Category: Number Theory

The book of squares by Leonardo Pisano Fibonacci

By Leonardo Pisano Fibonacci

The e-book of Squares via Fibonacci is a gem within the mathematical literature and essentially the most vital mathematical treatises written within the center a while. it's a selection of theorems on indeterminate research and equations of moment measure which yield, between different effects, an answer to an issue proposed by way of grasp John of Palermo to Leonardo on the court docket of Frederick II. The booklet was once devoted and awarded to the Emperor at Pisa in 1225. relationship again to the thirteenth century the e-book indicates the early and persevered fascination of guys with our quantity process and the connection between numbers with specified homes equivalent to major numbers, squares, and extraordinary numbers. The devoted translation into glossy English and the observation through the translator make this booklet available to specialist mathematicians and amateurs who've regularly been intrigued through the entice of our quantity procedure.

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Representations of Integers as Sums of Squares by E. Grosswald

By E. Grosswald

During the tutorial 12 months 1980-1981 i used to be educating on the Technion-the Israeli Institute of Technology-in Haifa. The viewers used to be small, yet con­ sisted of really proficient and keen listeners; regrettably, their again­ floor diverse commonly. What may one provide such an viewers, as a way to do justice to them all? i made a decision to debate representations of typical integers as sums of squares, beginning at the most simple point, yet with the inten­ tion of pushing forward so far as attainable in many of the diverse instructions that provided themselves (quadratic types, idea of genera, generalizations and sleek advancements, etc.), in accordance with the pursuits of the viewers. a couple of weeks after the beginning of the educational 12 months I obtained a letter from Professor Gian-Carlo Rota, with the recommendation that I post a manuscript for the Encyclopedia of Mathematical Sciences lower than his editorship. I spoke back that i didn't have a prepared manuscript to provide, yet that i'll use my notes on representations of integers via sums of squares because the foundation for one. certainly, approximately that point I had already begun considering the opportunity of any such booklet and had, in truth, relatively certain rules concerning the form of ebook i wished it to be.

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Basiswissen Zahlentheorie: Einfuehrung in Zahlen und by Kristina Reiss

By Kristina Reiss

Kenntnisse ?ber den Aufbau des Zahlsystems und ?ber elementare zahlentheoretische Prinzipien geh?ren zum unverzichtbaren Grundwissen in der Mathematik. Das vorliegende Buch spannt den Bogen vom Rechnen mit nat?rlichen Zahlen ?ber Teilbarkeitseigenschaften und Kongruenzbetrachtungen bis hin zu zahlentheoretischen Funktionen und Anwendungen wie der Kryptographie und Zahlencodierung. Wert wird dabei auf eine verst?ndliche und umfassende Darstellung des Stoffes gelegt. Beweisideen, die hinter stringent durchgef?hrten Beweisen stehen, und die Verkn?pfung von Fachwissen mit Schulbez?gen sind dabei als besondere Merkmale hervorzuheben. Erg?nzt wird die Darstellung durch viele ?bungsaufgaben, die mit L?sungshinweisen und vollst?ndigen L?sungen versehen sind.

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Third Update on Adult Learning Theory: New Directions for by Sharan B. Merriam

By Sharan B. Merriam

This Third replace on grownup studying Theory follows past volumes at the related subject, the 1st released in 1993 and the second one in 2001. just one subject, transformative studying conception, are available in all 3 updates, representing the continued advancements in examine and replacement theoretical conceptions of TL.

Thanks to a transforming into physique of analysis and theory-building, 3 subject matters in brief touched on in 2001 are actually separate chapters during this 3rd update:

  • spirituality and grownup learning
  • learning in the course of the body
  • narrative studying in adulthood

Also new during this replace is a bankruptcy on non-Western views on studying and realizing. New advancements in different components also are explored: figuring out the relationship among the mind and studying, and the way sleek and postmodern methods of understanding are converging and are deliver expressed in social events. The concluding bankruptcy identifies developments in grownup studying thought for the twenty-first century: awareness to context, and to the holistic nature of studying in adulthood.

This is 119th quantity of the Jossey-Bass quarterly record sequence New instructions for grownup and carrying on with Education. famous for its intensity of insurance, New instructions for grownup and carrying on with Education is an vital sequence that explores problems with universal curiosity to teachers, directors, counselors, and policymakers in a extensive variety of grownup and carrying on with schooling settings, comparable to schools and universities, extension courses, companies, libraries, and museums.

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Elliptic Functions according to Eisenstein and Kronecker by Andre Weil

By Andre Weil

"As a contribution to the background of arithmetic, it is a version of its sort. whereas adhering to the fundamental outlook of Eisenstein and Kronecker, it offers new perception into their paintings within the gentle of next advancements, correct as much as the current day. As one could anticipate from this writer, it additionally comprises a few pertinent reviews having a look into the long run. it's not in spite of the fact that only a bankruptcy within the historical past of our topic, yet a wide-ranging survey of 1 of the main energetic branches of arithmetic this day. The booklet has its personal very person flavour, reflecting a type of mixed Eisenstein-Kronecker-Weil character. established primarily on Eisenstein's method of elliptic features through limitless sequence over lattices within the advanced airplane, it stretches again to the very beginnings at the one hand and reaches ahead to a few of the latest examine paintings at the different. (...) The continual reader should be richly rewarded."
A. Fröhlich, Bulletin of the London Mathematical Society, 1978

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Surveys in Number Theory by George E. Andrews (auth.), Krishnaswami Alladi (eds.)

By George E. Andrews (auth.), Krishnaswami Alladi (eds.)

Number concept has a wealth of long-standing difficulties, the examine of which through the years has resulted in significant advancements in lots of parts of arithmetic. This quantity contains seven major chapters on quantity concept and comparable subject matters. Written by means of extraordinary mathematicians, key themes concentrate on multipartitions, congruences and identities (G. Andrews), the formulation of Koshliakov and Guinand in Ramanujan's misplaced Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating signal matrices and the Weyl personality formulation (D. M. Bressoud), theta features in complicated research (H. M. Farkas), illustration services in additive quantity conception (M. B. Nathanson), and ridicule theta features, ranks, and Maass varieties (K. Ono), and elliptic services (M. Waldschmidt).

All of the surveys have been outgrowths of featured talks given through the specified 12 months in quantity concept and Combinatorics on the collage of Florida, Gainesville, 2004-2005, and describe significant growth on a huge variety of topics.

This quantity is meant for mathematicians and graduate scholars attracted to quantity concept and similar areas.

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