This classic graduate-level text provides a rigorous and systematic introduction to the core structures of algebraic number theory. It covers foundational topics like the theory of ideals and units before moving into advanced areas such as ideles, adeles, and class field theory. Lang’s efficient style bridges the gap between basic algebra and modern research, making it a cornerstone resource …
This volume offers a rapid and self-contained introductory approach to the algebraic aspects of algebraic geometry, defined by Lang as the study of systems of algebraic equations in several variables and the structures formed by their solutions. Originally published in 1958, this 1972 printing serves as an amplification of lectures based on the Weil-Zariski approach. The text covers foundationa…
This textbook offers a unique and rigorous approach to secondary school geometry, written by the renowned mathematician Serge Lang and experienced teacher Gene Murrow. Departing from the standard "two-column proof" format common in many American high schools, this text emphasizes logical reasoning and the relationship between geometry and algebra. It introduces topics such as distance, area, an…