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The present text was first published in 1947 by the Courant Institute of Mathematical Sciences of New York University. Published under the title Modern Higher Algebra. Galois Theory, it was based on lectures by Emil Artin and written by Albert A. Blank. This volume became one of the most popular in the series of lecture notes published by Courant. Many instructors used the book as a textbook, and it was popular among students as a supplementary text as well as a primary textbook. Because of its popularity, Courant has republished the volume under the new title Algebra with Galois Theory. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. ... Read more

Customer Reviews (1)

Superb
This book is fun. Everyone who is interested in abstract algebra should read it. Artin's style is very intuitive, the clear remarks and comments add to the streamlined demonstrations. The exposition has some original details usually abscent from more modern books on the subject. For example, Artin defines a ring as a set where addition is not necessarily assumed to be commutative; then he derives the result that if the distributive laws apply then addition IS necessarily commutative (i.e., a+b=b+a) for every element expressible as a product. Obviously, in a ring with units this is always true. Someone could validly ask "Why isn't there systems of double composition where both operations are non commutative"?, and Artin anwers that that "Seldom happens" (i.e., such a generalization is of small use, if any) .

This books is not even similar to Artin's "Galois Theory"(Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2)), which is very succint and covers the contents in a different order. I recommend this one first, though both are valuable as a source. A good complement to this book (and by "complement" I do not mean that each one complements each other's contents, but rather having two different expositions on the same subject helps understanding)is John Stillwell's Elements of Algebra. ... Read more

Product Description
This classic book, originally published in 1968, is based on notes of a year-long seminar the authors ran at Princeton University. The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians. In this revised edition, two mathematical additions complementing the exposition in the original text are made. The new edition also contains several new footnotes, additional references, and historical comments. ... Read more

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Clearly presented elements of one of the most penetrating concepts in modern mathematics include discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 ed.
... Read more

Customer Reviews (11)

Best text on this subject
In my opinion this is without a doubt the best text on the subject. Do not be fooled by the small size of this book. It is lean, to the point and refreshingly laconic. A masterpiece!

Not a Self-Contained Book on Galois Theory
Galois Theory is in traditional mathematical format. The major elements of the book are definitions, lemmas, theorems, and proofs. The book introduces the major topics of Galois Theory. They are fields, extension fields, splitting fields, unique decomposition of polynomials into irreducible factors, solvable groups, permutation groups, and solution of equations by radical.

The last part of the book contains the major results of Galois Theory with proofs using the theorems from the second part of the book. They are theorem 5: The polynomial f(x) is solvable by radicals if and only if its group is solvable; theorem 4: The symmetric group G on n letters is not solvable for n > 4; theorem 6: The group of the general equation of degree n is the symmetric group on n letters. The general equation of degree n is not solvable by radicals if n > 4.

This is my second Galois Theory book. What impress me most is the involvement to prove the major results of Galois Theory such as theorem 5 and theorem 6. In order to prove the theorems, mathematicians invent many mathematical objects. They are root, group, symmetric group, solvable group, field, extension field, splitting field, Kummer field/extension, Abelian group, normal subgroup, normal extension, factor/quotient group, homomorph, fixed field, extension by radicals field, and more. Nowadays, we put all these objects under the domain of abstract algebra.

The book is certainly not self-contained because one would need an abstract algebra textbook for reference to the mathematical objects.

Artin is the man
Any student (graduate or undergraduate) who is learning Galois theory will benefit greatly from reading this book. Artin has a very elegant style of writing and many parts of the book read like a novel. At its current price, there's no reason to not buy this book; you may actually want to buy a few extra copies as they make great gifts and/or stocking stuffers.

I would also recommend Artin's Geometric Algebra.

the source!
This is modern Galois Theory, straight from the horse's mouth! Galois Theory is taught today using field extensions rather than by actually solving polynomials, students also learn to view a field extension as a vector space over the smaller field; both of these things were pioneered by Artin. The book also has short, clear proofs of all the main theorems. The only problem is that there are no problems to work on, so I have to say this is only a good reference for Galois Theory.

Succinct exposition of modern Galois theory by a pioneer.
Emil Artin's short book gets a mention in most texts on
Galois theory. It is very short - only 60 odd pages. Yet
it is a very clear, complete and readable account of the
essential elements of modern Galois theory. It is based
on lectures he gave over 50 years ago but you might think
it was written only yesterday and is comprehensible to
anyone familiar with current abstract algebra terminology.
And the price makes it a bargain. There are no worked
examples, exercises or index here. ... Read more

Product Description
Chapters: Austrian Expatriates in the Czech Republic, Emil Artin, Josef Bican, Rudolf Vytlačil, Max Pallenberg. Source: Wikipedia. Pages: 31. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt:Josef Bican Josef "Pepi" Bican (September 25, 1913 December 12, 2001) was a Czech -Austrian football forward . It is estimated by respected footballing statistics page RSSSF that Bican scored around 800 goals in all competitive matches, not including friendly games. This would make him the all-time most prolific scorer in football history known to date. He was a member of the Austrian Wunderteam of the 1930s and was the season's highest scorer in the whole of Europe on five separate occasions. Bican had the ability to play with both feet, he also had considerable pace and was able to run 100 metres in 10.8 seconds, which was as fast as many sprinters of the time. The IFFHS awarded Bican the "Golden Ball" as the greatest goalscorer of the last century.Early life Bican was born in Vienna to Ludmila and Franti ek Bican. Ludmila was Viennese Czech and Franti ek came from Sedlice in Southern Bohemia . Josef's father Franti ek was a footballer who played for Hertha Vienna. He went to fight in World War I and returned uninjured. However, Franti ek was to die at the age of just 30 in 1921 because he refused an operation to treat a kidney injury sustained in a football match. His mother worked in a restaurant kitchen. The family's poverty meant that Bican had to play football without any shoes, which helped him hone his ball control skills. Bican attended the Jan Amos Komenský school, a Czech school in Vienna. Four years after his father's death in 1925, twelve-year old Bican started to play for the Hertha Vienna junior team. When he was 18, Bican was spotted by Rapid Vienna , who were a big club in the city at the time.Club career When Bican fir... ... Read more

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Famous Norwegian mathematician Niels Henrik Abel advised that one should "learn from the masters, not from the pupils". When the subject is algebraic numbers and algebraic functions, there is no greater master than Emil Artin. In this classic text, originated from the notes of the course given at Princeton University in 1950-1951 and first published in 1967, one has a beautiful introduction to the subject accompanied by Artin's unique insights and perspectives. The exposition starts with the general theory of valuation fields in Part I, proceeds to the local class field theory in Part II, and then to the theory of function fields in one variable (including the Riemann-Roch theorem and its applications) in Part III.Prerequisites for reading the book are a standard first-year graduate course in algebra (including some Galois theory) and elementary notions of point set topology. With many examples, this book can be used by graduate students and all mathematicians learning number theory and related areas of algebraic geometry of curves. ... Read more

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Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. He also discovered and proved the Artin reciprocity law, the culmination of over a century and a half of progress in algebraic number theory. Artin had a great influence on the development of mathematics in his time, both by means of his many contributions to research and by the high level and excellence of his teaching and expository writing. In this volume we gather together in one place a selection of his writings wherein the reader can learn some beautiful mathematics as seen through the eyes of a true master. The volume's Introduction provides a short biographical sketch of Emil Artin, followed by an introduction to the books and papers included in the volume. The reader will first find three of Artin's short books, titled The Gamma Function, Galois Theory, and Theory of Algebraic Numbers, respectively. These are followed by papers on algebra, algebraic number theory, real fields, braid groups, and complex and functional analysis. The three papers on real fields have been translated into English for the first time. The flavor of these works is best captured by the following quote of Richard Brauer. "There are a number of books and sets of lecture notes by Emil Artin. Each of them presents a novel approach. There are always new ideas and new results. It was a compulsion for him to present each argument in its purest form, to replace computation by conceptual arguments, to strip the theory of unnecessary ballast. What was the decisive point for him was to show the beauty of the subject to the reader." Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity ... Read more

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Emil Artin (March 3, 1898, in Vienna December 20, 1962, in Hamburg) was an Austrian-Armenian mathematician. The mathematician Emil Artin was born on March 3, 1898 in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent. Several documents, including Emils birth certificate, list the fathers occupation as opera singer though others list it as art dealer. It seems at least plausible that he and Emma had met as colleagues in the theater. They had been married in St. Stephen's Parish on July 24, 1895. Emil entered school in September 1904, presumably in Vienna. By then, his father was already suffering symptoms of advanced syphilis, among them increasing mental instability, and was eventually institutionalized at the recently established (and imperially sponsored) insane asylum at Mauer Öhling, 125 kilometers west of Vienna. It is notable that neither wife nor child contracted this highly infectious disease. The senior Emil Artin died there July 20, 1906. Young Emil was eight. On July 15, 1907, Emils mother remarriedher second husband, Rudolf Hübner a prosperous manufacturer in the German-speaking city of Reichenberg, Czechoslovakia (now Liberec, in the Czech Republic). Documentary evidence suggests that Emma had already been resident in Reichenberg the previous year, and in deference to her new husband, she had abandoned her vocal career. Hübner deemed a life in the theater unseemly in the wife of a man of his position. In September, 1907, Emil entered the Volksschule in Strobnitz, a small town in southern Czechoslovakia near the Austrian border. For that year, he lived away from home, boarding on a local farm. The... More: http://booksllc.net/?id=245351 ... Read more

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Chapters: Emil Artin, Max Pallenberg. Source: Wikipedia. Pages: 24. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Emil Artin (March 3, 1898, in Vienna December 20, 1962, in Hamburg) was an Austrian-Armenian mathematician. The mathematician Emil Artin was born on March 3, 1898 in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent. Several documents, including Emils birth certificate, list the fathers occupation as opera singer though others list it as art dealer. It seems at least plausible that he and Emma had met as colleagues in the theater. They had been married in St. Stephen's Parish on July 24, 1895. Emil entered school in September 1904, presumably in Vienna. By then, his father was already suffering symptoms of advanced syphilis, among them increasing mental instability, and was eventually institutionalized at the recently established (and imperially sponsored) insane asylum at Mauer Öhling, 125 kilometers west of Vienna. It is notable that neither wife nor child contracted this highly infectious disease. The senior Emil Artin died there July 20, 1906. Young Emil was eight. On July 15, 1907, Emils mother remarriedher second husband, Rudolf Hübner a prosperous manufacturer in the German-speaking city of Reichenberg, Czechoslovakia (now Liberec, in the Czech Republic). Documentary evidence suggests that Emma had already been resident in Reichenberg the previous year, and in deference to her new husband, she had abandoned her vocal career. Hübner deemed a life in the theater unseemly in the wife of a man of his position. In September, 1907, Emil entered the Volksschule in Strobnitz, a small town in southern Czechoslovakia near the Austrian border. F...More: http://booksllc.net/?id=245351 ... Read more

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Chapters: Fritz Lang, Otto Neurath, Adolf Hitler, Emil Artin, Guido Von List, Rudolf Hilferding, Leo Birinski, Heinrich Ignaz Biber, Erich Kern, John Lhotsky, Fritz Grünbaum, Ernst Happel, Simon Von Stampfer, Anton Walbrook, Franz Limmer, Jascha Horenstein, Ludwig Guttenbrunn, Adolf Jellinek, Alexander Moissi, Wolf Huber, Franz Blei, Vladimir Malakhov, Friedrich Kraus, Martin Stranzl, Johannes Von Gmunden, Johannes Matthias Sperger, Julius Pokorny, Siegmund Nissel, Franz Hasil, Emil Orlík, Hermann Mittelberger, Tilla Durieux, Albert Ehrenstein, Max Pallenberg, Alfred Polgar, Fritz Saxl, Ernst Sigismund Fischer, Wilhelm Blaschke. Source: Wikipedia. Pages: 169. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Pogroms: Kristallnacht Bucharest Dorohoi Iai Kaunas Jedwabne Lviv (Lvov) Adolf Hitler (German pronunciation: ; 20 April 1889 30 April 1945) was an Austrian-born German politician and the leader of the National Socialist German Workers Party (German: , abbreviated NSDAP), commonly known as the Nazi Party. He was the absolute dictator of Germany from 1934 to 1945, with the title of chancellor from 1933 to 1945 and with the title head of state (Führer und Reichskanzler) from 1934 to 1945. A decorated veteran of World War I, Hitler joined the precursor of the Nazi Party (DAP) in 1919 and became leader of NSDAP in 1921. Following his imprisonment after a failed coup in Bavaria in 1923, he gained support by promoting German nationalism, anti-semitism, anti-capitalism, and anti-communism with charismatic oratory and propaganda. He was appointed chancellor in 1933, and quickly transformed the Weimar Republic into the Third Reich, a single-party dictatorship based on the totalitarian and autocratic ideals of national socialism. Hitler ultimately wanted to establish a New Order of absolute Nazi G...More: http://booksllc.net/?id=2731583 ... Read more

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Chapters: Emil Artin. Source: Wikipedia. Pages: 32. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Emil Artin (March 3, 1898, in Vienna December 20, 1962, in Hamburg) was an Austrian-Armenian mathematician. The mathematician Emil Artin was born on March 3, 1898 in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent. Several documents, including Emils birth certificate, list the fathers occupation as opera singer though others list it as art dealer. It seems at least plausible that he and Emma had met as colleagues in the theater. They had been married in St. Stephen's Parish on July 24, 1895. Emil entered school in September 1904, presumably in Vienna. By then, his father was already suffering symptoms of advanced syphilis, among them increasing mental instability, and was eventually institutionalized at the recently established (and imperially sponsored) insane asylum at Mauer Öhling, 125 kilometers west of Vienna. It is notable that neither wife nor child contracted this highly infectious disease. The senior Emil Artin died there July 20, 1906. Young Emil was eight. On July 15, 1907, Emils mother remarriedher second husband, Rudolf Hübner a prosperous manufacturer in the German-speaking city of Reichenberg, Czechoslovakia (now Liberec, in the Czech Republic). Documentary evidence suggests that Emma had already been resident in Reichenberg the previous year, and in deference to her new husband, she had abandoned her vocal career. Hübner deemed a life in the theater unseemly in the wife of a man of his position. In September, 1907, Emil entered the Volksschule in Strobnitz, a small town in southern Czechoslovakia near the Austrian border. For that year, he...More: http://booksllc.net/?id=245351 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Emil Artin, Martin Damm, Petr Nedvěd, Tomáš Enge, Barbara Bouchet, Vladimír Šlechta, Přemysl Sobotka, Konrad Henlein, Christoph Demantius, Petr Kellner, Herbert Feigl, Zuzana Hejnová, Edmund Nick, Guido Beck, Heinz Rutha, Otfried Preußler, Dagmar Bláhová, Josef Proksch, Jaroslav Řídký, Roderich Menzel, Heinrich Herkner, Josef Keil, Augustin Schramm, Zdeněk Hnát, Vlasta Burian, Friedrich Karl Ginzel, Lenka Maňhalová, Kateřina Průšová, Zbyněk Hauzr, Jan Holub, Heinrich Hlasiwetz, Kamila Rajdlová, Fritz Preissler, Jan Polák, Jaroslav Šír, Markus Lüpertz, Rudi Mittig, Jan Ludvig, Petr Zábojník, Zuzana Kocumová, Miloš Veselý, Harald Kreutzberg, Jiří Kittner, Lukáš Derner, Pavel Churavý, Martin Bulíř, Günther Rücker, Richard Culek, Pavel Hottmar. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Emil Artin (March 3, 1898, in Vienna December 20, 1962, in Hamburg) was an Austrian-Armenian mathematician. The mathematician Emil Artin was born on March 3, 1898 in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent. Several documents, including Emils birth certificate, list the fathers occupation as opera singer though others list it as art dealer. It seems at least plausible that he and Emma had met as colleagues in the theater. They had been married in St. Stephen's Parish on July 24, 1895. Emil entered school in September 1904, presumably in Vienna. By then, his father was already suffering symptoms of advanced syphilis, among them increasing mental instability, and was eventually institutionalized at the recently established (and imperially sponsored) insane asylum at Mauer Öhling, 125 kilometers west of Vienna. It is notable that neither ...More: http://booksllc.net/?id=245351 ... Read more