Gauhati University Question Papers for Mathematics 3rd Semester
Gauhati University Question Papers for Mathematics 3rd Semester
Question Paper from 2010 available
Please check your syllabus before downloading the question paper.
If syllabus does not match then don't download the question paper.
Year
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Paper 101
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Paper 102
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2010
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2011
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2012
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2014
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3rd Semester
Revised Syllabus of Mathematics For Three year Degree Course ( Major Course) Paper-M304
Abstract Algebra Marks:
Unit 1: Homomorphism of groups, Fundamental theorems of homomorphism, Caley’s theorem. 20 marks Unit 2: Rings Integral domains division rings and fields, subrings,characteristic of a ring, idempotent and nilpotent elements in a ring, principle ,prime, maximal ideals, simple rings, definition and examples of vector space and its subspaces. 20 marks Unit 3: Inner automorphisms, automorphisms groups,conjugacy relation, normaliser, centre of a group, class equation and Cauchy’s theorem, Sylow’s theorems,( statement and applications).
Unit 4:
Ring homomorphisms,quotient rings, field of quotients of an integral domain,
Euclidean rings, polynomial rings.
3rd Semester
Revised Syllabus of Mathematics
For
Three year Degree Course ( Major Course) Paper-M305
Linear Algebra and Vector 1
Linear Algebra:
Unit 1: Sums and direct sum of subspaces, linear span, linear dependence and
independence and their basic properties, basis, finite dimensional vector spaces, existence theorem for bases, invariance of the number of elements of a basis, dimensions, existence of complementary subspace of a subspace of finite dimension, dimension of sum of subspaces, quotient spaces and its dimension.
Unit 2:Linear transformations and their representation as matrices, the algebra of linear transformations, the rank nullity theorem, change of basis, dual spaces.
Unit 3: Eigenvalues ,eigenvector, characteristic equation of a matrix, Cayley
Hamilton theorem, minimal polynomial, characteristic and minimal polynomial of
linear operators, existence an uniqueness of solution of a system of linear
equations.
Vector:
Unit 4: Scalar triple product, vector triple product, product of four vectors.
Unit 5: Continuity and derivability of a vector point function, partial derivatives of vector point function, gradient, curl and divergence, identities.
Unit 6: vector integration, line, surface and volume integrals, Green, Stokes and Gauss’ theorems. 10 marks Text Books;
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