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BERGAMINI David
Mathematics.
Time Incorporated. 1963. In-4. Relié. Très bon état, Couv. fraîche, Dos satisfaisant, Intérieur frais. 200 pages, hardcover. Black & white illustrations and illustrations in colour. Illustrated cover.. . . . Classification Dewey : 420-Langue anglaise. Anglo-saxon
Reference : RO60003042
Life science library. Classification Dewey : 420-Langue anglaise. Anglo-saxon
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5 book(s) with the same title
"[GÖDEL] & CARNAP, RUDOLF + AREND HEYTING + JOHANN v. NEUMANN, etc.
Reference : 38312
(1931)
[Bericht uber die 2. Tagung für Erkenntnislehre der exakten Wissenschaften Königsberg 1930]. Die Logizistische Grundlegung der Mathematik + Die intuitionistische Grundlegung der Mathematik + Die formalistische Grundlegung der Mathematik. [In: Erkenntn... - [ENDING THE FOUNDATIONAL CRISIS OF MATHEMATICS]
Leipzig, Felix Meiner, 1931. The entire volume present. 8vo. Orig. printed green wrappers. Sunning to spine, and a bit of soiling and minor wear to front wrapper w. minor loss of upper layer of paper at two pages, not gone through paper. A few leaves w. marginal markings, quite discreet. Library marking to inside of front wrapper, library stamp to title-page (Mathematical Institute of the University of Amsterdam). Overall a fine and nice copy. Pp. (91) - 105 + (106) - 115 + (116) - 121. The entire volume: (2) pp., Pp. (91) - 190.
First edition of the Erkenntnis-volume from the Königsberg congress of 1930, where Gödel introduced his incompleteness results and Carnap, Heyting and von Neumann held the seminal papers (here printed for the first time) that ended the ""Grundlagenkrise der Mathematik"" (foundational crisis of mathematics). It is also in this volume that the seminal discussions following Gödel's announcements of his results are printed for the first time (""Discussion on the Foundation of Mathematics"", between Gödel, von Neumann, Carnap, Hahn, Reidemeister, Heyting, and Scholz) (Gödel, Collected Works, 1931a) as well as the article which inaugurated the logicist foundation of mathematics, in which the modern sense of ""logicism"" is introduced (Carnap's contribution).In Königsberg in September 1930, Gödel presented his incompleteness results, a landmark in mathematical logic, at the second congress of scientific epistemology, -a congress which proved to be a turning point in the history of philosophical and mathematical logic. It is the papers presented at this congress which are printed in the present volume, apart from the contributions by Gödel and Scholtz (which were printed elsewhere) together with the seminal discussions that followed the presentation of the papers. The groundbreaking papers that are printed here include Carnap's ""Die Logizistische Grundlegung der Mathematik"", which furthermore introduced the modern sense of the term ""logicism"", Arend Heyting's ""Die intuitionistische Grundlegung der Mathematik"" and Johann von Neumann's ""Die formalistische Grundlegung der Mathematik"" as well as papers by Neugebauer, Reichenbach and Heisenberg. The present papers, as well as the following discussion, mark a turning point in the history of logic and a cornerstone in the future development of the field. The so-called ""Foundational Crisis of Mathematics"" was a phase within mathematics begun in the early 20th century due to the search for proper foundations of mathematics and the uncertainty of this quest, which was supported by the many difficulties that philosophy of mathematics faced at the end of the 19th and beginning of the 20th century . The crisis took its actual beginning with the publication of Russell's ""principles of Mathematics"" of 1903, culminated in the 1920'ies with the main advocates of Formalism and Intuitionism respectively, Hilbert and Brouwer, in what is called the ""foundational struggle of mathematics"", and ended with the present volume in 1931, following the congress of 1930.With the discovery of non-Euclidean geometry in the 18th century, it became evident that not only one sort of mathematics was possible, and even that some propositions could be true in one mathematical system, but false in another. This was the actual basis for the awareness of a mathematical foundation in the mathematical public, which again was the basis for the fact that the question of the foundation of mathematics could develop -and could develop into an actual crisis. During the first 30 years of the 20th century, almost all great mathematicians worked on their answer to the question of the correct foundation of mathematics, and thus it came to a crisis that developed into a struggle. It is this struggle and crisis that Carnap, Heyting and von Neumann break in 1930, where they present the three great positions of the struggling years: logicism (Carnap), intuitionism (Heyting) and formalism (von Neumann), and it is these three papars that pave the way for the discussion that follows, ""Diskussion zur Grundlegung der Mathematik"", between Gödel, Hahn, Carnap, Heyting, von Neumann, Reidemeister, and Scholz. They all presented their positions in the most conciliatory manner, out of the comprehension that all parties who had contributed to the crisis had also contributed because they wanted to solve it, and because they were also searching for the best possible foundation. It is also this comprehension that Hilbert takes over, when he, in his program, sets out to prove the contradiction-freedom of infinite mathematics on the basis of finite arithmetic.Thus, the seminal papers in the present volume once and for all ended the foundational crisis of mathematics and any fear of new antinomies.
The Principles of Mathematics. Vol I (all). - [""RUSSELL'S PARADOX""]
Cambridge, at the University Press, 1903. Royal 8vo. Original blue full cloth binding, all edges uncut. Capitals and upper front hinge with a bit of wear and corners a little bumped. But otherwise a very nice copy. Internally fresh and clean. XXIX, (1), 534 pp.
The uncommon first edition of Russell's landmark work in mathematical logic, in which theory of logicism is put forth and in which Russell introduces that which is now known as ""Russell's Paradox"". The work constitutes the forerunner of Russell and Whitehead's monumental ""Principia Mathematica"", and it seminally influenced logical thought and theories of the foundations of mathematics at this most crucial time for the development of modern mathematical and philosophical logic.""The present work has two main objects. One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that its propositions are deducible from a very small number of fundamental logical principles, is undertaken in Parts II. - VI. Of this Volume, and will be established by strict symbolic reasoning in Volume II. ... The other object of the work, which occupies Part I., is the explanation of the fundamental concepts which mathematics accepts as indefinable. ..."" (Russell, Preface, p. (III)).At the age of 27, in 1898, Russell began working on the book that became ""The Principles of Mathematics"". He originally set out to investigate the contradiction that is inherent in the nature of number, and he originally imagined doing this from a Hegelian standpoint. However, after having read Whitehead's ""Universal Algebra"", Russell gave up his Hegelian approach and began working on a book that was to be entitled ""An Analysis of Mathematical Reasoning"". This book never appeared, as he gave it up in 1900, but much of it is what lies at the foundation of ""The Principles of Mathematics"". After having attended a congress in Paris in 1899, where Peano was present, Russell began rewriting large parts of the work, now with the aim of proving that all of mathematics could be reduced to a few logical concepts, that that which is called mathematics is in reality nothing but later deductions from logical premises. And thus he had developed his landmark thesis that mathematics and logic are identical"" a thesis that came to have a profound influence on logic and the foundations of mathematics throughout the 20th century.Since the congress, Russell had worked with the greatest of enthusiasm, and he finished the manuscript on the 31st of December 1900. However, in the spring of 1901, he discovered ""The Contradiction"", or as it is now called, ""Russell's Paradox"". Russell had been studying Cantor's proof, and in his own words, the paradox emerged thus: ""Before taking leave of fundamental questions, it is necessary to examine more in detail the singular contradiction, already mentioned, with regard to predicates not predictable of themselves. Before attempting to solve this puzzle, it will be well to make some deductions connected with it, and to state it in various different forms. I may mention that I was led to endeavour to reconcile Cantor's proof that there can be no greatest cardinal number with the very plausible supposition that the class of all termes (which we have seen to be essential to all formal propositions) has necessarily the greatest possible number of members."" (p. 101). The class of all classes that are not members of themselves, is this class a member of itself or not? The question was unanswerable (if it is, then it isn't, and if it isn't, then it is) and thus a paradox, and not just any paradox, this was a paradox of the greatest importance. Since, when using classical logic, all sentences are entailed by contradiction, this discovery naturally sparked a huge number of works within logic, set theory, foundations of mathematics, philosophy of mathematics, etc. Russell's own solution to the problem was his ""theory of types"", also developed in 1903.In December 1902 Russell had come to the point where he could write a preface, and the book finally appeared in May 1903. It was printed in merely 1.000 copies, and although it was well received, it was not a bestseller at its appearance. By 1909 the last copies of the first run were at the bookbinders. However, the book did play an enormous role in the development of mathematical and philosophical logic as well as the foundation of mathematics throughout the 20th century. Wittgentein's immense interest in the philosophy of logic stems from his reading of the present work and from Frege's ""Foundations of Arithmetic"", and no logician could neglect the impact of this seminal work, which still counts as one of the most important philosophical and logical works of the 20th century. The book also played an important part in spreading the works of Cantor and Frege to the English-speaking world. In 1903 the Spectator wrote ""we should say that Mr. Russell has an inherited place in literature or statesmanship waiting for him if he will condescend to come down to the common day."" Shearman's review in Mind hailed it as the most important work since Boole's ""Laws of Thought"". ""Bertrand Arthur William Russell (b.1872 - d.1970) was a British philosopher, logician, essayist, and social critic, best known for his work in mathematical logic and analytic philosophy. His most influential contributions include his defense of logicism (the view that mathematics is in some important sense reducible to logic), and his theories of definite descriptions and logical atomism. Along with G.E. Moore, Russell is generally recognized as one of the founders of analytic philosophy. Along with Kurt Gödel, he is also regularly credited with being one of the two most important logicians of the twentieth century."" (Stanford Encyclopedia of Philosophy).Russell had actually planned to write a second volume of the work, but as the contents of this further development would overlap considerably with the further research that Whitehead had undertaken after his ""Universal Algebra"", which he also planned two write a second volume of, the two great logicians decided to collaborate on that which became the ""Principia Mathematica"", which appeared 1910-13.
Great Breakthroughs in Mathematics: From Counting to Chaos Theory - How Numbers Changed the World
Arcturus Publishing Ltd 2020 192 pages 17 4x24 8x2 6cm. 2020. Relié. 192 pages.
Très bon état
Ewing (R.E.), Gross (K.I.) and Martin (C.F.), eds. - Thomas S. Banchoff - Christopher J. Byrnes - Lance Drager and Clyde Martin - Harley Flanders - Ismael Herrera - Peter Hilton - Kenneth J. Hochberg - Daniel J. Kleitman - Anil Nerode - H.O. Pollak - Donald St. P. Richards and Rameshwar D. Gupta - Steve Smale - Tetsuro Yamamoto - Sol Garfunkel - Gail Young
Reference : Cyb-6410
(1986)
Merging Disciplines : New Directions in Pure, Applied, and Computational Mathematics - Proceedings of a Symposium Held in Honor of Gail S. Young at the University of Wyoming, August 8-10, 1985 Sponsored by the Sloan Foundation, the National Science Foundation and the Air Force Office of Scientific Research , (Computer graphics applications in geometry - Modelling and algorithmic issues in intelligent control - Global observability of ergodic translations on compact groups - Mathematical modeling and large-scale computing in energy and environmental research - Symbolic manipulation - Some unifying concepts in applied mathematics - Teaching and research : The history of a pseudoconflict - Stochastic population theory : Mathematical evolution of a genetical model - Combinatorics and applied mathematics - Applied logic -Pure and applied mathematics from an industrial perspective - Letter values in multivariate exploratory data analysis - Newton's method estimates from data at one point - Error bounds for Newton's method under the Kantorovich assumptions - Panel discussion : Implications for undergraduate and graduate education in mathematics)
Springer Malicorne sur Sarthe, 72, Pays de la Loire, France 1986 Book condition, Etat : Bon hardcover, editor's printed yellow binding grand In-8 1 vol. - 230 pages
25 illustrations, a black and white photography of Gail S. Young in frontispiece 1st edition, 1986 Contents, Chapitres : Preface by Peter Hilton, Contents, Presentation, Introduction, xvi, Text, 214 pages - Thomas S. Banchoff : Computer graphics applications in geometry - Christopher J. Byrnes : Modelling and algorithmic issues in intelligent control - Lance Drager and Clyde Martin : Global observability of ergodic translations on compact groups - Richard E. Ewing : Mathematical modeling and large-scale computing in energy and environmental research - Harley Flanders : Symbolic manipulation - Ismael Herrera : Some unifying concepts in applied mathematics - Peter Hilton : Teaching and research : The history of a pseudoconflict - Kenneth J. Hochberg : Stochastic population theory : Mathematical evolution of a genetical model - Daniel J. Kleitman : Combinatorics and applied mathematics - Anil Nerode : Applied logic - H.O. Pollak : Pure and applied mathematics from an industrial perspective - Donald St. P. Richards and Rameshwar D. Gupta : Letter values in multivariate exploratory data analysis - Steve Smale : Newton's method estimates from data at one point - Tetsuro Yamamoto : Error bounds for Newton's method under the Kantorovich assumptions - Sol Garfunkel : Panel discussion : Implications for undergraduate and graduate education in mathematics - Epilogue by Gail Young binding is near fine, with light adhesive track on the bottom of the spine, inside is fine except few library marks on the title page, main text remains unmarked and clean, a very good reading copy
Pappi Alexandrini Mathematicae Collectione. A Federico Commandino Urbinatae In Latinum Conversae, & Commentarijs Illustratae. - [THE CULMINATION OF GREEK MATHEMATICS]
Colophon: Pisauri (Pesaro), Hieronymum Concordiam, 1588. (Having the reprinted title-page: Venetiis, Franciscum de Franciscis Senemsem, 1589). Folio. Cont. limp vellum. Repairs to upper part of back and small nicks to back repaired. Edges of covers with tiny loss of vellum. Covers slightly soiled. Calligraphed title on back. Title-page with and old, partly erased stamp. Woodcut printer's device on title. Ff (3), 334 (332) (= 664 pp). Numerous woodcut diagrams and illustrations in the text. Printed on good paper, Ff 2-3 with an old repair to inner margin (no loss). F 2 browned, but otherwise remarkably clean with only a few brownspots. A few small worm-tracts to some margins.
First edition of a work which constitutes the culmination of Greek Mathematics. This copy has the fresh title, but is the 1588-printing. - ""Pappos was the greatest mathematician of the final period of ancient science, and no one emulated him in Byzantine times. He was the last mathematical giant of antiquity."" (George Sarton, Ancient Science and Modern Civilization. p.82).""Pappus of Alexandria in ab. 320 composed a work with the title Collection (Synagoge) which is important for several reasons. In the first place it provides a most valuable historical record of parts of Greek Mathematics that otherwise would be unknown to us. For instance it is in Book V of the Collection that we learn of Archimedes' discovery of the thirteen semiregular polyhedra or ""Archimedian solids"". Then, too, the Collection includes alternative proofs and supplementary lemmas for propositions in Euclid, Archimedes, Appolonius and Ptolemy. Finally, the treatise includes new discoveries, and generalizations not found in any earlier work. The Collection, Pappus' most important treatise, contained eight Books, but the first Book and the first part of the second Book are now lost"" (Boyer, A History of Mathematics p. 205). ""Each book (8) is preceded by general reflexions which give to that group of problems its philosophical and historical setting. The prefaces are of deep interest to historians of mathematics and, therefore, it is a great pity that three of them are lost [...] Book VII is far the longest book of the Collection [...] [and here], we find in it the famous Pappo's problem: ""given several straight lines in a plane, to find the locus point, such that when straight lines are drawn from it to the given lines at a given angle, the products of certain of the segments shall be in a given ratio to the product of the remaining ones"". This problem is important in itself, but even so because it exercized Descartes' mind and caused him to invent the method of coordinates explained in his Geométrie (1637). Think of a seed lying asleep for more than thirteen centuries and then helping to produce that magnificent flowering, analytical geometry [...] The final Book VIII is mechanical and is largely derived from Heron of Alexandria. Following Heron, Pappos distinguished various parts of theoretical mechanics (geometry, arithmetic, astronomy and physics). The Book is considered the climax of Greek mechanics and helps us to realize the great variety of problems to which the Hellenistic mechanicians addressed themselves. If Book VIII is the climax of Greek mechanics, we may say as well that the whole collection is a treasury and to some extent the culmination of Greek mathematics. [...] The ideas collected or invented by Pappos did not stimulate Western mathematicians until very late, but when they finally did, they caused the birth of modern mathematics- analytical geometry, projective geometry, centrobaric method. That birth or rebirth from Pappos' ashes, occurred within four years (1637-40). This was modern geometry connected immediately with the ancient one as if nothing had happened between."" (Georg Sarton op.cit.). - It is from Pappus we have the famous words of Archimedes: ""Give me a place to stand, and I will move the earth"" (Se PMM No 72). - ""Without pretending to great originality, the whole work shows, on the part of the author, a thorough grasp of all the subjects treated, independent of judgement, mastery of technique" the style is terse and clear" in short, Pappus stands out as an accomplished and versatile mathematician, a worthy representative of the classical Greek geometry."" (Heath, A History of Greek mathematics Vol. II: p.358). - Adams P 224 (The sheets of the Pisauris edition with a fresh title).
