Curso de Álgebra, vol. 1 is a textbook for a first course in algebra for undergraduate students in mathematics and related areas. The book deals with the algebra of the number sets (integers, rationals, reals and complex) and contains many exercises.
The presentation is elementary and each introduced concept is illustrated with several examples. This book originated from class notes of a three-semester Algebra course taught several times over more than a decade at the University of Espirito Santo. This is the first of two volumes of a full course of algebra for undergraduate students of mathematics and related areas.
The global structure of the course is as follows. The first semester presents the integers and the rational numbers and the structure of rings and fields, emphasizing the properties of principal ideal domains and exploring the relationship between algebra and arithmetic. The second semester studies the complex numbers, rings of polynomials and the equations of the 3rd and 4th degrees by the classical and Lagrange methods, introducing permutation groups. The third semester is dedicated to Galois theory and to finite groups. The chapters about real numbers and Gaussian integers, where not part of the notes of the courses taught, and have been written and incorporated into the text with the purpose of completing it. They can be used as seminars.
ABOUT THE AUTHOR
Abramo Hefez
Abramo Hefez graduated in mathematcs at PUC-Rio and at Università di Pisa (Italia). He obtained his PhD at MIT (USA) in algebraic geometry and a “Livre Docente” at UNICAMP. Currently he is professor at the Federal University Fluminense.
