\"><b>Author<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.7391%;\"><span style=\"font-weight: 400;\">CSIR UGC NET Paper I<\/span><\/td>\n<td style=\"width: 172.283%;\"><span style=\"font-weight: 400;\">R. Gupta<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.7391%;\"><span style=\"font-weight: 400;\">CSIR-UGC-NET General Aptitude: Theory and Practice<\/span><\/td>\n<td style=\"width: 172.283%;\"><span style=\"font-weight: 400;\">Ram Mohan Pandey<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.7391%;\"><span style=\"font-weight: 400;\">General Aptitude: Comprehensive Theory &amp; Practice<\/span><\/td>\n<td style=\"width: 172.283%;\"><span style=\"font-weight: 400;\">Kailash Choudhary<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 71.7391%;\"><span style=\"font-weight: 400;\">CSIR NET General Aptitude \u2013 A New Outlook<\/span><\/td>\n<td style=\"width: 172.283%;\"><span style=\"font-weight: 400;\">Christy Varghese<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-chemistry\/\" target=\"_blank\" rel=\"noopener nofollow\"><b>CSIR NET Chemical Science Previous Year Question Paper<\/b><span style=\"font-weight: 400;\">,\u00a0<\/span><\/a><\/p>\n<h2><b>Recommended Books for CSIR NET Mathematics Sciences<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">To effectively prepare for the <\/span><b>CSIR NET Mathematical Sciences<\/b><span style=\"font-weight: 400;\"> exam, having a structured study plan and access to the right books is crucial. Below is a curated list of <\/span><b>essential reference books<\/b><span style=\"font-weight: 400;\"> for aspirants:<\/span><\/p>\n<table style=\"width: 96.7192%;\">\n<tbody>\n<tr>\n<td style=\"width: 65.767%;\"><b>Book Name<\/b><\/td>\n<td style=\"width: 123.295%;\"><b>Author<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">Complex Variables and Applications<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">Brown &amp; Churchill<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">Integral Equations and Boundary Value Problems<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">M. D. Raisinghania<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">Foundations of Functional Analysis<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">S. Ponnusamy<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">Real Analysis<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">H. L. Royden &amp; P. M. Fitzpatrick<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">CSIR-UGC NET\/JRF\/SLET Mathematical Sciences (Paper I &amp; II)<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">Dr. A. Kumar<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 65.767%;\"><span style=\"font-weight: 400;\">Fundamentals of Statistics<\/span><\/td>\n<td style=\"width: 123.295%;\"><span style=\"font-weight: 400;\">S. C. Gupta<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-weight: 400;\">These books cover all major areas of the syllabus including <\/span><b>Real Analysis, Complex Analysis, Functional Analysis, Integral Equations, and Statistics<\/b><span style=\"font-weight: 400;\">, providing a solid base for both theory and problem-solving practice.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/m.media-amazon.com\/images\/I\/51+NI5WfFVL._UF1000,1000_QL80_.jpg\" alt=\"Integratal Equation &amp; Boundary Value Problem eBook : Raisinghania, M.D.: Amazon.in: Kindle Store\" width=\"488\" height=\"687\" \/><\/p>\n<h2><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/m.media-amazon.com\/images\/I\/61pS9rNeOjL.jpg\" alt=\"Foundations of Functional Analysis : S. Ponnusamy: Amazon.in: Books\" width=\"411\" height=\"703\" \/><\/h2>\n<h2><b>CSIR NET Mathematics Sciences Preparation 3-Month\u00a0 Plan<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">CSIR NET Mathematical Sciences in 3 months with a plan that covers all important topics like Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics.<\/span><\/p>\n<h3><b>Month 1: Build Strong Fundamentals<\/b><\/h3>\n<p><b>Focus:<\/b><span style=\"font-weight: 400;\"> High-weightage topics &amp; conceptual clarity<\/span><\/p>\n<table style=\"width: 96.1907%;\">\n<tbody>\n<tr>\n<td style=\"width: 5.42857%;\"><b>Week<\/b><\/td>\n<td style=\"width: 21.0476%;\"><b>Topics<\/b><\/td>\n<td style=\"width: 99.8095%;\"><b>Activities<\/b><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 5.42857%;\"><span style=\"font-weight: 400;\">Week 1<\/span><\/td>\n<td style=\"width: 21.0476%;\"><span style=\"font-weight: 400;\">Linear Algebra<\/span><\/td>\n<td style=\"width: 99.8095%;\"><span style=\"font-weight: 400;\">Vector spaces, subspaces, basis, dimension, linear transformations; practice 30\u201340 problems<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 5.42857%;\"><span style=\"font-weight: 400;\">Week 2<\/span><\/td>\n<td style=\"width: 21.0476%;\"><span style=\"font-weight: 400;\">Linear Algebra &amp; Real Analysis<\/span><\/td>\n<td style=\"width: 99.8095%;\"><span style=\"font-weight: 400;\">Matrices, eigenvalues, Cayley-Hamilton theorem, Inner product spaces; sequences, series, limits<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 5.42857%;\"><span style=\"font-weight: 400;\">Week 3<\/span><\/td>\n<td style=\"width: 21.0476%;\"><span style=\"font-weight: 400;\">Real Analysis<\/span><\/td>\n<td style=\"width: 99.8095%;\"><span style=\"font-weight: 400;\">Continuity, differentiability, mean value theorem, uniform convergence, Riemann integration<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 5.42857%;\"><span style=\"font-weight: 400;\">Week 4<\/span><\/td>\n<td style=\"width: 21.0476%;\"><span style=\"font-weight: 400;\">Real Analysis<\/span><\/td>\n<td style=\"width: 99.8095%;\"><span style=\"font-weight: 400;\">Improper integrals, functions of several variables, metric &amp; normed spaces, compactness and connectedness<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Weekend Tasks:<\/b><span style=\"font-weight: 400;\"> Solve previous year questions for Linear Algebra &amp; Real Analysis<\/span><\/p>\n<h3><b>Month 2: Core Topics + Application<\/b><\/h3>\n<p><b>Focus:<\/b><span style=\"font-weight: 400;\"> High &amp; medium-weightage topics<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Week<\/b><\/td>\n<td><b>Topics<\/b><\/td>\n<td><b>Activities<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 5<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Complex Analysis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Algebra of complex numbers, analytic functions, Cauchy-Riemann equations, contour integration<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 6<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Complex Analysis &amp; ODEs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Taylor &amp; Laurent series, residues, Cauchy\u2019s theorem; First-order ODEs, existence\/uniqueness, singular solutions<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 7<\/span><\/td>\n<td><span style=\"font-weight: 400;\">ODEs &amp; PDEs<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Linear ODEs (homogeneous\/non-homogeneous), variation of parameters, Sturm-Liouville problems; First-order PDEs (Lagrange &amp; Charpit), Cauchy problem<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 8<\/span><\/td>\n<td><span style=\"font-weight: 400;\">PDEs &amp; Numerical Analysis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Second-order PDEs classification, separation of variables; Numerical solutions of algebraic equations, Newton-Raphson, Gauss-Seidel, interpolation<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Weekend Tasks:<\/b><span style=\"font-weight: 400;\"> Attempt topic-wise mock tests for Complex Analysis, ODEs, PDEs<\/span><\/p>\n<h3><b>Month 3: Revision, Practice &amp; Low-Weight Topics<\/b><\/h3>\n<p><b>Focus:<\/b><span style=\"font-weight: 400;\"> Revision, low-weight topics, and mock tests<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><b>Week<\/b><\/td>\n<td><b>Topics<\/b><\/td>\n<td><b>Activities<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 9<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Abstract Algebra<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic &amp; permutation groups, Sylow theorems<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 10<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Rings &amp; Fields<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Rings, ideals, quotient rings, UFD, PID, Euclidean domain; Polynomial rings, irreducibility; Field extensions, Galois theory<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 11<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Calculus of Variations &amp; Classical Mechanics<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Euler-Lagrange equation, variational methods; Lagrange\u2019s &amp; Hamilton\u2019s equations, rigid body motion, small oscillations<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Week 12<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Integral Equations, Topology &amp; Final Revision<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Fredholm &amp; Volterra equations, resolvent kernel; Basis, dense sets, subspace\/product topology, connectedness, compactness; Full syllabus revision + Previous year papers<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<table style=\"width: 100.346%;\">\n<tbody>\n<tr>\n<td style=\"width: 215.276%;\" colspan=\"2\">\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\">Related Topics\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.8661%;\"><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-physical-science\/\" target=\"_blank\" rel=\"noopener nofollow\"><span style=\"font-weight: 400;\">important topics for csir net Physical Science<\/span><\/a><\/td>\n<td style=\"width: 164.409%;\"><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-life-science\/\" target=\"_blank\" rel=\"noopener nofollow\"><span style=\"font-weight: 400;\">important topics for csir net Life Science<\/span><\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50.8661%;\"><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-chemistry\/\" target=\"_blank\" rel=\"noopener nofollow\"><span style=\"font-weight: 400;\">important topics for csir net Chemistry<\/span><\/a><\/td>\n<td style=\"width: 164.409%;\"><a href=\"https:\/\/vedprep.com\/exams\/csir-net\/important-topics-for-csir-net-mathematics-2025\/\" target=\"_blank\" rel=\"noopener nofollow\"><span style=\"font-weight: 400;\">important topics for csir net Mathematics\u00a0<\/span><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2><b>Structural Overview of the CSIR NET Mathematical Sciences Examination<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is organized to test candidates through three parts\u2014Part A, Part B, and Part C. Part A focuses on General Aptitude, while Part B and Part C dive deep into the core mathematical disciplines. The syllabus demands a transition from computational proficiency to rigorous logical proofs, making it significantly more advanced than the standard <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> found in many postgraduate entrance exams.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A key feature of the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is the credit-based scoring system. Part B consists of single-choice questions, while Part C features multiple-select questions where no partial credit is awarded. This structure forces candidates to have an exhaustive understanding of every theorem and counter-example. While students might use <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> to brush up on basic algebra, the CSIR NET necessitates specialized advanced texts to cover the depth required for the NET qualification.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Understanding the unit-wise distribution is critical for time management. Unit I covers Analysis and Linear Algebra, which generally carry the highest weightage. Unit II moves into Abstract Algebra and Complex Analysis. Unit III includes Applied Mathematics topics like ODE, PDE, and Calculus of Variations. Finally, Unit IV is dedicated to Statistics. This breadth ensures that the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">remains the gold standard for evaluating research potential in India.<\/span><\/p>\n<h2><b>Unit I: Mastery of Analysis and Linear Algebra<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Within the <\/span><b>CSIR NET Mathematics Sciences Syllabus<\/b><span style=\"font-weight: 400;\">, Unit I acts as the foundational pillar. Real Analysis involves the study of topology of R, sequences, series, and Riemann integration. Linear Algebra focuses on vector spaces, linear transformations, and canonical forms. These topics are not merely about solving equations; they require proving existence and uniqueness, which is a departure from the more application-heavy <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Candidates often find that the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> provides a surface-level introduction to these fields, but the CSIR NET requires delving into Lebesgue measure and metric spaces. Linear Algebra in this syllabus also extends to inner product spaces and bilinear forms. Successful aspirants prioritize these sections because they appear in both Part B and Part C, offering the highest potential for accumulating marks through conceptual clarity.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Proficiency in Unit I is often the deciding factor for ranking. Unlike the <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\">, which may rely on speed, the CSIR NET rewards the ability to identify subtle nuances in mathematical statements. For example, understanding the difference between pointwise and uniform convergence is a recurring theme that requires more than just a basic overview of calculus found in standard <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h2><b>Unit II: Advanced Algebra and Complex Analysis<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Unit II of the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">shifts toward Abstract Algebra and Complex Analysis. This section evaluates a candidate&#8217;s grasp of groups, rings, and fields, including advanced concepts like Sylow theorems and Galois theory. Complex Analysis covers the geometry of complex numbers, analytic functions, and the residue theorem. These topics form the bridge between pure mathematics and its various theoretical applications.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For many, the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> covers basic group theory, but the CSIR NET extends this to polynomial rings and irreducibility criteria. Complex Analysis requires a deep understanding of Cauchy\u2019s integral formula and the maximum modulus principle. These are high-yield topics where precision is paramount. Using specialized literature instead of general <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> is highly recommended to master the rigorous proof-based nature of this unit.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The difficulty level in Unit II is characterized by its abstractness. Candidates must be comfortable with visualizing transformations in the complex plane and understanding the structural properties of algebraic systems. While the <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> might focus on direct computations, the CSIR NET often asks about the properties of entire functions or the number of non-isomorphic groups of a certain order, demanding a higher level of intellectual engagement.<\/span><\/p>\n<h2><b>Unit III: Applied Mathematics and Differential Equations<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">dedicates Unit III to Applied Mathematics, covering Ordinary and Partial Differential Equations (ODE &amp; PDE), Numerical Analysis, and the Calculus of Variations. This unit is often a favorite for candidates who prefer algorithmic problem-solving over abstract proofs. It includes the study of Green\u2019s functions, wave equations, and boundary value problems, which are essential for physical science applications.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">While the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> includes basic ODE and PDE, the CSIR NET delves into second-order linear equations and the classification of first-order PDEs. Numerical Analysis requires understanding errors, interpolation, and numerical integration methods like Runge-Kutta. This section is highly scoring because the problems are often structured and follow predictable patterns, provided the candidate has practiced extensively with relevant materials.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Calculus of Variations and Linear Integral Equations are also critical components of this unit. These subjects involve finding extremals of functionals and solving Fredholm and Volterra equations. These topics are rarely covered in the <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\">, giving candidates who master them a distinct competitive advantage. Success here relies on a balance between theoretical derivations and numerical accuracy.<\/span><\/p>\n<h2><b>Unit IV: Probability and Statistics for Mathematics<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Unit IV of the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is specialized for students with a background in Statistics. It covers Descriptive Statistics, Probability Distributions, and Statistical Inference. Topics include Markov chains, sampling distributions, and hypothesis testing. For a mathematics student, this unit offers an alternative path to scoring, especially in Part C where specific statistics problems can be less time-consuming than complex analysis proofs.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The overlap between this unit and the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> is minimal for pure math tracks but significant for those appearing in Statistics papers. The CSIR NET version focuses on the mathematical rigor of probability spaces and multivariate analysis. Understanding the properties of the Normal, Binomial, and Poisson distributions is standard, but the syllabus also requires knowledge of Gauss-Markov models and design of experiments.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Aspiring researchers often find that Unit IV requires a different mental framework than the rest of the <\/span><b>CSIR NET Mathematics Sciences Syllabus<\/b><span style=\"font-weight: 400;\">. It is less about absolute certainty and more about likelihood and estimation. Using the right <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> as a starting point for probability can be helpful, but the advanced inference and regression topics in the NET require focused study of graduate-level statistics texts.<\/span><\/p>\n<h2><b>Critical Analysis: Why Traditional Proof-Learning May Fail<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">A common strategy for the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is to memorize standard proofs. However, this approach often fails in the contemporary exam environment. The current trend in the <\/span><b>CSIR NET Exam Pattern<\/b><span style=\"font-weight: 400;\"> is to present &#8220;modified theorems&#8221; or specific counter-examples that test the boundaries of a rule. If a student knows the proof of the Mean Value Theorem but cannot apply it to a non-differentiable function, they will likely struggle.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The limitation of many <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> is that they focus on &#8220;solved examples&#8221; rather than &#8220;conceptual boundaries.&#8221; To mitigate this, candidates should practice &#8220;mathematical stress-testing.&#8221; This involves taking a known theorem and seeing what happens when one of its conditions is removed. For instance, what happens to the Fundamental Theorem of Calculus if the function is not continuous? This analytical depth is what the CSIR NET rewards over rote memorization.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Furthermore, the &#8220;breadth-first&#8221; approach often leads to superficial knowledge. Given the choice in the <\/span><b>CSIR NET Mathematics Sciences Syllabus<\/b><span style=\"font-weight: 400;\">, it is often more strategic to be an expert in three units than a novice in four. Over-extending into Unit IV without a statistics background, for example, can waste valuable preparation time that could be spent mastering the nuances of Lebesgue integration in Unit I.<\/span><\/p>\n<h2><b>Strategic Comparison: CSIR NET vs. CUET PG<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Understanding the difference between the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">and the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> is vital for career planning. The CUET PG is an entrance test for Master&#8217;s programs, focusing on undergraduate-level proficiency. In contrast, the CSIR NET is a qualifying exam for research and teaching, demanding a postgraduate-level grasp of complex systems. The <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> is generally faster-paced with more questions, whereas the CSIR NET is slower and more analytical.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">While you can use <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> for revising basic concepts of Group Theory or Vector Calculus, they will not suffice for the Advanced Topology or Measure Theory sections of the NET. The <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> typically avoids the multiple-select questions (MSQs) that define Part C of the CSIR NET. In MSQs, if three options are correct and you only mark two, you receive zero marks. This lack of partial credit makes the NET significantly more punishing.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For students transitioning from the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> level to the CSIR NET, the first step is to upgrade their reading list. Transitioning from &#8220;how-to&#8221; books to &#8220;why&#8221; books is essential. This means moving from simple calculation-based exercises to proof-heavy literature that explores the underlying structure of mathematical logic.<\/span><\/p>\n<h2><b>Practical Application: The Role of Linear Algebra in Data Science<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">To see the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">in action, consider the role of Linear Algebra in modern technology. Singular Value Decomposition (SVD) and Eigenvalue problems, which are core parts of the syllabus, are the mathematical engines behind Google\u2019s Search algorithm and Netflix\u2019s recommendation systems. These are not just abstract concepts; they are tools for dimensionality reduction in massive datasets.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In a research scenario, a mathematician might use the properties of Hilbert spaces (Unit I) to develop new signal processing techniques. Similarly, the study of Differential Equations (Unit III) is the basis for modeling everything from the spread of infectious diseases to the behavior of financial markets. The <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">ensures that qualifiers have the mathematical maturity to contribute to these high-impact fields.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">By viewing the syllabus through the lens of application, the abstract nature of topics like &#8220;Inner Product Spaces&#8221; becomes more grounded. Whether you are using <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> for a refresh or diving into advanced research papers, realizing that these mathematical structures govern our digital world provides extra motivation for the rigorous study required to clear the exam.<\/span><\/p>\n<h2><b>Recommended Books for Mathematics Sciences<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Selecting the right resources is the most critical part of tackling the <\/span><b>CSIR NET Mathematics Sciences Syllabus<\/b><span style=\"font-weight: 400;\">. For Real Analysis, H.L. Royden or Bartle and Sherbert are highly regarded for their clarity and rigor. Linear Algebra is best studied through Kenneth Hoffman and Ray Kunze, which provides the depth needed for the NET that standard <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> might lack.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For Unit II, Joseph Gallian\u2019s &#8220;Contemporary Abstract Algebra&#8221; is excellent for group and ring theory, while Ponnusamy\u2019s &#8220;Foundations of Complex Analysis&#8221; is a staple for the complex units. Unit III students should look toward S.L. Ross for Differential Equations. While the <\/span><b>CUET PG Syllabus<\/b><span style=\"font-weight: 400;\"> might be covered by general guides, the CSIR NET requires these standard reference books to handle the conceptual challenges of Part C.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It is also beneficial to keep a set of <\/span><b>CUET PG Books<\/b><span style=\"font-weight: 400;\"> for the General Aptitude section (Part A). Topics like logical reasoning, graphical analysis, and basic percentage calculations are common to both exams. Mastering these &#8220;easier&#8221; marks using the <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> logic can provide a vital buffer for the more difficult math sections.<\/span><\/p>\n<h2><b>Effective Revision Strategies for the Mathematics Syllabus<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Finalizing the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">requires a disciplined revision phase. Creating a &#8220;Counter-Example Bank&#8221; is a highly effective technique. For every major theorem in the syllabus, write down at least two examples where the theorem does not apply because a specific condition is violated. This prepares you specifically for the &#8220;multiple-select&#8221; challenges of Part C.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Regularly practicing with the <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> in mind for Part A, but switching to deep-thinking mode for Parts B and C, helps in cognitive flexibility. Mock tests should be taken in a single three-hour sitting to build the mental endurance needed for the actual exam. Since the <\/span><b>CSIR NET Mathematics Sciences Syllabus 2026<\/b><span style=\"font-weight: 400;\">is vast, do not attempt to revise everything in the last week; focus on your &#8220;High-Yield&#8221; topics like Linear Algebra and Real Analysis.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Lastly, ensure you are familiar with the digital interface of the CBT mode. Unlike the paper-based <\/span><b>CUET PG Exam Pattern<\/b><span style=\"font-weight: 400;\"> of the past, the current NET requires comfort with on-screen reading and virtual navigation. By integrating these technical habits with a deep understanding of the <\/span><b>CSIR NET Mathematics Sciences Syllabus<\/b><span style=\"font-weight: 400;\">, you position yourself for success in the 2025 examination cycle.<\/span><\/p>\n<h2><b>CSIR NET Mathematics Sciences preparation<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Prepare for CSIR NET Mathematical Sciences with a complete syllabus covering Linear Algebra, Algebra, Complex Analysis, Topology, ODEs, PDEs, Integral Equations, Numerical Analysis, Calculus of Variations, Classical Mechanics, and Statistics.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">Priority Level<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Topics \/ Areas<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Focus \/ Tips<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">High Priority<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Linear Algebra, Real Analysis, Complex Analysis, ODEs &amp; PDEs, Abstract Algebra<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Must be mastered thoroughly; frequent in past papers; focus on concepts, problem-solving, and previous year questions<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Medium Priority<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Numerical Analysis, Topology, Calculus of Variations, Classical Mechanics<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Important but less frequent; understand key methods and applications; practice selectively<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Low Priority<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Integral Equations, Functional Analysis<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Appear rarely; prepare basics and key formulas; attempt only if time permits<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">General Aptitude<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Logical reasoning, quantitative ability, analytical reasoning<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Daily 20\u201330 min practice; easy scoring area, ensure maximum marks in Part A<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Revision<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Entire Syllabus<\/span><\/td>\n<td><span style=\"font-weight: 400;\">Last 7\u201310 days should be dedicated to full syllabus revision and mock tests for speed, accuracy, and confidence<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2><b>CSIR NET Mathematics Sciences Syllabus FAQs<\/b><\/h2>\n<style>#sp-ea-3769 .spcollapsing { height: 0; overflow: hidden; transition-property: height;transition-duration: 300ms;}#sp-ea-3769{ position: relative; }#sp-ea-3769 .ea-card{ opacity: 0;}#eap-preloader-3769{ position: absolute; left: 0; top: 0; height: 100%;width: 100%; text-align: center;display: flex; align-items: center;justify-content: center;}#sp-ea-3769.sp-easy-accordion>.sp-ea-single {margin-bottom: 10px; border: 1px solid #e2e2e2; }#sp-ea-3769.sp-easy-accordion>.sp-ea-single>.ea-header a {color: #444;}#sp-ea-3769.sp-easy-accordion>.sp-ea-single>.sp-collapse>.ea-body {background: #fff; color: #444;}#sp-ea-3769.sp-easy-accordion>.sp-ea-single {background: #eee;}#sp-ea-3769.sp-easy-accordion>.sp-ea-single>.ea-header a .ea-expand-icon { float: left; color: #444;font-size: 16px;}<\/style><div id=\"sp_easy_accordion-1763816640\">\n<div id=\"sp-ea-3769\" class=\"sp-ea-one sp-easy-accordion\" data-ea-active=\"ea-click\" data-ea-mode=\"vertical\" data-preloader=\"1\" data-scroll-active-item=\"1\" data-offset-to-scroll=\"0\">\n\n\t<div id=\"eap-preloader-3769\" class=\"accordion-preloader\">\n\t\t<img decoding=\"async\" src=\"https:\/\/www.vedprep.com\/exams\/wp-content\/plugins\/easy-accordion-free\/public\/assets\/ea_loader.svg\" alt=\"Loader image\"\/>\n\t<\/div>\n\t<!-- Start accordion card div. -->\n<div class=\"ea-card ea-expand sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-37690\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse37690\" aria-controls=\"collapse37690\" href=\"#\"  aria-expanded=\"true\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-minus\"><\/i> Where can I find the CSIR NET Mathematical Science Syllabus?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse collapsed show\" id=\"collapse37690\" data-parent=\"#sp-ea-3769\" role=\"region\" aria-labelledby=\"ea-header-37690\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p><span style=\"font-weight: 400\">The <\/span><b>official CSIR NET Mathematical Sciences syllabus<\/b><span style=\"font-weight: 400\"> can be accessed on the<\/span><a href=\"https:\/\/csirnet.nta.nic.in\" rel=\"nofollow noopener\" target=\"_blank\"> <span style=\"font-weight: 400\">CSIR NET website<\/span><\/a><span style=\"font-weight: 400\">. Candidates should check the <\/span><b>\u201cSyllabus\u201d<\/b><span style=\"font-weight: 400\"> or <\/span><b>\u201cInformation Bulletin\u201d<\/b><span style=\"font-weight: 400\"> sections to download the PDF and get detailed information.<\/span><\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-37691\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse37691\" aria-controls=\"collapse37691\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i>  Who prescribes the CSIR NET syllabus?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse37691\" data-parent=\"#sp-ea-3769\" role=\"region\" aria-labelledby=\"ea-header-37691\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p><span style=\"font-weight: 400\">The <\/span><b>CSIR NET syllabus<\/b><span style=\"font-weight: 400\"> is prescribed by the <\/span><b>Council of Scientific and Industrial Research (CSIR)<\/b><span style=\"font-weight: 400\"> in India, and the exam is conducted by the <\/span><b>National Testing Agency (NTA)<\/b><span style=\"font-weight: 400\"> following the guidelines set by CSIR.<\/span><\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-37692\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse37692\" aria-controls=\"collapse37692\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> How are questions distributed in each part of the CSIR NET Mathematical Science exam?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse37692\" data-parent=\"#sp-ea-3769\" role=\"region\" aria-labelledby=\"ea-header-37692\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p><span style=\"font-weight: 400\">CSIR NET Mathematical Sciences exam consists of two papers. Paper 1 tests general aptitude with 50 questions carrying 35\u201350 marks, while Paper 2 is subject-specific with 75 questions worth 100 marks, covering Units 1\u20134. The question distribution generally reflects the syllabus weightage: Units 1 and 2 focus on Algebra, Analysis, and Topology; Unit 3 covers ODE, PDE, and Mechanics; and Unit 4 deals with Probability and Statistics. However, the NTA may slightly adjust the weightage each year.<\/span><\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-37693\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse37693\" aria-controls=\"collapse37693\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> How can exam analysis help me prepare for future CSIR NET Mathematical Science exams?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse37693\" data-parent=\"#sp-ea-3769\" role=\"region\" aria-labelledby=\"ea-header-37693\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p><span style=\"font-weight: 400\">Analyzing past CSIR NET Mathematical Sciences exams helps candidates <\/span><b>identify trends<\/b><span style=\"font-weight: 400\">, such as repeated topics and frequently asked concepts. It also aids in <\/span><b>time management<\/b><span style=\"font-weight: 400\">, showing which sections require more time and attention. By focusing on <\/span><b>weak areas<\/b><span style=\"font-weight: 400\">, students can prioritize units where mistakes are common, while practicing <\/span><b>question patterns<\/b><span style=\"font-weight: 400\"> improves familiarity with multiple-choice strategies and tricky conceptual problems, ultimately enhancing overall preparation and performance.<\/span><\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-37694\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse37694\" aria-controls=\"collapse37694\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What does the CSIR NET Mathematical Science Syllabus cover?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse37694\" data-parent=\"#sp-ea-3769\" role=\"region\" aria-labelledby=\"ea-header-37694\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p><span style=\"font-weight: 400\">The <\/span><b>CSIR NET Mathematical Sciences syllabus<\/b><span style=\"font-weight: 400\"> covers four main units. <\/span><b>Unit 1<\/b><span style=\"font-weight: 400\"> focuses on Linear Algebra and Real Analysis, including matrices, determinants, vector spaces, sequences, series, and Riemann integration. <\/span><b>Unit 2<\/b><span style=\"font-weight: 400\"> includes Algebra, Complex Analysis, and Topology, covering group theory, rings, fields, analytic functions, and topological concepts. <\/span><b>Unit 3<\/b><span style=\"font-weight: 400\"> deals with Ordinary and Partial Differential Equations, Integral Equations, Calculus of Variations, and Classical Mechanics. <\/span><b>Unit 4<\/b><span style=\"font-weight: 400\"> covers Probability and Statistics, including probability theory, distributions, correlation, regression, and hypothesis testing.<\/span><\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<script type=\"application\/ld+json\">{ \"@context\": \"https:\/\/schema.org\", \"@type\": \"FAQPage\", \"mainEntity\": [{ \"@type\": \"Question\", \"name\": \"Where can I find the CSIR NET Mathematical Science Syllabus?\", \"acceptedAnswer\": { \"@type\": \"Answer\", \"text\": \"The<b>official CSIR NET Mathematical Sciences syllabus<\/b>can be accessed on the<a href='https:\/\/csirnet.nta.nic.in'>CSIR NET website<\/a>. Candidates should check the<b>\u201cSyllabus\u201d<\/b>or<b>\u201cInformation Bulletin\u201d<\/b>sections to download the PDF and get detailed information.\" } },{ \"@type\": \"Question\", \"name\": \" Who prescribes the CSIR NET syllabus?\", \"acceptedAnswer\": { \"@type\": \"Answer\", \"text\": \"The<b>CSIR NET syllabus<\/b>is prescribed by the<b>Council of Scientific and Industrial Research (CSIR)<\/b>in India, and the exam is conducted by the<b>National Testing Agency (NTA)<\/b>following the guidelines set by CSIR.\" } },{ \"@type\": \"Question\", \"name\": \"How are questions distributed in each part of the CSIR NET Mathematical Science exam?\", \"acceptedAnswer\": { \"@type\": \"Answer\", \"text\": \"CSIR NET Mathematical Sciences exam consists of two papers. Paper 1 tests general aptitude with 50 questions carrying 35\u201350 marks, while Paper 2 is subject-specific with 75 questions worth 100 marks, covering Units 1\u20134. The question distribution generally reflects the syllabus weightage: Units 1 and 2 focus on Algebra, Analysis, and Topology; Unit 3 covers ODE, PDE, and Mechanics; and Unit 4 deals with Probability and Statistics. However, the NTA may slightly adjust the weightage each year.\" } },{ \"@type\": \"Question\", \"name\": \"How can exam analysis help me prepare for future CSIR NET Mathematical Science exams?\", \"acceptedAnswer\": { \"@type\": \"Answer\", \"text\": \"Analyzing past CSIR NET Mathematical Sciences exams helps candidates<b>identify trends<\/b>, such as repeated topics and frequently asked concepts. It also aids in<b>time management<\/b>, showing which sections require more time and attention. By focusing on<b>weak areas<\/b>, students can prioritize units where mistakes are common, while practicing<b>question patterns<\/b>improves familiarity with multiple-choice strategies and tricky conceptual problems, ultimately enhancing overall preparation and performance.\" } },{ \"@type\": \"Question\", \"name\": \"What does the CSIR NET Mathematical Science Syllabus cover?\", \"acceptedAnswer\": { \"@type\": \"Answer\", \"text\": \"The<b>CSIR NET Mathematical Sciences syllabus<\/b>covers four main units.<b>Unit 1<\/b>focuses on Linear Algebra and Real Analysis, including matrices, determinants, vector spaces, sequences, series, and Riemann integration.<b>Unit 2<\/b>includes Algebra, Complex Analysis, and Topology, covering group theory, rings, fields, analytic functions, and topological concepts.<b>Unit 3<\/b>deals with Ordinary and Partial Differential Equations, Integral Equations, Calculus of Variations, and Classical Mechanics.<b>Unit 4<\/b>covers Probability and Statistics, including probability theory, distributions, correlation, regression, and hypothesis testing.\" } }] }<\/script><\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>CSIR NET Mathematics Sciences syllabus aims to strengthen understanding of mathematical principles and their applications. It emphasizes problem-solving, logical reasoning, and analytical skills across areas such as real analysis, complex analysis, algebra, and statistics. CSIR NET Mathematics preparation is a question many aspirants ask. The key lies in understanding the syllabus thoroughly, covering all important [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":3770,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","rank_math_seo_score":83},"categories":[29],"tags":[662,665,664,666,663],"class_list":["post-3760","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-csir-net","tag-csir-net-mathematical-science-syllabus-2025","tag-csir-net-mathematical-science-syllabus-2025-pdf-download","tag-csir-net-mathematics-science-syllabus","tag-csir-net-mathematics-sciences-syllabus","tag-csir-ugc-net-mathematical-science-syllabus","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/3760","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/comments?post=3760"}],"version-history":[{"count":9,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/3760\/revisions"}],"predecessor-version":[{"id":5555,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/3760\/revisions\/5555"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media\/3770"}],"wp:attachment":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media?parent=3760"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/categories?post=3760"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/tags?post=3760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}