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  Field Arithmetic

  Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.

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  I and Thou , Hörbuch, Digital, ungekürzt, 318min

  Martin Buber’s I and Thou has long been acclaimed as a classic. Many prominent writers have acknowledged its influence on their work; students of intellectual history consider it a landmark; and the generation born after World War II considers Buber one of its prophets. Buber’s main proposition is that we may address existence in two ways: (1) that of the “I” toward an “It,” toward an object that is separate in itself, which we either use or experience; (2) that of the “I” toward “Thou,” in which we move into existence in a relationship without bounds. One of the major themes of the book is that human life finds its meaningfulness in relationships. All of our relationships, Buber contends, bring us ultimately into relationship with God, who is the Eternal Thou. The need for a new English translation had been felt for many years. The old version was marred by many inaccuracies and misunderstandings, and its recurrent use of the archaic “thou” was seriously misleading. Professor Walter Kaufmann, a distinguished writer and philosopher in his own right who was close to Buber, retranslated the work at the request of Buber’s family. He added a wealth of informative footnotes to clarify obscurities and bring the reader closer to the original and wrote an extensive prologue that opened up new perspectives on the book and on Buber’s thought. This volume provided a new basis for all subsequent discussions of Buber. Martin Buber (1878–1965) was a Jewish philosopher, theologian, Bible translator, and editor of Hasidic tradition. He was also known as one of the paramount spiritual leaders of the twentieth century and is best known as the author of I and Thou - the basic formulation of his philosophy of dialogue - and for his appreciation of Hasidism, which made a deep impact on Christian as well as Jewish thinkers. Fleeing Nazi Germany in 1938, he immigrated to Israel, where he taught social philosophy at the Hebrew University. ungekürzt. Language: English. Narrator: John Lescault. Audio sample: https://samples.audible.de/bk/blak/004594/bk_blak_004594_sample.mp3. Digital audiobook in aax.

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  The Warm & Witty Side of Attila the Hun , Hörbuch, Digital, ungekürzt, 270min

  The Warm and Witty Side of Attila the Hun is a collection of historical anecdotes; odd, humourous facts; and things you will never forget, once you know them. They are the product of a life devoted to history. In the words of the author: "I once had a student ask me point blank and in all seriousness, 'Do you really know all this stuff, or are you just making it up?' Delightful question, and unwittingly flattering. There is no need for any serious teacher of History to make up any unbelievable stories, because so much of it is unbelievable in the first place. I mean, really, think about it: if the story of Henry VIII and his six wives hadn't actually happened, for example, would anyone believe it? Is there any drama more intense than the story of Cleopatra, Caesar, Antony, and Octavian? (Heck, the entire story of the Julio-Claudian dynasty reads like one long soap opera!) And if Shakespeare had known the details of the life of his two-thousand-mile-away contemporary Ivan the Terrible, my God, what a tragic drama he could have written! (Speaking of which, let us not forget that Macbeth is based on a true story.)"There is no particular order to these anecdotes (except that I tried to adhere to chronology with the presidents), and no claim is made to comprehensiveness or, for that matter, importance. This is simply a collection of things I have come across over the years, things that I remembered, things with which I amused, horrified, and intrigued my students, nothing more, nothing less. Think of it as the mental junkyard of an aging History teacher." "If the reader is constrained by the chains of political correctness, please be forewarned that the writer is not. There may be material here that some people will find offensive. I don't care. Other readers may recognize some of these stories and may object to inaccuracies or distortions. I don't care about that either. This is something of an eclectic and eccentric reminiscence, not ungekürzt. Language: English. Narrator: Craig Allen. Audio sample: https://samples.audible.de/bk/acx0/000277/bk_acx0_000277_sample.mp3. Digital audiobook in aax.

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