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We cover the following Algebra Bsc 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, cosets, lagrage's theorem, permutation groups.

Rings, fields, vector spaces, subspaces, 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, adjoint 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 biquadratic 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.

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