Classical Galois Theory with Examples

Classical Galois Theory with Examples
Author :
Publisher : American Mathematical Soc.
Total Pages : 258
Release :
ISBN-10 : 9780821813751
ISBN-13 : 0821813757
Rating : 4/5 (51 Downloads)

Synopsis Classical Galois Theory with Examples by : Lisl Gaal

Galois theory is one of the most beautiful subjects in mathematics, but it is heard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout the text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is intended for beginning graduate students who already have some background in algebra, including some elementary theoryof groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity. The book is for students and intends to make them take an active part in mathematics rather than merely read, nod their heads atappropriate places, skip the exercises, and continue on to the next section.

Galois Theory Through Exercises

Galois Theory Through Exercises
Author :
Publisher : Springer
Total Pages : 296
Release :
ISBN-10 : 9783319723266
ISBN-13 : 331972326X
Rating : 4/5 (66 Downloads)

Synopsis Galois Theory Through Exercises by : Juliusz Brzeziński

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.

Galois Theory for Beginners

Galois Theory for Beginners
Author :
Publisher : American Mathematical Soc.
Total Pages : 202
Release :
ISBN-10 : 9780821838174
ISBN-13 : 0821838172
Rating : 4/5 (74 Downloads)

Synopsis Galois Theory for Beginners by : Jörg Bewersdorff

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.

A Classical Introduction to Galois Theory

A Classical Introduction to Galois Theory
Author :
Publisher : John Wiley & Sons
Total Pages : 296
Release :
ISBN-10 : 9781118336847
ISBN-13 : 1118336844
Rating : 4/5 (47 Downloads)

Synopsis A Classical Introduction to Galois Theory by : Stephen C. Newman

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.

Fields and Galois Theory

Fields and Galois Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 230
Release :
ISBN-10 : 9781852339869
ISBN-13 : 1852339861
Rating : 4/5 (69 Downloads)

Synopsis Fields and Galois Theory by : John M. Howie

A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews

Field and Galois Theory

Field and Galois Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 294
Release :
ISBN-10 : 9781461240402
ISBN-13 : 1461240409
Rating : 4/5 (02 Downloads)

Synopsis Field and Galois Theory by : Patrick Morandi

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

Galois Theory of Linear Differential Equations

Galois Theory of Linear Differential Equations
Author :
Publisher : Springer Science & Business Media
Total Pages : 446
Release :
ISBN-10 : 9783642557507
ISBN-13 : 3642557503
Rating : 4/5 (07 Downloads)

Synopsis Galois Theory of Linear Differential Equations by : Marius van der Put

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

The Mathematical Writings of Évariste Galois

The Mathematical Writings of Évariste Galois
Author :
Publisher : European Mathematical Society
Total Pages : 426
Release :
ISBN-10 : 303719104X
ISBN-13 : 9783037191040
Rating : 4/5 (4X Downloads)

Synopsis The Mathematical Writings of Évariste Galois by : Évariste Galois

Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Evariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics.

Galois Theory

Galois Theory
Author :
Publisher :
Total Pages : 54
Release :
ISBN-10 : 1950217027
ISBN-13 : 9781950217021
Rating : 4/5 (27 Downloads)

Synopsis Galois Theory by : Emil Artin

The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org

Galois Theory

Galois Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 220
Release :
ISBN-10 : 9780387875750
ISBN-13 : 0387875751
Rating : 4/5 (50 Downloads)

Synopsis Galois Theory by : Steven H. Weintraub

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.