This is a map, not a set of notes. Every line of the official syllabus is listed below and pointed at the page here that teaches it — or marked as not here, where nothing does. The statistics itself lives in the study sections and is linked to rather than copied, so correcting a proof once corrects it for every exam that points at it.
The syllabus answers this itself, in its closing paragraph:
“All students are expected to answer questions from Unit I. Students in mathematics are expected to answer additional question from Unit II and III. Students with in statistics are expected to answer additional question from Unit IV.”
— CSIR-UGC NET common syllabus for Part B and C, Mathematical Sciences (quoted verbatim, including its own grammar)So a statistics candidate reads Unit 1 and Unit 4. Units 2 and 3 are for mathematics candidates; they are listed at the foot of this page so you can see what is being left out, and why.
No exam pattern appears on this page. Marks, duration, negative marking, the number of papers and eligibility are not in the syllabus document this page was built from, and they change between notifications. Read the current official notification for those. Use this page for the statistics, not for the rules.
deep a full unit page here, with derivations and worked problems — usually more than the exam needs. brief covered, at exam level, on one page. not here nothing on this site teaches it; you will need another source.
Every candidate answers this unit. Most of it is covered by the existing Real Analysis & Matrix Algebra page written for UGC NET, which is why so many rows point at one destination. The measure-theoretic and abstract-algebraic parts are the real holes.
| Syllabus line | Where it is taught here | Depth |
|---|---|---|
| Elementary set theory, finite, countable and uncountable sets; real number system as a complete ordered field, Archimedean property, supremum, infimum | UGC NET Unit II §1 | brief |
| Sequences and series, convergence, limsup, liminf; Bolzano–Weierstrass, Heine–Borel | UGC NET Unit II §2–3 | brief |
| Continuity, uniform continuity, differentiability, mean value theorem | UGC NET Unit II §5–6 | brief |
| Sequences and series of functions, uniform convergence | nothing on this site teaches it | not here |
| Riemann sums and Riemann integral, improper integrals | UGC NET Unit II §7 | brief |
| Monotonic functions, types of discontinuity | UGC NET Unit II §5 | brief |
| Functions of bounded variation | nothing on this site teaches it | not here |
| Lebesgue measure, Lebesgue integral | nothing on this site teaches it | not here |
| Functions of several variables, directional derivative, partial derivative, derivative as a linear transformation, inverse and implicit function theorems | UGC NET Unit II §8 (partial) | brief |
| Metric spaces, compactness, connectedness, normed linear spaces, spaces of continuous functions | nothing on this site teaches it | not here |
| Vector spaces, subspaces, linear dependence, basis, dimension, algebra of linear transformations | nothing on this site teaches it | not here |
| Algebra of matrices, rank and determinant of matrices, linear equations | UGC NET Unit II §10–12 | deep |
| Eigenvalues and eigenvectors, Cayley–Hamilton theorem | UGC NET Unit II §14–15 | deep |
| Matrix representation of linear transformations, change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms | nothing on this site teaches it | not here |
| Inner product spaces, orthonormal basis | UGC NET Unit II §13 (Gram–Schmidt) | brief |
| Quadratic forms, reduction and classification of quadratic forms | UGC NET Unit II §17 | deep |
This is the statistics candidate's second unit, and where this site is strongest. Several of these rows point at pages rewritten from textbook sources, with every step shown and every worked answer recomputed — more than a question paper will ask for.
| Syllabus line | Where it is taught here | Depth |
|---|---|---|
| Descriptive statistics, exploratory data analysis | Descriptive Statistics (5 units) Descriptive Statistics in R | deep |
| Sample space, discrete probability, independent events, Bayes theorem | Theory of Probability Unit 1 UGC NET Unit I | deep |
| Random variables and distribution functions (univariate and multivariate); expectation and moments | Theory of Probability Unit 2 Mathematical Expectation | deep |
| Independent random variables, marginal and conditional distributions | Bivariate Random Variables | deep |
| Characteristic functions | Generating Functions, LLN & CLT | brief |
| Probability inequalities (Tchebyshef, Markov, Jensen) | Mathematical Expectation | brief |
| Modes of convergence, weak and strong laws of large numbers, Central Limit theorems (i.i.d. case) | Generating Functions, LLN & CLT | brief |
| Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes | UGC NET Unit IX — Stochastic Processes | brief |
| Standard discrete and continuous univariate distributions | Discrete Distributions (5 units) Continuous Distributions (5 units) | deep |
| Sampling distributions, standard errors and asymptotic distributions | Standard Normal & Sampling Distributions | deep |
| Distribution of order statistics and range | UGC NET Unit IV | brief |
| Methods of estimation, properties of estimators, confidence intervals | Inferential Statistics Unit 1 | deep |
| Tests of hypotheses: most powerful and uniformly most powerful tests, likelihood ratio tests | Inferential Statistics Unit 2 | deep |
| Analysis of discrete data and chi-square test of goodness of fit | Inferential Statistics Unit 4 | deep |
| Large sample tests | Inferential Statistics Unit 3 | deep |
| Simple nonparametric tests for one and two sample problems, rank correlation and test for independence | Inferential Statistics Unit 5 Which Statistical Test to Use | deep |
| Elementary Bayesian inference | nothing on this site teaches it | not here |
| Gauss–Markov models, estimability of parameters, best linear unbiased estimators, confidence intervals, tests for linear hypotheses | Econometrics Unit 2 — Models and Estimation UGC NET Unit VI | deep |
| Analysis of variance and covariance | Design of Experiments Unit 1 — ANOVA | deep |
| Fixed, random and mixed effects models | UGC NET Unit III | brief |
| Simple and multiple linear regression, elementary regression diagnostics | Econometrics (5 units) Multiple & Partial Correlation | deep |
| Logistic regression | UGC NET Unit VI Machine Learning — Classification | brief |
| Multivariate normal distribution, Wishart distribution and their properties; distribution of quadratic forms | UGC NET Unit VIII — Multivariate Analysis | brief |
| Inference for parameters, partial and multiple correlation coefficients and related tests | Concurrent Deviation, Multiple & Partial Correlation | deep |
| Data reduction: principal component analysis, discriminant analysis, cluster analysis, canonical correlation | UGC NET Unit VIII Machine Learning — Clustering | brief |
| Simple random sampling, stratified sampling and systematic sampling | Sampling Techniques (5 units) | deep |
| Probability proportional to size sampling | Sampling Techniques UGC NET Unit III | brief |
| Ratio and regression methods | Sampling Techniques UGC NET Unit III | brief |
| Completely randomized designs, randomized block designs and Latin-square designs | Design of Experiments (5 units) | deep |
| Connectedness and orthogonality of block designs, BIBD | UGC NET Unit III | brief |
| 2ᵏ factorial experiments: confounding and construction | Design of Experiments UGC NET Unit III | brief |
| Hazard function and failure rates, censoring and life testing | Clinical Trials Unit 4 | brief |
| Series and parallel systems | nothing on this site teaches it | not here |
| Linear programming problem, simplex methods, duality | Operations Research (5 units) | deep |
| Elementary queuing and inventory models | nothing on this site teaches it | not here |
| Steady-state solutions of Markovian queuing models: M/M/1, M/M/1 with limited waiting space, M/M/C, M/M/C with limited waiting space, M/G/1 | UGC NET Unit IX | brief |
Naming these is the point of the map. Across both units, 9 lines have nothing on this site behind them:
The Unit 1 gaps are pure mathematics — measure theory, metric-space topology and abstract linear algebra — which is a long way from the rest of this site. The three Unit 4 gaps are closer to home and are the more likely additions.
These are the mathematics candidate's units. This site does not teach them and is not planning to. They are listed so that a candidate can tell in one glance whether this is the wrong place to be.
| Unit | Topics, as the syllabus lists them |
|---|---|
| Unit 2 | Complex analysis — algebra of complex numbers, analytic functions, Cauchy’s theorem and integral formula, Liouville, maximum modulus, Taylor and Laurent series, residues, conformal and Möbius mappings. Algebra — permutations and combinations, congruences, Chinese remainder theorem, groups, Sylow theorems, rings and ideals, unique factorization and Euclidean domains, polynomial rings, fields and Galois theory. Topology — basis, dense sets, product topology, separation axioms, connectedness and compactness. |
| Unit 3 | Ordinary differential equations, partial differential equations, numerical analysis, calculus of variations, linear integral equations and classical mechanics. |
Built from the official CSIR-UGC NET common syllabus for Part B and C, Mathematical Sciences, as supplied. Syllabus lines are quoted from that document; the wording is the syllabus’s own, not a paraphrase. Nothing on this page comes from any other source, and nothing that was not in the document — marks, dates, eligibility — appears at all.
← Back to Statistics for Examinations
The courses this exam’s map sends you to, in learning order — 13 of them. Each is listed because the map links into it, not because it was judged relevant, so a course missing here is one no line of this syllabus points at.