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CSIR-NET Mathematical Sciences — which book for which unit

The CSIR-UGC NET in Mathematical Sciences (conducted by the NTA) is the national eligibility test for Junior Research Fellowship and Assistant Professor / Lectureship in mathematics. The paper has three parts — Part A (General Aptitude, common to all subjects), Part B and Part C (the subject paper, organised into four units).

This guide takes the official Part B/C syllabus unit by unit and maps each unit to the Shree Sai Prakashan M.Sc titles that cover it — so you can see exactly which book to open for which topic, instead of guessing from a book list. Where a unit is not yet covered by our range, we say so plainly.

Official exam rule: every candidate answers Unit 1; mathematics-stream candidates answer additional questions from Units 2 and 3, while Unit 4 (statistics) is answered mainly by statistics-stream candidates. So for a mathematics aspirant, Units 1–3 plus the operations-research topics of Unit 4 are the core — which is where our range is strongest.

How the paper is structured

The Mathematical Sciences paper has three parts. The four syllabus units below make up Parts B and C.

Part A

General Aptitude — 20 questions (logical reasoning, graphical & numerical ability, data interpretation). Common to every CSIR-NET subject; not maths-specific.

Part B

Subject (Mathematical Sciences) — conventional MCQs drawn from the four units below.

Part C

Subject (higher value) — analytical/multi-concept problems from the same four units. This is where deep textbook understanding pays off.

The syllabus, unit by unit — mapped to our books

Each unit below links to a full page with the complete topic list and the books that cover it.

Unit 1

Analysis & Linear Algebra

Real analysis (the largest single scoring area of the paper) together with linear algebra — the foundation the rest of the syllabus builds on.

Real Analysis

Covers: The whole analysis strand — sequences & series, continuity & uniform convergence, Riemann & Lebesgue integration, functions of several variables, metric spaces, compactness & connectedness.

Functional Analysis

Covers: The normed-linear-space and spaces-of-continuous-functions topics this unit flags, and the functional-analysis foundations that carry into Part C problems.

Not in our range yet — Linear Algebra as a standalone title (vector spaces, eigenvalues, Cayley–Hamilton, canonical/Jordan forms, inner-product & quadratic forms) — not yet in our range.

See Unit 1 in full

Unit 2

Complex Analysis, Algebra & Topology

Three high-yield areas where our M.Sc range is strongest — a dedicated book for each.

Complex Analysis

Covers: The full complex-analysis block — analytic functions, Cauchy’s theorem & integral formula, Taylor/Laurent series, residues, conformal & Möbius maps.

Advanced Abstract Algebra

Covers: The algebra block — groups & Sylow theory, rings & ideals, UFD/PID/Euclidean domains, fields, finite fields and Galois theory.

Advanced Discrete Mathematics

Covers: The combinatorics & elementary number-theory strand of this unit — permutations/combinations, pigeon-hole, inclusion–exclusion, divisibility and congruences.

Topology

Covers: The topology block — basis & dense sets, subspace & product topology, separation axioms, connectedness and compactness.

See Unit 2 in full

Unit 3

Differential Equations, Integral Equations & Mechanics

ODEs, PDEs and integral equations — covered directly — alongside numerical analysis, calculus of variations and classical mechanics.

Advanced Ordinary Differential Equations

Covers: The ODE block — existence & uniqueness, systems of first-order ODEs, linear ODE theory, variation of parameters, Sturm–Liouville BVP and Green’s function.

Partial Differential Equations

Covers: The PDE block — Lagrange & Charpit methods, the Cauchy problem, classification of second-order PDEs, and separation of variables for Laplace/Heat/Wave.

Integral Equations with Boundary Value Problems

Covers: The linear-integral-equations block — Fredholm & Volterra equations, separable kernels, characteristic numbers & eigenfunctions, and the resolvent kernel.

Special Functions

Covers: Supporting title — the special functions (Bessel, Legendre and others) that arise when the PDE topics are solved by separation of variables.

Not in our range yet — Numerical Analysis as a standalone M.Sc title — not yet in our range.

Not in our range yet — Calculus of Variations and Classical Mechanics (Lagrangian/Hamiltonian dynamics) — not yet published at M.Sc level.

See Unit 3 in full

Unit 4

Statistics, Data Analysis & Operations Research

Probability, statistical inference and multivariate analysis, plus operations research (linear programming, queuing & inventory). Per the official exam rule this unit is answered mainly by statistics-stream candidates — for a mathematics aspirant the operations-research topics are the relevant part, and our Operations Research title covers them.

Operations Research

Covers: The operations-research strand of this unit — the linear programming problem & simplex method, duality, and elementary queuing & inventory models.

Not in our range yet — The statistics core of this unit — probability, statistical inference and multivariate analysis — is not yet in our M.Sc range (and is answered mainly by statistics-stream candidates). Pair with a dedicated statistics title if you need it.

See Unit 4 in full

Also in our M.Sc mathematics series

These titles fall outside the CSIR-NET syllabus but are standard M.Sc papers, useful for GATE Mathematics, UGC-NET, the IAS mathematics optional and state PCS.

Differential Geometry (UGC Edition 2026)

UGC NET & M.Sc. Mathematics