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35
21
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I have recently been told of a proposal to produce an English translation of Landau's Handbuch der Lehre von der Verteilung der Primzahlen, and this prompts me to ask a more general question:
These could be classics of historical interest, books you would like your students to read, books you would like to teach from, or books of use in your own research. |
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56
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Grothendieck's EGA and SGA. |
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27
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The other two volumes of Kazuya Kato's trilogy on Number Theory (the first vol. is "Fermat's Dream"). |
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17
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Gabriel's dissertation,Serre's FAC and Beilinson-Bernstein-Deligne |
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16
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Oh my. Since English is already so overwhelming in international scientific literature, I think it will look a bit peculiar to the non-native English speakers who read this site to see a question like this asking for yet more work to be put in English. Perhaps those of us who already speak that language should expend some more effort in the other direction if we want to read something in those other languages. |
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14
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Hanspeter Kraft's invariant theory book. |
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12
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"Champs algébriques" by Laumon and Moret-Bailly. |
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11
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"La Clef des Songes", "Récoltes et Semailles" and the Long March through Galois Theory. |
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10
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I'd second Allen Knutson's suggestion that the book Geometrische Methoden in der Invariantentheorie by Hanspeter Kraft (Vieweg, 1984) is a good candidate for translation into English. Since AMS distributes several Vieweg series in English versions, I'd suggest asking Sergei Gelfand at AMS whether such a translation could be commissioned by them. Like most native users of English, I find mathematical French far easier than mathematical German. In any event, French books and papers are less likely to get translated than German ones. As far as books go, I regret that J.C. Jantzen's useful Springer Ergebnisse volume on primitive ideals in enveloping algebras is not available in English. His later books in English have become standard references for representations of algebraic groups and for quantized enveloping algebras. |
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9
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Don Zagier's German book about quadratic forms. |
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8
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8
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G.M. Fichtenholz - Analysis (3 Tomes) - The course of real analysis for budding mathematicians beyond the Iron Curtain. Everyone knows it. It's the first book you read, and the last one you refer to before finishing your master's degree. It takes you from the definition of a set to advanced multivariate calculus; it gives you a lot of tools for classical mechanics in the meantime. It is so trustworthy that the single wrong theorem that it contained caused a telltale student to fail his dissertation, because neither he nor his professor checked the proof and they based the whole thesis on the false premise - that was a decade or two ago and the book is, right now, free of errors. Originally in Russian. Another book that kept the Russians strong during the cold war. Wikipedia entry about the author |
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7
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Analysis Situs by Poincare. This is the foundation of algebraic topology and illustrates its historical connection with dynamics. According to Wikipedia it has been translated, but I can't find a copy in English. |
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6
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Endliche Gruppen by Huppert, though the German is like the French in EGA: "easy" going. |
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6
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As far as I know, none of Wilhelm Blaschke's books have ever been published in English, and he is the the author of possibly the most exciting and elegant serious mathematics books that I've ever encountered (comparable to the best of Felix Klein, but on a much higher mathematical level). I especially regret that his Einführung in die Differentialgeometrie (1950; 2nd ed with Reichardt, 1960) and Elementare Differentialgeometrie (5th edition with Leichweiss, 1973) have not been available, but really, all his books, from the elementary "Kreis und Kugel" to the state-of-the-art research "Geometrie der Gewebe" are incredible. Fortunately, most of them have been translated into Russian. Does anyone know a credible explanation of why he was completely ignored in the English-speaking world? Anything to do with WWII? Although even Hasse got translated. |
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4
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G. Banaszak, W. Gajda - Elementy Algebry Liniowej (Elements of Linear Algebra), Poland, WNT - 2 tomes - Don't let the name fool you. This recent publication has more linear algebra than you can shake a stick at. It's a very comprehensive course of linear, and some abstract, algebra; very beautifully printed, lots of decorative markup. The book is very well structured, but is not easy and requires the reader to be fully aware of what's going on. It can be a bit of a mind wringer, but on the other hand that can force you to look at many things from the writers' - quite original sometimes - viewpoint. Tome 1 on the publisher's website This is just a quick round-up of some good books in Mathematics. Hope this helps! |
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4
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Kalkül der abzählenden Geometrie By Hermann Schubert Lehrbuch der abzählenden Methoden der Geometrie By Hieronymus Georg Zeuthen |
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3
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Geometrie der Gewebe by W. Blaschke, and G. Bol Geradenkonfigurationen und algebraische Flächen by G. Barthel, F. Hirzebruch, and T. Höfer |
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3
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Gesammelte Abhandlungen (Collected Works) of Carl Ludwig Siegel (According to Amazon.com a trilingual version of this once existed, but I can't find it.) |
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3
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Bombieri's "Le Grand Crible dans la Théorie Analytique des Nombres" |
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3
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The Collected Work of Carl Ludwig Siegel. |
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3
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"Arithmetique Des Algebres De Quaternions" by MF Vigneras |
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3
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Groupes Algebriques by Demazure and Gabriel. Someone tried to translate the first half of this book, but it's not very good (some of the mathematics is incorrect too). |
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3
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The following wonderful 54 page survey by O. Neumann on Kronecker's divisor theory could easily be turned into a book and would fill a very large gap in the English literature on such. I'm interested in helping if anyone is game for such (but, alas, my German is weak). Neumann, O.(D-FSU-MI) 2003k:13021 13F05 (01A55 13G05 20M14) In the first part of this paper a survey is given of the development of Kronecker's theory of divisors. In the second part the author develops a theory of integral domains $R$ having a divisor theory in the following sense: there exists a monoid $D$ (i.e., a commutative semigroup with cancellation and a unit element) with the GCD-property for the associated group $G$ of quotients, and a homomorphism $\mathrm{div}$ of the multiplicative group $K^*$ of the quotient field of $R$ into $G$ with the following two properties: (i) If $a,b \in K^*$ and $b/a \in R$, then $\mathrm{div}(b)/\mathrm{div}(a) \in D$, and (ii) for every element $d \in D$ there exists a set $A \subseteq K^*$ The author states that a similar theory was presented in the thesis of
F. Lucius ["Ringe mit einer Theorie des groessten gemeinsamen Teilers", Ph.D.
thesis, Univ. Gottingen, Gottingen, 1996; Zbl 0901.13002]. After developing
the fundamental properties of such divisor theory, relations to the approaches
of Kronecker, Zolotarev and Dedekind are established. |
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2
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Friedrich Levi, Geometrische Konfigurationen |
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2
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Chirurgie des grassmanniennes by Laurent Lafforgue. |
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2
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Chebotarev's "Grundzüge der Galois'schen Theorie" |
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2
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Over de Grondslagen der Wiskunde , L.E.J Brouwer, his thesis (in Dutch) on the foundations of mathematics. |
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2
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Catégories et structures by Charrles Ehresmann |
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2
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B. P. Demidovich - Problems on Multivariate Analysis (approximate translation). A very tough book about analysis on $\mathbb{R}^n$; in fact all problems 'can' be solved by first or seond-year students, but it's got lots of tricky questions that will not let you sleep at night. Only the best need apply - the book gives you the most basic definitions and then throws you out with a broken pontoon in the middle of the ocean, at night. I believe the writer is Russian or Belorussian, I have only encountered a few tattered copies that have been doing the rounds between students for a decade at least. Haven't found a better book for tough multivariate analysis. |
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2
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I.N. Bronstein, K.A. Semyendayev - Mathematics Handbook - an awesome, very complete mathematics handbook for applied mathematicians, physicists, and engineers. Also useful for the pure mathematics researcher who just wants to quickly look up how a basic item in mathematics worked. This work has not lost any of its gleam since it was first written; numerous updates have been made; it is the reference compendium in Central and Eastern Europe. It has received prizes for being the best illustrated engineering book; indeed, the drawings are exact and even beautiful, and have not become outdated in the time of computer generated imagery. Definitely one of the books that put the Russians in outer space. Numerous German editions of the book on Amazon |
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