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An introduction to one of the most celebrated theories of mathematics Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox’s Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real...
Praise for the First Edition ". . .will certainly fascinate anyone interested in abstractalgebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel’s theory of Abelian equations, casusirreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of severaltopics not covered in standard t...
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Treetops is Oxford Reading Tree's new series of fiction with built-in progression for pupils aged 7 to 11. Specially written for children who need the support of carefully monitored language levels, the stories are accessible, motivating, and humorous. The series is organized into Oxford Reading Tree Stages (from Stage 10 to Stage 14), with each stage introducing more complex narrative forms, including flashbacks and changes in viewpoint; descriptive writing; extended readingvocabulary; and more pages, more text, and fewer illustrations.Each stage is supported by the Teacher's Guide, which offers guidance on using Treetops to assess children's reading ability, and includes a variety of activities (comprehension. writing for a range of audiences and in different forms, discussion and role play) many on photocopiable sheets.
Crime in England 1688-1815 covers the ‘long’ eighteenth century, a period which saw huge and far-reaching changes in criminal justice history. These changes included the introduction of transportation overseas as an alternative to the death penalty, the growth of the magistracy, the birth of professional policing, increasingly harsh sentencing of those who offended against property-owners and the rapid expansion of the popular press, which fuelled debate and interest in all matters criminal. Utilising both primary and secondary source material, this book discusses a number of topics such as punishment, detection of offenders, gender and the criminal justice system and crime in contempora...
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Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border...
Reprint of the original, first published in 1881.
Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.