Stephen Newman C. A Classical Introduction to Galois Theory

Stephen Newman C. A Classical Introduction to Galois Theory

Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions. The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through: A study of the solvability of polynomials of prime degree Development of the theory of periods of roots of unity Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic. A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.

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David Cox A. Galois Theory

David Cox A. Galois Theory

Praise for the First Edition «. . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!» —Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of prime or prime-squared degree Abel's theorem about geometric constructions on the lemniscates Galois groups of quartic polynomials in all characteristics Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study. Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.

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M. A. R. Habib Literary Criticism from Plato to the Present. An Introduction

M. A. R. Habib Literary Criticism from Plato to the Present. An Introduction

Literary Criticism from Plato to the Present provides a concise and authoritative overview of the development of Western literary criticism and theory from the Classical period to the present day An indispensable and intellectually stimulating introduction to the history of literary criticism and theory Introduces the major movements, figures, and texts of literary criticism Provides historical context and shows the interconnections between various theories An ideal text for all students of literature and criticism

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Michele Dillon Introduction to Sociological Theory, eTextbook. Theorists, Concepts, and their Applicability to the Twenty-First Century

Michele Dillon Introduction to Sociological Theory, eTextbook. Theorists, Concepts, and their Applicability to the Twenty-First Century

Combining carefully chosen primary quotes with extensive discussion and everyday illustrative examples, this book provides an in-depth introduction to classical and contemporary theory. Uses a wide range of newspaper examples to illustrate the relevance to sociological theory Contains excerpts from theorists’ primary texts Includes chapter-specific glossaries of all theoretical concepts discussed in the book Short biographies and historical timelines of significant events provide context to various theorists’ ideas Incorporates a range of pedagogical features Supporting website includes multiple choice and essay questions, PowerPoint slides, a quotation bank, and other background materials Visit www.wiley.com/go/dillon for additional student and instructor resources.

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Terry Eagleton Literary Theory. An Introduction

Terry Eagleton Literary Theory. An Introduction

A quarter of a century on from its original publication, Literary Theory: An Introduction still conjures the subversion, excitement and exoticism that characterized theory through the 1960s and 70s, when it posed an unprecedented challenge to the literary establishment. Eagleton has added a new preface to this anniversary edition to address more recent developments in literary studies, including what he describes as “the growth of a kind of anti-theory”, and the idea that literary theory has been institutionalized. Insightful and enlightening, Literary Theory: An Introduction remains the essential guide to the field. 25th Anniversary Edition of Terry Eagleton’s classic introduction to literary theory First published in 1983, and revised in 1996 to include material on developments in feminist and cultural theory Has served as an inspiration to generations of students and teachers Continues to function as arguably the definitive undergraduate textbook on literary theory Reissue includes a new foreword by Eagleton himself, reflecting on the impact and enduring success of the book, and on developments in literary theory since it was first published

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David Cox A. Primes of the Form x2+ny2. Fermat, Class Field Theory, and Complex Multiplication

David Cox A. Primes of the Form x2+ny2. Fermat, Class Field Theory, and Complex Multiplication

An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.

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Gregory Castle The Blackwell Guide to Literary Theory

Gregory Castle The Blackwell Guide to Literary Theory

This student-friendly text introduces students to the history and scope of literary theory, as well as showing them how to perform literary analysis. Designed to be used alongside primary theoretical texts as an introduction to theory or alongside literary texts as a model for performing literary analysis. Presents a series of exemplary readings of particular literary texts such as Jane Eyre, Heart of Darkness, Ulysses, To the Lighthouse and Midnight's Children. Provides a brief history of the rise of literary theory in the twentieth century, in order that students understand the historical contexts for different theories. Presents an alphabetically organized series of entries on key figures and publications, from Adorno to Žižek. Features descriptions of the major movements in literary theory, from critical theory through to postcolonial theory.

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J. Oden Tinsley An Introduction to Mathematical Modeling. A Course in Mechanics

J. Oden Tinsley An Introduction to Mathematical Modeling. A Course in Mechanics

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

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Amy Wharton S. The Sociology of Gender. An Introduction to Theory and Research

Amy Wharton S. The Sociology of Gender. An Introduction to Theory and Research

Featuring extensive revisions and updates, the Second Edition of The Sociology of Gender: An Introduction to Theory and Research presents an introductory overview of gender theory and research, and continues to offer a unique and compelling approach to one of the most important topics in the field of sociology. Features extensive revisions and updates, and incorporates recent cross-national research on gender Expands and develops frameworks introduced in first edition Treats gender as a multilevel system operating at the individual, interactional, and institutional levels Stresses conceptual and theoretical issues in the sociology of gender Offers an accessible yet intellectually sophisticated approach to current gender theory and research Includes pedagogical features designed to encourage critical thinking and debate

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