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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.
To get professional teachers call us at +92332-3343253, or add our Skype Id: ascc576.
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