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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.
Cryptology and Error Correction
This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie–Hellman, and Blum–Goldwasser cryptosystems and Hamming and Reed–Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra—rings, fields, finite abelian groups, basic theory of numbers, computational number theory,...
Thomas the Turkey
Thomas is a turkey and he has lost all his feathers-gasp! In this book, readers will retrace Thomas’s steps around the house, picking up a feather at each location until they have helped Thomas find all seven of his brightly colored feathers. (The secret of this book is this: The child’s parents or older siblings must first hide the feathers for the child to find, making the hunt easy or hard depending on the child’s age.) The child will love taking part in this feather hunt, and families will adore this new Thanksgiving tradition.
The Welfare of Children
Takes a critical look at the child welfare system, finding that the emphasis on abuse has produced a system that serves largely as a last resort for only the worst and most dramatic cases in child welfare. This book is a blueprint for the comprehensive reform of the child welfare system.
The Night Box
Invites young readers to discover what happens between sunset and sunrise as a little boy opens the Night Box and darkness swoops out to cavort and explore, caring for all its creatures until morning comes, and it's time for Night to rest again.
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.
Caterflies and Ice
With magical animals, science, mystery, and adventure -- the brand new series Zoey and Sassafras has something for everyone! Easy-to-read language and illustrations on nearly every page make this series perfect for a wide range of ages. In the fourth book, an unexpected snow storm causes trouble for the magical creatures of the forest. When Zoey and Sassafras attempt to rescue trapped caterfly eggs, they make a mistake. Can they figure out a way to fix things before the baby caterflies hatch?
Children in Antiquity
This collection employs a multi-disciplinary approach treating ancient childhood in a holistic manner according to diachronic, regional and thematic perspectives. This multi-disciplinary approach encompasses classical studies, Egyptology, ancient history and the broad spectrum of archaeology, including iconography and bioarchaeology. With a chronological range of the Bronze Age to Byzantium and regional coverage of Egypt, Greece, and Italy this is the largest survey of childhood yet undertaken for the ancient world. Within this chronological and regional framework both the social construction of childhood and the child’s life experience are explored through the key topics of the definition...
