BICT | BICTE Mathematics II (2nd Sem)

Tribhuvan University

Faculty of Education

Course Title: Mathematics II

Course no: Math Ed. 426

Nature of course: Theory+Pratical

Full Marks: 100

Pass Marks: 40

Credit Hours: 3

Course Description : 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.

Course Objective : This module aims to impart the basic management knowledge, and skills to the students so as to enhance their managerial capabilities and enable them to apply in the practical field

Course Contents:

Unit 1. Complex Number 3 Hrs.

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.

Unit 2. Basics of Number Theory 3 Hrs.

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.

Unit 3. Fundamentals of Calculus 3 Hrs.

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.

Unit 4. Analytic Geometry 3 Hrs.

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

Unit 5. Fundamental Concepts of Graph Theory 3 Hrs.

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.

Unit 6. Algebra 3 Hrs.

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.