‎Mathématiques‎

‎"TORTOLINI, BARNABA.‎

‎Sur les transformations et les valeur de plusieurs intégrales définies qui se rapportent aux surfaces et aux solidités des volumes.‎

‎Berlin, G. Reimer, 1843. 4to. In ""Journal für die reine und angewandte Mathematik, 26. Band, 4 Heft, 1843"". In the original printed wrappers, without backstrip. Fine and clean. [Tortolini:] Pp. 277-310. [Entire issue: Pp. 277-368, (2) + 1 plate.].‎

‎"TSCHIRNHAUS, EHRENFRIED W. V. [FIRST PUBLICATION OF THE ""TSCHIRNHAUS TRANSFORMATION"".]‎

‎Methodus datae figurae, rectis lineis & curva Geometrica terminate, aut Quadraturam, aut impossibilitatem ejusdem Quadraturae determinandi. (+) Nova Methodus determinandi Maxima & Minima (+) Aufrendi omnes terminos intermedios ex data aequatione. - [FORCED LEIBNIZ TO PUBLISH THE CALCULUS]‎

‎Leipzig, Grosse & Gleditsch, 1683. 4to. Contemporary full vellum. Handwritten title on spine. Library label to pasted down front free end-paper and a small stamps on titlepage. In: ""Acta Eruditorum Anno MDCLXXXIII"". As usual with various browning to leaves and plates. Tschirnhaus' paper: pp. 122-124" Pp. 204-207 " Pp. 433-437. [Entire volume: (8), 561, (7) pp + 13 plates].‎

‎"TURING, A.M. (+) H. A. NEWMAN.‎

‎A formal theorem in Church s theory of types (+) The use of dots as brackets in Church's system. (In: ""The Journal Of Symbolic Logic""). - [TURING ON CHURCH'S TYPE THEORY]‎

‎(No place), The Association for Symbolic Logic, 1942. Large 8vo. Bound in blue half cloth with silver lettering to spine. In ""Journal of Symbolic Logic"", Volume 7. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 28-33"" 146-156 (Entire copy: (4), 180 pp.).‎

‎First appearance of these two paper's by Turing.Turing's paper ""A Formal Theorem in Church's Theory of Types"" is a significant contribution to the fields of computer science and mathematical logic. By providing a formal proof within Church's theory, Turing expanded our understanding of computation and its relationship to logic. His work on computability and the theory of types laid the foundation for the development of theoretical computer science, proof theory, and automated reasoning. Turing's paper continues to be a landmark in the study of computation, inspiring further research and practical applications in diverse areas of science and technology. In ""The Use of Dots as Brackets in Church's System"", introducing the dot parentheses notation, Turing simplified the representation and manipulation of lambda calculus expressions, making them more intuitive and manageable. His work highlighted the relationship between syntax and semantics, laying the foundation for further research in formal semantics and the development of programming languages. Turing's paper continues to be influential, shaping the way complex expressions are represented and reasoned about in the fields of computation, formal systems, and logic.‎

Ссылка продавца : 60431

‎"TURING, A. M.‎

‎Computability and Lambda-Definability. (Extracted from The Journal of Sybolic Logic, Volume 2, 1937, pp.153-64.).‎

‎1937. 8vo. Bound in recent marbled boards. Title-page for volume 2 of Journal of Symbolic Logic withbound.‎

‎First edition of Turing's important paper, in which he links Kleene's recursive functions, Church's lambda-definable functions and his own computable functions and proves them to be identical. In the appendix of his milestone-paper ""On Computable Numbers"" from 1936, Turing gave a short outline of a method for proving that his notion of computability is equivalent with Alonzo Church's notion of lambda-definabilty. It was not until the present article, however, that it was proved that Steven Kleene's general recursive functions, Church's lambda-definable functions and Turing's computable functions were all identical. Kleene had already proved that every general recursive function is lambda-definable, so by showing that computability follows from lambda-definability and that general recursiveness follows from computability, Turing had ended the circle, which was a primary reason for its acceptance as a notion of ""effective calculable"" demanded by Hilbert's Entscheidungsproblem.""The purpose of the present paper is to show that the computable functions introduced by the author (in ""On computable numbers"") are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene."" Turing wrote this paper while at Princeton studying with Church.""(Hook and Norman No. 395)‎

Ссылка продавца : 25248

‎"TURING, A. M.‎

‎Rounding-off Errors in Matrix Processes. - [TURING'S LU FACTORIZATION]‎

‎Oxford, Clarendon Press, 1948. 8vo. Bound in contemporary full calf with gilt lettering to spine. In ""The Quarterly Journal of Mechanics and Applied Mathematics"", Vol. 1, 1948. Previous owner's name written to front free-endpaper. Ver fine and clean. Pp. 287-380. [Entire volume: (4), 474 pp.].‎

‎First printing of this important paper in which Turing for the very first time introduced the concept of LU factorization or LU decomposition. ""Turing's paper was one of the earliest attempts to examine the error analysis of the various methods of solving linear equations and inverting matrices. His analysis was basically sound. The main importance of the paper was that it was published at the dawn of the modern computing era, and it gave indications of which methods were 'safe' when solving such problems on a computer"". (Burgoyne, Collected Works of A M Turing).""In 1945, [Turing] declined an offer of a Fellowship at King's [College, Cambridge] in favour of joining the newly formed Mathematical Division at the National Physical Laboratory (NPL). His early work on computability, combined with his wartime experience in electronics, had fired him with an enthusiasm for working on the design of an electronic computer. ethe machine he designed, which was called the Automatic Computing Engine (ACE) in recognition of Babbage's pioneering work, was characteristically original…""While in the Mathematics Division of NPL, Turing became keenly interested in numerical analysis. His paper, ""Rounding-off Errors in Matrix Processes"", showed that the acute anxiety about the effect of rounding errors in Gaussian elimination was largely unjustified. This paper has been overshadowed to some extent by the von Neumann and Goldstine paper on matrix inversion, but it is a brilliant piece of work and would have repaid closer study at the time"". (""Turing, Alan M."" by James H. Wilkinson, p. 1803, in Encyclopedia of Computer Science, A. Ralston et al (eds.), 4th edition, Nature Publishing Group, 2000).In linear algebra, LU decomposition factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. Not in Origins of Cyberspace nor The Erwin Tomash Library.‎

Ссылка продавца : 47095

‎"TURING, A.M.‎

‎Systems of Logic based on Ordinals. [Received 31 May, 1938. - Read 16 June, 1938.]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 45]. - [TURING'S PH.D.-THESIS]‎

‎London, Hodgson & Son, 1939. Royal8vo. In a recent nice red full cloth binding with gilt lettering to spine. Entire volume 45 of ""Proceedings of the London Mathematical Society. Second Series"". Small white square paper label pasted on to lower part of spine, covering year of publication stating: ""A Gift / From /Anna Wheeler"". A very nice and clean copy without any institutional stamps. Pp. 161-240. [Entire volume: (4), 475 pp.].‎

‎The rare first printing of Turing's Ph.D.-thesis, which ""opened new fields of investigation in mathematical logic"". This seminal work constitutes the first systematic attempt to deal with the Gödelian incompleteness theorem as well as the introduction to the notion of relative computing. After having studied at King's College at Cambridge from 1931 to 1934 and having been elected a fellow here in 1935, Turing, in 1936 wrote a work that was to change the future of mathematics, namely his seminal ""On Computable Numbers"", in which he answered the famous ""Entscheidungsproblem"", came up with his ""Universal Machine"" and inaugurated mechanical and electronic methods in computing. This most famous theoretical paper in the history of computing caught the attention of Church, who was teaching at Princeton, and in fact he gave to the famous ""Turing Machine"" its name. It was during Church's work with Turing's paper that the ""Church-Turing Thesis"" was born. After this breakthrough work, Newman, under whom Turing had studied at Cambridge, urged him to spend a year studying with Church, and in September 1936 he went to Princeton. It is here at Princeton, under the guidance of Church, that Turing in 1938 finishes his thesis [the present paper] and later the same year is granted the Ph.D. on the basis of it. The thesis was published in ""Proceedings of the London Mathematical Society"" in 1939, and after the publication of it, Turing did no more on the topic, leaving the actual breakthroughs to other generations. In his extraordinary Ph.D.-thesis Turing provides an ingenious method of proof, in which a union of systems prove their own consistency, disproving, albeit shifting the problem to even more complicated matters, Gödel's incompleteness theorem. It would be many years before the ingenious arguments and striking partial completeness result that Turing obtained in the present paper would be thoroughly investigated and his line of research continued. The present thesis also presents other highly important proofs and hypotheses that came to influence several branches of mathematics. Most noteworthy of these is the idea that was later to change the face of the general theory of computation, namely the attempt to produce an arithmetical problem that is not number-theoretical (in his sense). Turing's result is his seminal ""o-machines"""" he here introduces the notion of relative computing and augments the ""Turing Machines"" with so-called oracles (""o""), which allowed for the study of problems that could not be solved by the Turing machine. Turing, however, made no further use of his seminal o-machine, but it is that which Emil Post used as the basis for his theory of ""Degrees of Unsolvability"", crediting Turing with the result that for any set of natural numbers there is another of higher degree of unsolvability. This transformed the notion of computability from an absolute notion into a relative one, which led to entirely new developments and in turn to vastly generalized forms of recursion theory. ""In 1939 Turing published ""Systems of Logic Based on Ordinals,""... This paper had a far-reaching influence"" in 1942 E.L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing's ideas to use ordinal logics in predicative mathematics."" (D.S.B. XIII:498). A part from these groundbreaking points, which Turing never returned to himself, he here also considers intuition versus technical ingenuity in mathematical reasoning, does so in an interesting and provocative manner and comes to present himself as one of the most important thinkers of modern mathematical as well as philosophical logic.""Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (1938), which then appeared as ""Systems of Logic based on Ordinals"" (Turing 1939). It is generally the view, as expressed by Feferman (1988), that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 198), there are 'formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.' Turing's theory of 'ordinal logics' was an attempt to 'avoid as far as possible the effects of Gödel's theorem' by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.In his investigation, Turing introduced the idea of an 'oracle' capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some 'black box' component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 1998). An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined 'oracle-machines' as Turing machines with an additional configuration in which they 'call the oracle' so as to take an uncomputable step. But these oracle-machines are not purely mechanical. They are only partially mechanical, like Turing's choice-machines. Indeed the whole point of the oracle-machine is to explore the realm of what cannot be done by purely mechanical processes...Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity."" (SEP).Following an oral examination in May, in which his performance was noted as ""Excellent,"" Turing was granted his PhD in June 1938.‎

Ссылка продавца : 54748

‎"TUKEY, JOHN. (+) ET AL‎

‎Compactness in General Spaces (+)Generalized ""Sandwich"" Theorems (+) Named and Faceless Values: An Initial Exploration in Memory of Prasanta C. Mahalanobis (+) Some Sèlected Quick and Easy Methods of Statistical Analysis (+) Correlation of Ranges of c... - [LARGE COLLECTION OF OFFPRINTS]‎

‎[Various places and printer] ,1945 - 1974. Collection of 24 offprint from various academic journals. All with wrappers (or as issued) and in fine condition. Contained in a black kassett.‎

‎"TURING, A. M.‎

‎Computability and Lambda-Definability. (Extracted from The Journal of Sybolic Logic, Volume 2, 1937, pp.153-64.).‎

‎1937. 8vo. Bound in recent marbled boards. Title-page for volume 2 of Journal of Symbolic Logic withbound.‎

‎"TURING, A.M.‎

‎A Method for the Calculation of the Zeta-Function. [Received 7 March, 1939. - Read 16 March, 1939]. [In: Proceedings of the London Mathematical Society. Second Series. Volume 48]. - [TURING'S FIRST WORK ON THE ZETA-FUNCTION]‎

‎London, Hodgson & Son, 1945. Royal8vo. In a recent nice green full cloth binding with gilt lettering to spine. Entire volumes 48 of ""Proceedings of the London Mathematical Society. Second Series"". A very nice and clean copy without any institutional stamps. Pp. 180-197. [Entire volume: (4),477 pp.]‎

‎"TURING, M. (+) H. A. NEWMAN.‎

‎A Formal Theorem in Church's Theory of Types (+) Practical forms of type theory‎

‎(No place), The Association for Symbolic Logic, 1942, 1943 &1948. Lev8vo. Bound in two uniform red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 7, 8 [Bound together] & 13.. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. Minor scratches to extremities of volume 13. A fine set. Pp. 28-33" Pp. 80-94. [Entire volumes: IV, 164 pp. " IV, 236 pp.).‎

‎"URSIN, GEORG FREDERIK.‎

‎Logarithmer med 6 Decimaler for Tallene fra 1 til 100000 for Sinus og Tangens for hver 10"" tilligemed forskjellige constante Logarithmer og Tal, der ere af vigtighed i Mathematiken.‎

‎Kjøbenhavn, Schultz, 1827. Samtidigt hldrbd. Rygforgyldning. papirsetiket påsat øverst på ryg. Stempler på titelbladet. XXIV pp. + ca. 500 upaginerede sider. Indvendig ren og frisk, trykt på svært skrivepapir.‎

‎Bibl. Dan. II,14.‎

Ссылка продавца : 53031

‎"URSIN, GEORG FREDERIK.‎

‎Logarithmer med 6 Decimaler for Tallene fra 1 til 100000 for Sinus og Tangens for hver 10"" tilligemed forskjellige constante Logarithmer og Tal, der ere af vigtighed i Mathematiken.‎

‎Kjøbenhavn, Schultz, 1827. Samtidigt hldrbd. Rygforgyldning. papirsetiket påsat øverst på ryg. Stempler på titelbladet. XXIV pp. + ca. 500 upaginerede sider. Indvendig ren og frisk, trykt på svært skrivepapir.‎

‎"URSIN, GEORG FREDRIK.‎

‎Logarithmer med 6 Decimaler for Tallene fra 1 til 100000 for Sinus og Tangens for hver 10"" tilligemed forskjellige Constante Logarithmer og Tal der ere af Vigtighed i Mathematiken. Kbhvn., 1827.‎

‎Orig. hollanderet papbd med shirtryg. Revne i false og rep. med tape. Stempel p. titel. Indvendig frisk, trykt på svært papir. XXIV,ca. 1000 pp.‎

‎"VON NEUMANN, JOHN.‎

‎Die Einführung analytischer Parameter in topologischen Gruppen.‎

‎Princeton & Hamburg, 1933. Offprint from 'Annals of Mathematics' volume 34, pp. 170-190. Royal8vo. Original printed wrappers. Small tear to back wrapper. Corners a little bumped and frayed. Internally fine and clean. In all a good copy.‎

‎First edition offprint issue. ""One of the highlights of Von Neumann's career... solving Hilbert's fifth problem for compact groups."" (DSB).‎

Ссылка продавца : 34733

‎"VOLTERRA, VITO.‎

‎Sur les Vibrations des Corpes élastiques isotropes.‎

‎(Berlin, Stockholm, Paris, Alqvist & Wiksell, 1894). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", vol. 18, pp. 161-232.‎

‎First edition. ""Vito Volterra (1860-1940), who succeeded Beltrami as professor of mathematical physics at Rome, is the first of the founders of a general theory of integral equations. He wrote papers on the subject from 1884 on and principal ones in 1896 and 1897."" (Morris Kline).‎

Ссылка продавца : 39161

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎First printing of Volterra's paper on the vibrations of light in a birefringence media.‎

Ссылка продавца : 45842

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎First printing of Volterra's paper on the vibrations of light in a birefringence media.‎

Ссылка продавца : 49650

‎"VOLTERRA, VITO.‎

‎Lecons sur la Théorie mathematique de la Lutte pour la Vie. (Mathematical theory of the struggle for life) - [THE MATEMATIZATION OF BIOLOGY]‎

‎Paris, Gauthier-Villars, 1931. Royal 8vo. Uncut in orig. printed wrappers. Uppe and lower part of backstrip gone. VI,214 pp. + Publisher's cat. (7) pp.‎

‎"VOLTERRA, VITO.‎

‎Sur les Vibrations des Corpes élastiques isotropes.‎

‎(Berlin, Stockholm, Paris, Alqvist & Wiksell, 1894). 4to. Without wrappers as extracted from ""Acta Mathematica. Hrsg. von G. Mittag-Leffler."", vol. 18, pp. 161-232.‎

‎"VOLTERRA, VITO.‎

‎Sur les vibrations lumineuses dans les milieux biréfringents.‎

‎[Berlin, Stockholm, Paris, Beijer, 1892]. 4to. Without wrappers as extracted from ""Acta Mathematica. Hrdg. von G. Mittag-Leffler."", Bd. 16, pp. 153-215.‎

‎"VON NEUMANN, JOHN.‎

‎Die Einführung analytischer Parameter in topologischen Gruppen.‎

‎Princeton & Hamburg, 1933. Offprint from 'Annals of Mathematics' volume 34, pp. 170-190. Royal8vo. Original printed wrappers. Small tear to back wrapper. Corners a little bumped and frayed. Internally fine and clean. In all a good copy.‎

‎"WEIERSTRASS, KARL.‎

‎Abhandlungen aus der Functionenlehre.‎

‎Berlin, Julius Springer, 1886. Lex8vo. Contemp. hcalf. Spine gilt and with gilt lettering. (8),262 pp. A faint dampstain to inner lower corners on some leaves. The last 5 leaves a bit soiled.‎

‎First edition in book form of Weierstarss' s main papers in Function Theory. In this collected form the papers were slightly revised by the author. - Parkinson: Breakthroughs (He rigorously develops the theory of functions in ""Abhandlungen aus Functionentheorie"").‎

Ссылка продавца : 41357

‎"WESSEL, CASPAR.‎

‎Om Directionens analytiske Betegning, et forsøg, anvendt fornemmelig til plane og sphæriske Polygoners Opløsning. - [THE FIRST SYSTEMATICAL THREATMENT OF COMPLEX NUMBERS]‎

‎Kiøbenhavn, Johan Rudolph Thiele, (1797) 1799. 4to. Recently bound in a nice pastiche-binding of brown half calf with five raised bands and gilt red leather title-label to elaborately gilt spine. Vellum corners and marbled paper over boards. Published in: ""Nye Samling af det Kongelige Danske Videnskabernes Selskabs Skrifter."" Vol. V. A very nice copy. Pp.469-518 + 3 folded engraved plates.‎

‎First edition of this seminal publication in which Wessel presents the first systematical treatment of the theory of complex numbers and furthermore being the first work to add vectors in three-dimensional space.""Wessel’s fame as a mathematician is based entirely on one paper, written in Danish and published in the Mémoires of the Royal Danish Academy, that established his priority in publication of the geometric representation of complex numbers. John Wallis had given a geometric representation of the complex roots of quadratic equations in 1685"" Gauss had had the idea as early as 1799 but did not explicitly publish it until 1831. Robert Argand’s independent publication in 1806 must be credited as the source of this concept in modern mathematics because Wessel’s work remained essentially unknown until 1895, when its significance was pointed out by Christian Juel. The title of Wessel’s treatise calls it an ""attempt"" to give an analytic representation of both distance and direction that could be used to solve plane and spherical polygons. The connection of this goal with Wessel’s work as a surveyor and cartographer is obvious. The statement of the problem also suggests that Wessel should be credited with an early formulation of vector addition. In fact, Michael J. Crowe, in A History of Vector Analysis (University of Notre Dame Press, 1967), defines the first period in that history as that of a search for hypercomplex numbers to be used in space analysis and dates it from the time of Wessel, whom he calls the first to add vectors in three-dimensional space."" (DSB).‎

Ссылка продавца : 60128

‎"WEIL, ANDRÉ. - WEIL PAIRING INTRODUCED.‎

‎Sur les fonctions algébriques à corps de constantes fini.‎

‎(Paris, Gauthier-Villars et Cie, 1940). 4to. Without wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 210, No 17. Pp. (589-) 616. (Entire issue offered). Stamp on front page. Weil's paper: pp. 592-594.‎

‎First printing of Weil's importent paper in which he introduced the concept of Weil-pairing, giving a proof of the Riemann hypothesis for curves over finite fields.The Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. The Weil pairing is used in number theory and algebraic geometry, and has also been applied in elliptic curve cryptography and identity based encryption.""The Weil pairing, first introduced by André Weil in 1940, plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to those objects.""(Victor S. Miller).The Weil pairing is used in number theory and algebraic geometry, and has also been applied in elliptic curve cryptography and identity based encryption.‎

Ссылка продавца : 49417

‎"WEIERSTRASS, KARL & LEOPOLD KRONECKER.‎

‎Über die Flächen, deren mittlere Krümmung überall gleich Null ist"" (And Kronecker:) Über bilineare Formen.‎

‎Berlin, Königl. Akad. d. Wissenschaften, 1866. Uncut in orig. printed wrappers in ""Monatsbericht der Königlichen Preussischen Akademie der Wissenschaften zu Berlin"", Sept., October 1866. Pp. 595-655. Weierstrass' paper: pp.612-625. Kronecker's paper: pp. 597-612‎

‎Both papers first edition. Weierstrass is considered the most importen nineteenth-century german mathematician after Gauss and Riemann.‎

Ссылка продавца : 39156