Calcutta University Msc Applied Mathematics Syllabus Pdf

Milsap Mustrien · Wednesday, 17 November 2021

#2

Old 29th November 2016, 02:55 PM

Default Re: Calcutta University Msc Mathematics Syllabus

Yes I have Calcutta University Msc Mathematics Syllabus and on your demand I am sharing with you here :

Algebra-I
Semester : I
Course ID : PM1/01 Full Marks : 50
Minimum number of classes required : 60
Index Elective I Elective II
• Group Theory : External direct product and internal direct product of groups. Direct product of cyclic
groups. Group actions, extended Cayley's theorem, Burnside theorem. Conjugacy classes, class–equation.
Cauchy's theorem on finite groups, p-group, Centre of p-groups. Sylow's theorems, some applications
of Sylow's theorems, Simple groups, characterizations of commutative simple groups, non simplicity of
groups of order pn(n > 1), pq, p2q, p2q2(p, q are primes), determination of all simple groups of order ≤ 60,
nonsimplicity of An (n ≥ 5). Finite groups, classification of all groups of order 6, the groups D4 and Q8,
classification of all groups of order 8. Structure theorem for finite Abelian groups. Normal and subnormal
series, composition series, Jordan – Holder theorem, solvable groups and nilpotent groups.
• Ring Theory : Ideal, Quotient ring, Ring embeddings, direct sum of rings, Euclidean domain, principal
ideal domain, prime elements and irreducible elements, maximal ideals, prime ideals, primary ideals, chain
condition, polynomial ring and factorization of polynomials over a commutative ring with identity, poly-
nomials over rational field, the division algorithm in K[x] where K is a field, K[x] as Euclidean domain,
unique factorization domain, If D is UFD , then so are D[x] and D[x1,x2,...,xn], Application of unique
factorization domain to the introductory algebraic number theory, Eisenstein's criterion of irreducibility,
Noetherian and Artinian rings, Hilbert Basis Theorem. Algebraic approach to Fermat's Theorem, Euler's
Theorem, Willson's Theorem, Chinese Remainder Theorem, primitive roots.