This book is concerned with the structure of linear semigroups, that is, subsemigroups of the multiplicative semigroup Mn(K) of n x n matrices over a field K (or, more generally, skew linear semigroups - if K is allowed to be a division ring) and its applications to certain problems on associative algebras, semigroups and linear representations. It is motivated by several recent developments in the area of linear semigroups and their applications. It summarizes the state of knowledge in this area, presenting the results for the first time in a unified form. The book's point of departure is a structure theorem, which allows the use of powerful techniques of linear groups. Certain aspects of a combinatorial nature, connections with the theory of linear representations and applications to various problems on associative algebras are also discussed.

This book is an indispensable source for anyone with an interest in semigroup theory or whose research overlaps with this increasingly important area of mathematics. It is a clear and readable introduction to the subject, with emphasis on various classes of regular and semigroups. More than 150 exercises, accompanied by relevant references to the literature,give pointerse to areas of the subject not explicitly covered in the text.

A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations

Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study

Previous books by Howie in the SUMS series have attracted excellent reviews

Understanding the concepts and methods of real analysis is an essential skill for every undergraduate mathematics student. Written in an easy-to-read style, Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, Real Analysis covers all the key topics with fully worked examples and exercises with solutions. Featuring: * Sequences and series - considering the central notion of a limit * Continuous functions * Differentiation * Integration * Logarithmic and exponential functions * Uniform convergence * Circular functions All these concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject.

Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a self-study text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers differentiation integration Cauchy's theorem and its consequences Laurent series and the residue theorem applications of contour integration conformal mappings and harmonic functions A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

Theoretical models of simple computing mahcines, known as automata, play a central role in theoretical computer science. This textbook presents an introduction to the theory of automata and to their connections with the study of languages. At the heart of the book is the notion that by considering a language as a set of words it is possible to construct automata which `recognize' words in the language. Consequently one can generate a correspondence between a hierarchy of machines and a corresponding hierarchy of grammars and languages. Professor Howie leads the reader from finite state automata through pushdown automata to Turing machines. He demonstrates clearly and elegantly the fundamental connections between automata and abstract algebra via the notions of syntactic monoid and minimal automaton. The author presupposes a basic familiarity with modern algebra, but beyond this the book is self-contained. As a result, the book will make ideal reading for students of mathematics and computer science approaching this subject for the first time.

This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.