LNMU B.Sc. part-1 mathematics honours Syllabus

Lalit narayan mithila university, Darbhanga B.Sc. part-1 mathematics honours Syllabus

Paper-I

Twelve questions to be set and six to be answered. "Schoelder Partial and total order relations, countability, Cardinality. Bernstein theorem, Cardinal and ordinal numbers and their arithmetic, Axiom choice and its various forms, Zor well ordering theorem (3 questions) properties, Definition of a group with examples and simple of groups, Cyclic groups, Coset decomposition, Lagrange's theorem and its consequences, Fer and Euler's theorems, Homomorphism and Isomorphism, Normal subgroups. Quotient groups, Fundamental theorem of homomorphism. Permutation groups. Even and odd permutations, the alternating groups, Cayley's theorem, Introduction of rings, sub rings. Integral domains and fields, characteristic of a ring. (3 questions) Symmetric, Skew symmetric, Hermitian and Skew Hermitian matrices. Elementary operations on matrices, Inverse of a matrix. Linear independence of row and column matrices. Rank of a matrix, Eigen values, Eigen vectors and the characteristic equation of a matrices to system of linear (both homogenous and non-homogeneous) equations Theorems on consistency of a system of linear equation. (3questions) General properties of polynomials and equation. Fundamental theorem of algebra, Descarte's rule of sing, Relation between roots and coefficients. Evaluations of symmetric functions of roots of eubic and biquadratic, of equations, Reciprocal equations Transformation of cubic and biquadratic.

Paper-II

Twelve questions to be set and six to be answered.
Analytical Geometr of Two dimensions :- General equation of second degree, tracing of conics, system of conics, confocal conics, polar equation of conic. equation of chord. tangent, normal. asymptote and director circle. (4 questions) Analytical Geometry of Three dimension :- Equations of plane and straight lines, Coplanarity. Shortest distance. volume of tetra hedron Sphere, Radical plane. tangent plane, cone, generating line, condition for three mutually perpendicular generators. central conicoids, normal and conguage diameters of ellipsoids and its properties questions)
Higher Trigonometry :- De moivers theorem and its applications circular, inverse circular and hyperbolic functions. Logarithm o complex quantity. Expansion of trigonometrical functions, Greogorys series, summation of series, Resolution into factors.