← CSIR-NET Mathematics guide CSIR-NET Mathematics · 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.
Books that cover Unit 1
Looking for the right book for this unit? These are the titles from our M.Sc range that cover it — tap through for full contents, price and buy options.
Real Analysis
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The whole analysis strand — sequences & series, continuity & uniform convergence, Riemann & Lebesgue integration, functions of several variables, metric spaces, compactness & connectedness.
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Functional Analysis
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
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.
View details Full syllabus — Unit 1
- Elementary set theory; finite, countable and uncountable sets
- Real number system as a complete ordered field; Archimedean property; supremum & infimum
- Sequences and series; convergence; limsup, liminf; Bolzano–Weierstrass & Heine–Borel theorems
- Continuity, uniform continuity, differentiability, mean value theorem
- Sequences & series of functions; uniform convergence
- Riemann sums & Riemann integral; improper integrals; functions of bounded variation
- Lebesgue measure & Lebesgue integral
- Functions of several variables; directional & partial derivatives; inverse & implicit function theorems
- Metric spaces; compactness; connectedness; normed linear spaces; spaces of continuous functions
- Linear algebra: vector spaces, basis, dimension, linear transformations, matrices, rank & determinant
- Eigenvalues & eigenvectors; Cayley–Hamilton theorem; canonical, diagonal, triangular & Jordan forms
- Inner product spaces; orthonormal basis; quadratic forms & their classification
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.