Bibliography

Published Papers

Books

Conference Papers

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Bibliography

Published Papers

Books

Conference Papers

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Brahmagupta (598-670) writes Khandakhadyaka which solves quadratic equations and allows for the possibility of negative solutions.

pre

1136 Abraham bar Hiyya Ha-Nasi writes the work Hibbur ha-Meshihah ve-ha-Tishboret, translated in 1145 into Latin as Liber embadorum, which presents the first complete solution to the quadratic equation.

1484 Nicolas Chuquet (1445-1500) writes Triparty en la sciences des nombres. The fourth part of which contains the "Regle des premiers," or the rule of the unknown, what we would today call an algebra. He introduced an exponential notation, allowing positive, negative, and zero powers. In solving general equations he showed that some equations lead to imaginary solutions, but dismisses them ("Tel nombre est ineperible").

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Leonhard Euler is considered by many to be the most prolific mathematician in history. He published 866 books and papers and won the Paris Academy Prize 12 times. He was born in Basel, Switzerland on April 15, 1707 and died on September 18, 1783. Euler was the son of a Lutheran minister and entered the University of Basel to study theology like his father but opted to change his major to mathematics under the advice of Johann Bernoulli. He worked at the St. Petersburg Academy of Science and later at the Berlin Academy of Science. In 1735, Euler lost sight in one eye, and in the late 1760's, he became completely blind. Although blind, Euler had such an incredible memory and mathematical mind, he was able to dictate treatises on algebra, optics, and lunar motion until his death. Francois Arago said of his mathematical talents, "He calculated just as men breathe, as eagles sustain themselves in the air." Once, Euler settled an argument between students whose calculation differed by a digit at the fifteenth decimal place by calculating the answer in his head. Euler's contributions to mathematics include the introduction of the symbols e, i, f(x), , and sigma for summations. He also made significant contributions to differential calculus, mathematical analysis, and number theory, as well as optics, mechanics, electricity, and magnetism.

Euler developed the function, which is defined as the number of positive integers not exceeding m that are relatively prime to m. For example, would equal:

> with(numtheory);

> phi(7);

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For the mathematical community, Kustaa Inkeri is the author of significant papers on number theory, especially on topics related to Fermat's Last Theorem. Finnish mathematicians know Inkeri as the founder of the school of number theory in Finland. At the University of Turku, many of us still think of Inkeri as the Head of the Mathematics Department, a position he held for about 20 years.

The present contribution is intended to give a picture of the man behind these achievements. So this is an essay expressly about the person of a mathematician and no attempt will be made to describe or sum up Inkeri's mathematical work. For an appreciation of the latter the reader is asked to take advantage of the rich material in the rest of this volume.

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MAIN PUBLICATIONS

(i) Monographs

Pell's equation. (Russian) Tbilisi, 1952, pp. 90.

Gitterpunkte in mehrdimensionalen Kugeln. Panstwowe Wydawnictwo Naukowe, Warszawa, 1957, pp. 471.

Lattice points in many-dimensional spheres. (Russian) Publ. Academy of Sci., Tbilisi, 1960, pp. 460.

Weylsche Exponentialsummen in der neueren Zahlentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, pp. 231. vskip+0.3cm

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Kurt Mahler was born on 26 July 1903 at Krefeld am Rhein in Germany; he died in his 85th year on 26 February 1988 in Canberra, Australia. From 1933 onwards most of his life was spent outside of Germany, but his mathematical roots remained in the great school of mathematics that existed in Germany between the two world wars. Above all Mahler lived for mathematics; he took great pleasure in lecturing, researching and writing. It was no surprise that he remained active in research until the last days of his life. He was never a narrow specialist and had a remarkably broad and thorough knowledge of large parts of current and past mathematical research. At the same time he was oblivious to mathematical fashion, and very much followed his own path through the world of mathematics, uncovering new and simple ideas in many directions. In this way he made major contributions to transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Towards the end of his life, Kurt Mahler wrote a considerable amount about his own experiences; see 'Fifty years as a mathematician', 'How I became a mathematician', 'Warum ich eine besondere Vorliebe fur die Mathematik habe', 'Fifty years as a mathematician II'. There is also a recent excellent account of his life and work by Cassels (J.W.S. Cassels, 1991, 'Obituary of Kurt Mahler', Acta Arith. (3), 58, 215-228). In preparing this memoir we have freely used these sources. We have also drawn on our knowledge of and conversations with Mahler, whom we first met when we were undergraduates in Australia in the early 1960s.

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A timeline history of the IBM Typewriter with old ads to show what the machines looked like. Click on the thumbnail to see an enlargement of that ad.

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Twain was also keenly aware, however, of the limitations of technology. A Connecticut Yankee in King Arthur's Court shows technology improving communication, productivity, and personal hygiene. But it is unable to conquer what Twain considered the true problem: a society in which people do not think for themselves. Machines can be wonderful tools, Twain suggests, but they are only tools. The finest technology in all the realm does not excuse us from exercising our own judgment, a theme Twain would doubtless return to were he publishing today.

As we enter a new millennium, we take for granted much of what was new and marvelous to the people of Twain's era. Understanding the technological developments of Twain's lifetime (1835 - 1910) may provide greater appreciation of this novel, one of the first science fiction novels written in America.

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This subject has a rich history attached to it. In order to understand the full discovery and development of moving pictures, we must study the various elements of not only this medium, but all others which are related to cinematography and especially photography. This timeline will provide more than a substantial glimpse into the discoveries of these elements which include; optics, pinhole images, camera obscura, persistence of vision, showmen, magic lanterns, light, lenses, light-sensitive substances, phantasmagoria, motion study analysis, photography, and stop-action series photography in the overall growth of photography and ultimately, the movement of pictures.

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This website presents a retrospective history of the dawn of film, and a pre-history of cinema. In fifteen chapters, broken down chronologically, the text deals with the origin of motion pictures and the ancestors of cinema, culminating with the birth of motion pictures in the nineteenth century. This site provides a substantial glimpse into the history and discovery of the marriage of photography, light and shadow, optics and lenses, glass and celluloid, into movement known as cinematography. Each chapter includes brief essays on various innovations and important figures in the development of new technologies, as well as numerous images. A bibliography and page of links to related sites should provide researchers with additional avenues to explore.

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Read here: Ethnoarchaeology of Ironsmelting, a comparison of several (sub-Saharan) African ethnographical cases of ironsmelting with the 10th - 8th century BC iron smelting remains from Tell Hammeh az-Zarqa in Jordan here. The description of each case can be read in a separate screen, by clicking on the name of the 'tribe' under the "the cases" header