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This book is based on a course given by the author at Harvard University inthe fall semester of 1988. The course focused on the inverse problem of GaloisTheory: the construction of field extensions having a given finite group as Galoisgroup. In the first part of the book, classical methods and results, such asthe Scholz and Reichardt construction for p-groups, p not equal 2, as well as Hilbert sirreducibility theorem and the large sieve inequality, are presented. The secondhalf is devoted to rationality and rigidity criteria and their application inrealizing certain groups as Galois groups of regular extensions of Q(T). Whileproofs are not carried out in full detail, the book contains a number of examples,exercises, and open problems. ... Read more

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This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here. The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number theory and Galois cohomology. ... Read more

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This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

Customer Reviews (2)

Extremely concise -- no illustrative examples.
I'm using this book as an undergraduate, so my rating is clearly skewed, as evidenced by the huge "Graduate Texts in Mathematics" on the cover.We've only covered the first five chapters so far, and while the overarching ideas are quite clear, I find the notation confusing.No (even small) reviews of the linear algebra you studied years ago; it just dives in.Perhaps graduate students can follow it all quickly with no concrete examples, but it takes me a few readings through each section to begin to understand what is being said.By concrete I mean a real-world see-it put-your-hands-on-it example, or at least an example involving a few numbers as elements.

Here is an excerpt (so you can judge for yourself how helpful the first chapter will be for you) of a representation example from section 1.2 entitled 'Basic Examples:' "Leg g be the order of G, and let V be a vector space of dimension g, with a basis (e-sub-t)sub-t-in-g indexed by the elements t of G.For s-in-G, let rho-sub-s be the linear map of V into V which sends e-sub-t to e-sub-st; this defines a linear representation, which is called the regular representation of G.Its degree is equal to the order of G.Note that e-sub-s = rho-sub-s(e-sub1); hence note that the images of e-sub1 form a basis of V.Conversely, let W be a representation of G containing a vector w such that the rho-sub-s(w), s-in-G, form a basis of W; then W is isomorphic to the regular representation (an isomorphism tau: V --> W is defined by putting tau(e-sub-s) = rho-sub-s(w))."

The language is very concise and usually quite clear, and I suppose for someone with a sophisticated math background it could be a preferred book.For someone like me who has had only one semester of introductory linear algebra two years ago, I would prefer a more "bridging" text -- that is, one which often and quickly reviewed basic concepts from linear algebra and was less concise in its explanations of definitions and examples.

Typical Serre, concise, clean, clear.
This is a an excellent introduction to the subject.The book really breaks into 3 distinct parts.The first 5 chapters are a rapid introduction to the basics, similar to what one would get from any indroductory text.They are most notable for actually going through the details on D_n, S_n cyclic groups... The second section (chapters 6-13) gives a more graduate level presentation of the material.Starting with a discussion of group algebras, moving onto inducted representations Artin's theorem (the existence of virtual characters) The third section is Brauer Theory. The book is by Serre so it goes without saying it one of the best if not the best book on the market.His failure to deal with the additional complexities of the infinite group case (which he indicates in the title) is a small problem.He could have spent at least 1 chapter addressing how the results of the book could be extended.The index of notation is a fantastic asset for a subject where notation plays such a large role. ... Read more

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This is an updated English translation of Cohomologie Galoisienne, published more than 30 years ago as one of the very first Lecture Notes in Mathematics. It includes a reproduction of an influential paper of R. Steinberg, together with some new material and an expanded bibliography. ... Read more

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Chapters: Alexander Grothendieck, André Weil, Nicolas Bourbaki, Séminaire Nicolas Bourbaki, Serge Lang, Jean-Pierre Serre, Claude Chevalley, Laurent Schwartz, Henri Cartan, Jean Dieudonné, Jacques Tits, Samuel Eilenberg, Armand Borel, John Tate, Charles Ehresmann, Szolem Mandelbrojt, Pierre Samuel, René de Possel, Roger Godement, Jacques Dixmier, Pierre Cartier, Jean-Louis Koszul, Jean Delsarte, François Bruhat. Source: Wikipedia. Pages: 119. 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: Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is one of the most influential mathematicians of the twentieth century. He is known principally for his revolutionary advances in algebraic geometry, and also for major contributions to number theory, category theory and homological algebra, and his early achievements in functional analysis. He was awarded the Fields Medal in 1966. He was co-awarded the Crafoord Prize with Pierre Deligne in 1988, but Grothendieck declined this. He is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. In particular, he demonstrated the ability to derive concrete results using only very general methods. Relatively little of his work after 1960 was published by the conventional route of the learned journal, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal, on French mathematics and the Zariski school at Harvard University. He retired in 1988 and within a few years became reclusive. Grothendieck's early mathematical work was done in functional analysis between 1949 and 1953 working on his doctoral thesis in Nancy, supervised by Jean Dieudonné and Laurent Schwartz. His key contributions include topological tensor products of to...More: http://booksllc.net/?id=2042 ... Read more

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Articles by twenty-six leading mathematicians, all reflecting the influence of one of the seminal figures in modern mathematics, Andre Weil.

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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. Chapters: Michael Atiyah, Abel Prize, Jean-Pierre Serre, S. R. Srinivasa Varadhan, John G. Thompson, Peter Lax, Jacques Tits, Lennart Carleson, Isadore Singer. Excerpt:The Abel Prize is an international prize presented annually by the King of Norway to one or more outstanding mathematicians . The prize is named after Norwegian mathematician Niels Henrik Abel (1802 1829). It has often been described as the "mathematician's Nobel" prize and is among the most prestigious awards in mathematics. It comes with a monetary award of six million kroner , which is approx. (2010) 740,000 or US $ 992,000. The Norwegian Academy of Science and Letters annually declares the winner of the Abel Prize after selection by a committee of five international mathematicians. The committee is headed by Kristian Seip . The amount of money that comes with the prize is usually close to US $ 1 million, similar to the Nobel Prize , which is awarded in Sweden and Norway and excludes mathematics . Norway gave the prize an initial funding of NOK 200,000,000 (about US $23,000,000) in 2001. The prize is an attempt at creating publicity for mathematics, making the discipline more prestigious, especially for young people. The prize board has also established an Abel symposium, administered by the Norwegian Mathematical Society . History The prize was first proposed to be part of the 1902 celebration of 100th anniversary of Abel's birth. In 1899, shortly before his death, Sophus Lie proposed establishing an Abel Prize when he learned that Alfred Nobel 's plans for annual prizes, made known in 1897, would not include a prize in mathematics. King Oscar II was willing to finance a mathematics prize in Abel's name, and the mathematicians Ludwig Sylow and Carl Størmer drew up statutes and rules for the proposed prize. However, Li... ... Read more