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Mathematics II

Mathematics II covers advanced calculus, linear algebra, discrete mathematics, probability, and statistics to enhance analytical and problem-solving abilities. Students engage in lectures, practical exercises, and collaborative projects, receiving feedback to deepen their understanding. Emphasis is placed on applying mathematical theories to real-world ICT problems, utilizing software tools for computations, and developing logical reasoning skills. Practical activities include solving complex equations, analyzing data sets, implementing algorithms, and using mathematical software for simulations.

Complex Number

Definition of complex number and, Geometrical representation, Conjugate and absolute value of complex number, Square roots of complex number Polar and Exponential forms of complex numbers, nth roots of complex numbers using DeMoivre's Theorem.

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Fundamentals of Calculus

Limits and continuity of a function, ε − δ definition of limit and continuity, Evaluate the limit of the function, Continuity of the function, Derivatives of function, Definition and Geometrical interpretation, Derivatives of the functions (Algebraic only), Maxima and minima of functions, Indefinite and Definite Integral, Meanings of Integrals, Some Standard Integrals, Meaning of ∫ f(x)dx b a, Problems on finding definite integral, Area of plane regions.

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Basics of Number Theory

Odd, Even and Divisibility Relationships, The Divisibility Rules, The Division Algorithm, The Greatest Common Divisor (GCD) and Euclidean Algorithm Different Base Number System, Modular Arithmetic.

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Analytic Geometry

Straight Lines, Equation of straight lines, Perpendicular distance of a line, Angle between lines, Conic Section [Definitions and equations on Standard forms with examples].Circle, Parabola, Ellipse, Hyperbola, Coordinate in space, Coordinates of a point in space Distance between two points Directions Cosines and Ratios Projection

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Fundamental Concepts of Graph Theory

Introduction of graph, Different types of Graphs, Vertex and edges of graphs, Walks, paths and cycles of Graphs, Eulerian and Hamiltonian graphs concept and examples only. Trees and Forest concept with examples.

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Algebra

Algebra, Group Theory, Binary operation, Algebraic Structure and its properties, Group and its properties, Sub-groups, Cyclic groups and Permutation group, Ring and Field, Definition of rings and its properties, Subring definition with examples, Field definition and examples.

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