Jonathan S. Golan Livres

Focusing on the advancements in semiring theory, this revised edition significantly expands on its predecessor, incorporating recent developments and applications in areas like idempotent analysis and discrete-event dynamical systems. While maintaining the original structure, the text has been extensively rewritten to enhance clarity and depth. An extensive collection of examples is included to spark interest in practical applications, along with a comprehensive index of citations for further exploration. This makes it a valuable resource for both theoretical and applied mathematics.

This book serves as a comprehensive resource for advanced undergraduate and beginning graduate students in linear algebra, addressing gaps in theoretical and computational knowledge. It includes new theorems, examples, and over 130 exercises, making it suitable for self-study, coursework, or exam preparation, while assuming a basic familiarity with core concepts.

Aimed at mathematics majors, this textbook offers a comprehensive one-year course in linear algebra, presuming students have prior knowledge in set theory, mathematical induction, and calculus. It emphasizes both abstract theory and practical applications, particularly in algebraic coding theory and computer science. The text incorporates computational aspects later in the course, assuming students are proficient in programming by that stage. Key topics include finite fields and the solution of linear equations, tailored for those with a mathematical and computational background.

Focusing on the intersection of abstract algebra and applied mathematics, this book delves into semiring theory and its applications in optimization, discrete-event dynamical systems, and automata theory. It specifically addresses the challenge of finding the equalizer of affine maps between semimodules. The volume provides a comprehensive overview of current advancements in solving this problem, along with numerous practical applications, making it a valuable resource for those in theoretical computer science and physics.

Focusing on the exploration of semirings and their applications, this monograph delves into the structures of sets formed by RA, where R is a semiring. It seeks to establish a natural translation of these structures, bridging various mathematical and theoretical computer science topics, including formal language theory and fuzzy algebraic structures. Unlike previous works, this text adopts a more exploratory approach, grappling with foundational philosophical questions about the relationship between algebra, topology, and set theory amidst ongoing research in the field.