Course No:           Act 317

Course Name:      Mathematics - 1 (Algebra)

Course Description:      

SECTION - A

Number System: Real and complex number systems. Demoivres theorem with applications, exponential, trigonometric, hyperbolic, logarithmic, inverse hyperbolic and inverse circular functions

Infinite Series: Sequences, limits and bounds of sequences. Infinite series comparison test, limit comparison test, integral; ratio and root tests. Alternating series, absolute and conditional convergence.

SECTION - B

Set Theory: Binary relations, functions and their graphs, composition of functions. Group Theory: Groups and their properties, subgroups, order of groups, cyclic groups, cossets, Lagrange’s theorem, and permutation groups. Rings, fields, vector spaces, subspaces, linear combinations and spanning set, linear dependence and basis, dimension, linear transformations.

SECTION-C

Matrices: Elementary row operations, echelon and reduced echelon forms, inverse, rank and normal form of a matrix. Matrix of linear transformation. Partitioning of a matrix.

Determinants: Axiomatic definitions of a determinant, determinant as sum of products of elements, adjoint and inverse of matrix.

Systems of Linear Equations: Gauss elimination and Gauss –Jordan, methods Cramer’s rule, consistent and inconsistent systems.

SECTION - D

Equations: Solution of cubic and biquadratic equations, Numerical solutions of equations, Newton-Raphson, Regula Falsi and bisection methods.

Interpolation: interpolation by graph: Newton’s forward and backward formula. Newton's divided difference formula. Lagrange’s formula, inverse interpolation. Central Difference formula (Gauss, Stirlings, Bessel)

Course Review:

This course familiarizes students with number systems, Demoivre’s theorem and its applications, trigonometric, hyperbolic, logarithmic, inverse hyperbolic and inverse circular functions; infinite series, sequences, infinite series comparison test, alternating series, absolute and conditional convergence; set theory, which includes binary relations, functions and their graphs; group theory, which includes properties of groups, Lagrange’s theorem, rings, fields, vector spaces, linear dependence and basis, linear transformations; matrices of linear transformations, elementary row operations, echelon and reduced echelon forms, inverse, rank and normal form of a matrix, partitioning of a matrix; Axiomatic definition of a determinant, determinant as sum of products of elements, adjoint and inverse of a matrix; systems of linear equations including Gauss Jordan and Gauss Elimination methods, and Cramer’s rule, consistent and inconsistent systems; solution of cubic and biquadratic equations, numerical solutions of equations, Newton-Raphson and bisection methods.