This series offers advanced mathematical concepts tailored for upper-level undergraduate students. It aims to provide readers with fresh perspectives and innovative approaches to mathematical subjects. Each volume includes motivation to foster an appreciation for the interrelations between different areas of study. The texts are enriched with illustrative examples and exercises to solidify comprehension.
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.
Cryptography is a key technology in electronic key systems. It is used to keep data secret, digitally sign documents, access control and other such areas. Based on courses taught at Technical University in Darmstadt, Germany, this book explains the basic methods of modern cryptography.