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We cover the following Algebra B. Sc. syllabus during classes:
Number System: Real and complex number system, 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.
Set Theory: Binary relation, functions and their graphs, composition of functions.
Group Theory: Groups and their properties, subgroups, order of groups, cyclic groups, co sets, lagrange’s theorem, permutation groups. Rings, fields, vector spaces, sub spaces, linear combinations and spanning set, linear dependence and basis, dimension, linear transformations.
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, Ad joint and inverse of matrix.
System of Linear Equations: Gauss elimination and Gauss Jordan methods, Cramer’s Rule, consistent and inconsistent systems.
Equations: Solution of cubic and bi quadratic equations, Numerical solution of equations, Newton-Raphson, Regular Falsi and bisection methods.
Probability: Axioms of probability, conditional probability, Discrete and continuous random variables, probability distributions, Binomial, Poisson’s and normal distributions.