This book is intended as a textbook for a one-term senior undergraduate (or graduate) course in Ring and Field Theory, or Galois theory. The book is ready for an instructor to pick up to teach without making any preparations.The book is written in a way that is easy to understand, simple and concise with simple historic remarks to show the beauty of algebraic results and algebraic methods. The book contains 240 carefully selected exercise questions of varying difficulty which will allow students to practice their own computational and proof-writing skills. Sample solutions to some exercise questions are provided, from which students can learn to approach and write their own solutions and proofs. Besides standard ones, some of the exercises are new and very interesting. The book contains several simple-to-use irreducibility criteria for rational polynomials which are not in any such textbook.This book can also serve as a reference for professional mathematicians. In particular, it will be a nice book for PhD students to prepare their qualification exams.

Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness, and overall student usability. Its inclusion of calculus-related examples, true/false problems, section summaries, integrated applications, and coverage of Cn make it a superb text for the sophomore or junior-level linear algebra course. This Third Edition retains the features that have made it successful over the years, while addressing recent developments of how linear algebra is taught and learned. Key concepts are presented early on, with an emphasis on geometry.

This is a book for the second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. The knowledge gained from a particular case, that encapsulates the main idea of a general theorem, can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.

This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences.

Offering the most geometric presentation available, Linear Algebra with Applications, Fifth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author's creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.

For courses in Advanced Linear Algebra. This top-selling, theorem-proof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.

Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.