Cette série propose des concepts mathématiques avancés destinés aux étudiants de premier cycle universitaire. Elle vise à offrir aux lecteurs de nouvelles perspectives et des approches innovantes sur des sujets mathématiques. Chaque volume comprend des éléments de motivation qui encouragent à apprécier les interrelations entre différents domaines d'étude. Les textes sont enrichis d'exemples illustratifs et d'exercices pour approfondir la compréhension.
Covering essential topics in advanced mathematics, the book delves into complex vector spaces, inner products, and the Spectral theorem for normal operators. It also explores dual spaces, the minimal polynomial, and the Jordan canonical form. Engaging exercises throughout enhance understanding and application of these concepts, making it a valuable resource for students and enthusiasts in the field.
Aimed at mathematics, science, and engineering majors in their final undergraduate quarter, this text addresses the gap in existing analysis books that cater specifically to aspiring mathematicians. It provides a foundational understanding of analysis, emphasizing rigorous thinking and proof-based approaches, contrasting with the intuitive methods typically encountered in earlier studies. Designed for students who have completed calculus and possibly some modern algebra, the book prepares them for advanced mathematical concepts and further academic pursuits in the field.
This revised edition of "Functions of Several Variables" offers a comprehensive introduction to differential and integral calculus, including new content on elementary topology and physical applications. It emphasizes vector notation and includes advanced topics like the Lebesgue theory of integrals, suitable for a one-year advanced undergraduate course.
The Mathematics of Finance is tailored for advanced undergraduates or beginning graduates in mathematics, finance, or economics. It focuses on discrete derivative pricing models, including a thorough derivation of the Black-Scholes formulas. This second edition features improved organization and expanded discussions on options, while maintaining rigorous mathematics suitable for the target audience.
In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19 th century. Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
Les techniques de cryptographie présentent de nombreux usages. De la signature des documents électroniques à la protection du copyright, elles permettent d'assurer la confidentialité, l'accès et l'identification des documents. Ce livre présente, sans formalisme mathématique excessif, les outils mathématiques et algorithmiques utiles à la compréhension de la cryptographie. Le cours est complété par des exercices simples dont la moitié trouvent leurs corrigés en fin d'ouvrage. Ce manuel s'adresse aux étudiants en Licence 3 ou Master 1 de mathématiques appliquées ou d'informatique ainsi qu'aux élèves ingénieurs.
This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalisation to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. A compact, but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.