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A Concrete Introduction to Higher Algebra
An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.
A Concrete Introduction to Higher Algebra
This book is written as an introduction to higher algebra for students with a background of a year of calculus. The book developed out of a set of notes for a sophomore-junior level course at the State University of New York at Albany entitled Classical Algebra. In the 1950s and before, it was customary for the first course in algebra to be a course in the theory of equations, consisting of a study of polynomials over the complex, real, and rational numbers, and, to a lesser extent, linear algebra from the point of view of systems of equations. Abstract algebra, that is, the study of groups, rings, and fields, usually followed such a course. In recent years the theory of equations course has disappeared. Without it, students entering abstract algebra courses tend to lack the experience in the algebraic theory of the basic classical examples of the integers and polynomials necessary for understanding, and more importantly, for ap preciating the formalism. To meet this problem, several texts have recently appeared introducing algebra through number theory.
Hopf Algebras and Galois Module Theory
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
A Concrete Introduction to Higher Algebra
This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.
That Pup!
What is that pup up to? That pup digs. And digs. And digs some more. What is that pup looking for? And why should this squirrel care?
Adventure Girl
On a family visit to her grandparents in Israel, tomboy Dabi finds a kindred spirit in her aunt, who takes her on a new adventure where Dabi makes more than one important discovery. Includes author's note.
How a Seed Grows
Read and find out about how a tiny acorn grows into an enormous oak tree in this colorfully illustrated nonfiction picture book. This is a clear and appealing environmental science book for early elementary age kids, both at home and in the classroom. Plus it includes a find out more activity section with a simple experiment encouraging kids to discover what a seed needs to grow. This is a Level 1 Let's-Read-and-Find-Out, which means the book explores introductory concepts perfect for children in the primary grades. The 100+ titles in this leading nonfiction series are: hands-on and visual acclaimed and trusted great for classrooms Top 10 reasons to love LRFOs: Entertain and educate at the s...
Contested Issues in the Evaluation of Child Sexual Abuse
This book represents a significant contribution to the highly contested debate surrounding how allegations of child sexual abuse should be evaluated. Despite decades of substantial research in this sensitive area, professional consensus remains elusive. A particular source of contention is the sensitivity vs. specificity debate; whether evaluators should aim to reduce the number of true allegations that are labelled false or to reduce the number of false allegations that are labelled true. This edited collection aims to address directly and offer new insights into this debate. It responds directly to Kuehnle and Connell's edited volume, The Evaluation of Child Sexual Abuse Allegations: A Comprehensive Guide to Assessment and Testimony (2009), which included chapters which advocated strong specificity positions at the expense of sensitivity. The chapters in this collection feature both challenges to, and replies by, the authors in Kuehnle and Connell's book, making this an essential resource that moves the debate forward. This book was originally published as a special issue of the Journal of Child Sexual Abuse.
Rings, Extensions, and Cohomology
"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."
