This course handout is intended for first-year university students enrolled in Science
and Technology programmes (Licence and Engineer cycle). It provides a self-contained
and progressive introduction to the fundamental concepts of Algebra, spanning seven
chapters that cover the essential mathematical structures required for advanced study
in mathematics, physics, computer science, and engineering.
The handout opens with the basic language of set theory, relations, and functions, before
developing the algebraic and geometric theory of complex numbers. It then introduces
vector spaces and linear maps, examining their properties and the relationship between
linear transformations and matrices. A thorough treatment of matrix algebra and
determinants follows, including methods for computing inverses and solving linear
systems. The handout concludes with the reduction of matrices, covering eigenvalues,
eigenvectors, and diagonalisation. Throughout, theoretical results are supported by
detailed worked examples and exercises designed to reinforce understanding and build
problem-solving skills.
