MJC MATH B.Sc SEM-1

MJC-01: Algebra (06 credits)  (Lecture: 60)

Unit 1                                               (Lecture: 10)

Polar representation of complex numbers, De-Moivre’s theorem and its applications, Logarithms of complex quantities, Hyperbolic functions, Gregory series, Summation of series, Resolution into factors.

Unit 2                                                                          (Lecture: 12)

Cartesian product of sets, Equivalence relations, partition, partial and total order relation Functions, Composition of functions, Invertible functions, Cardinality of a set, Countable and Uncountables sets, Cantor’s theorem.

Unit 3                                                                          (Lecture: 12)

Well-ordering property of positive integers, Division algorithm, Euclidean algorithm, Fundamental Theorem of Arithmetic, Modular arithmetic and basic properties of congruences, Principle of mathematical induction.

Unit 4                                                                          (Lecture: 12)

Matrices, Operation on Matrices, Kinds of matrices, Transpose, symmetric & skew symmetric Matrices, Hermitian, skew Hermitian Matrices, Adjoint and Inverse of a matrix, orthogonal matrix, Solution of a system of linear equations by matrix methods. Echelon forms, Rank of a matrix.

Unit 5                                                                          (Lecture: 14)

Fundamental theorem of algebra, Relation between roots and coefficients of a polynomial equation, Symmetric Function of roots, Transformation of equation, Descartes rule of signs, Solution of Cubic equation (Cardon’s method) and bi quadratic equation (Euler’s method).

MJC-1 (PRACTICAL)-2 Credit

The CIA examination in Practical should be just as Mock test and it must be on the Pattern of proper 3hrs End-semester Examination.

                                                                                                            Total = 100 Marks

Ranjeet Kumar Pathak

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धन्यवाद
Ranjeet Kumar Pathak
( B.Sc Physics V.K.S. University )