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.
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.