← CSIR-NET Mathematics guide CSIR-NET Mathematics · Unit 2
Complex Analysis, Algebra & Topology
Three high-yield areas where our M.Sc range is strongest — a dedicated book for each.
Books that cover Unit 2
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.
Complex Analysis
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The full complex-analysis block — analytic functions, Cauchy’s theorem & integral formula, Taylor/Laurent series, residues, conformal & Möbius maps.
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Advanced Abstract Algebra
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The algebra block — groups & Sylow theory, rings & ideals, UFD/PID/Euclidean domains, fields, finite fields and Galois theory.
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Advanced Discrete Mathematics
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The combinatorics & elementary number-theory strand of this unit — permutations/combinations, pigeon-hole, inclusion–exclusion, divisibility and congruences.
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Topology
M.A. & M.Sc. Mathematics · Dr. H.K. Pathak
Covers: The topology block — basis & dense sets, subspace & product topology, separation axioms, connectedness and compactness.
View details Full syllabus — Unit 2
- Complex analysis: algebra of complex numbers; analytic functions; Cauchy–Riemann equations
- Cauchy’s theorem & integral formula; Liouville’s theorem; maximum modulus principle; Schwarz lemma
- Taylor & Laurent series; calculus of residues; conformal & Möbius transformations
- Number theory & combinatorics: permutations, combinations, pigeon-hole & inclusion–exclusion principles
- Divisibility, congruences, Chinese Remainder Theorem, Euler’s φ-function, primitive roots
- Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic & permutation groups
- Cayley’s theorem, class equations, Sylow theorems
- Rings, ideals, prime & maximal ideals; UFD, PID, Euclidean domains; polynomial rings & irreducibility
- Fields, finite fields, field extensions, Galois theory
- Topology: basis, dense sets, subspace & product topology, separation axioms, connectedness & compactness