Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. To get the free app, enter your mobile phone number. This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century.
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries. In my case, I first encountered Artin indirectly, through what is still my favorite graduate algebra text, B. Of course, Artin was himself influenced by the inimitable Noether, whom Alexandroff another of her collaborators christened der Noether.
What a cast! Well, the professors I was taking higher algebra from, Ernst Straus and, later, Ian Morrison, had very classical tastes in algebra texts: the books referenced were not only the aforementioned classic, but courtesy of Morrison also Galois Theory by Artin himself.
Varadarajan, was giving a course on class field theory that was based on his own very detailed notes, flavored differently. Then, maybe five years or so later, I spent some time looking at his book with Hel Braun providing an Introduction to Algebraic Topology : I dare say that the discussion given there of the business of constructing the connecting homomorphisms in forming long exact sequences in co homology is arguably superior to others, if only because of, again, style, clarity and concision.
What does all this lead up to, then? Well, simply put: even in these days of pedagogical evolution, replete with shifting sands as far as curricula are concerned, it is still the case that getting mathematics under your belt by studying classical exposition with bis style, clarity and concision is highly desirable. You simply learn the stuff better. But the reader should be warned: Artin is going off the beaten track. In the Preface he states that while. Despite the foregoing disclaimer, it has some very sexy stuff in it.
This last chapter even includes material on Clifford algebras and spinors. So there. What more is there to say? Artin is always more than worth reading, even or maybe especially in these latter days, and the material he covers in this book clearly transcends many boundaries, with geometers, number theorists and even physicists called to play with the things Artin discusses so beautifully in these five chapters. Skip to main content.
Search form Search. Login Join Give Shops. Halmos - Lester R. Ford Awards Merten M. Emil Artin. Publication Date:. Number of Pages:. BLL Rating:. In the Preface he states that while [m]any parts of classical geometry have developed into great independent theories… [e.
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The book also deals with symplectic and orthogonal geometry and also the structure of the symplectic and orthogonal groups. I intend to blog on this subject for as long as I can, and this will be my first serious project for now. There are some neat things I learned in chapter I which basically deals with preliminary notions. But, chapter I has some cool techniques too, and I wish to share them in my subsequent posts. Comments feed for this article. March 10, at am. Interestingly, it is crucial to his approach that he quantizes the Hamiltonian constraint rather than the densitized Hamiltonian constraint.
Geometric Algebra – Emil Artin
This concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication, noting that "mathematicians will find on many pages ample evidence of the author's ability to penetrate a subject and to present material in a particularly elegant manner. Subsequent chapters explore affine and projective geometry, symplectic and orthogonal geometry, the general linear group, and the structure of symplectic and orthogonal groups. The author offers suggestions for the use of this book, which concludes with a bibliography and index. Dover republication of the edition originally published by Interscience Publishers, Inc. See every Dover book in print at www.