04-Polycopiés Pédagogiques

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Algebra
(Echahid Cheikh Larbi Tebessi University-Tebessa, 2026) Bouaziz Khelifa
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.