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This book provides a bridge between high school and undergraduate mathematics courses on algebra and geometry.The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics. The remaining chapters form the mathematical core of the book.

This book provides a bridge between high school and undergraduate mathematics courses on algebra and geometry.The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics. The remaining chapters form the mathematical core of the book.

Interest in semigroup theory and automata is currently on the rise, and the ideas of finite automata are becoming more accepted by the mathematical community. The time is right to begin introducing those ideas to students in mathematics and theoretical computer science. This book presents a well-motivated introduction to finite automata and semigroup theory and makes clear connections to other areas, including combinatorial group theory and sy...

The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts. This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research. Along with a translation of Wagner’s main work in this area, his 1953 paper ‘Theory of generalised heaps and general...

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Interest in semigroup theory and automata is currently on the rise, and the ideas of finite automata are becoming more accepted by the mathematical community. The time is right to begin introducing those ideas to upper-level students in both mathematics and theoretical computer science. This book--the first of its kind--presents a well-motivated introduction to finite automata and semigroup theory and that will serve as a firm foundation for t...