Introduction to Algebra: DE

This book, intended for first-year students in Mathematics and Computer Science, covers the fundamental structures of modern algebra. It begins with logic and methods of reasoning (implication, quantifiers, mathematical induction), then addresses sets and mappings (injection, surjection, bijection). Binary relations are studied through equivalence relations and order relations.The chapter on algebraic structures introduces groups, subgroups, morphisms, Lagrange's theorem, then rings, ideals, and fields, with an example of finite fields FpF_pFp¿. The ring of polynomials is presented together with arithmetic operations, Euclidean division, factorization, and the Fundamental Theorem of Algebra.The second part is devoted to linear algebra: vector spaces, bases, dimension, linear transformations, kernel, image, and rank. Matrices are then defined as representations of linear transformations, with operations, inversion, and change of basis. Finally, the last chapter deals with systems of linear equations through determinants.

Pages: 196, Paperback, LAP Lambert Academic Publishing