File Name: a computational introduction to number theory and algebra .zip
Show all documents Besides the general fact that such hand-crafted code is more e ffi cient than that produced by a compiler, there is another, more important reason for using assembly language.
The last three or four decades have seen an interesting array of applications of algebra and number theory to computer science and related areas, from securing the interchange of information public key cryptography to error-correcting codes widely used in the storage, retrieval and transmission of information. Conversely, the increasing capacity of computers has given rise to a vast area of algebra including number theory and algebraic geometry that emphasizes the algorithmic aspects of these branches of mathematics that somehow were at best latent. The book under review, now in its Second Edition, weaves together both aspects of algebra and number theory summarized above, balancing the exposition between the purely theoretical developments and the straight-forward applications to cryptography and coding theory, including algorithms and pseudo-codes that could be easily implemented by the interested reader. What is the running time of a program implementing these algorithms? This part of the book ends with the now familiar application to RSA public key cryptosystem and an application of the Chinese remainder theorem to an example of an error-correcting code analog to the Reed-Solomon code.
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Shoup Published Computer Science, Mathematics. This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience.
The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. View via Publisher. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Background Citations. Methods Citations. Results Citations. Figures, Tables, and Topics from this paper. Figures and Tables. Citation Type.
Has PDF. Publication Type. More Filters. Theoretical concept of number fields theory. View 1 excerpt, cites background. Research Feed. An Exploration of Mathematical Applications in Cryptography.
Mathematics of Public Key Cryptography. Introduction to Cryptography Foreword This chapter is based on lecture notes from coding theory courses taught by Venkatesan. Good reduction of Puiseux series and applications. Modern computer algebra. View 2 excerpts, references methods and background. Introduction to analytic number theory. An Introduction to the Theory of Numbers. Highly Influential. View 3 excerpts, references methods and background.
Description This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
was to provide an introduction to number theory and algebra, with an emphasis on algorithms and applications, that would be accessible to a broad audience.
Solutions manual for "A computational introduction to number theory and algebra". July 07, If you follow me on Twitter, you've probably known that I've been into " A computational introduction to number theory and algebra " aka NTB for the last two or three months. IMHO, NTB is the best introductory-level book on number theory and algebra, especially for those who want to study these two mathematic subjects from a computer science and cryptography perspective. Moreover, the complete book is freely available online in PDF format under a Creative Common license.
Subject Computational. Number Theory. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.
This text is an introduction to number theory and abstract algebra; based on its presentation, it appears appropriate for students coming from computer science. The book starts with basic properties of integers e. Comprehensiveness rating: 5 see less. The book also includes an introduction to probability.
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Коммандер? - позвала Сьюзан. Свет внутри исходил лишь от светящихся компьютерных мониторов Стратмора. - Коммандер! - повторила. - Коммандер. Внезапно Сьюзан вспомнила, что он должен быть в лаборатории систем безопасности.
А вместо этого он заразил вирусом главный банк данных Агентства национальной безопасности. И этот вирус уже невозможно остановить - разве что вырубить электроэнергию и тем самым стереть миллиарды бит ценнейшей информации. Спасти ситуацию может только кольцо, и если Дэвид до сих пор его не нашел… - Мы должны выключить ТРАНСТЕКСТ! - Сьюзан решила взять дело в свои руки.
Сьюзан Флетчер словно была рождена для тайных поисков в Интернете.
У вас есть кое-что, что мне очень нужно, - сказал Беккер. - Да-да, конечно, - быстро проговорил немец, натужно улыбаясь. Он подошел к туалетному столику, где лежал бумажник. - Сколько. Беккер изобразил крайнюю степень негодования.
Нет. Сьюзан словно окаменела, ничего не понимая. Эхо выстрела слилось с царившим вокруг хаосом.
PDF | On Sep 1, , Igor Shparlinski published A computational introduction to number theory and algebra. | Find, read and cite all the.Reply
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In mathematics and computer science , computational number theory , also known as algorithmic number theory , is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry , including algorithms for primality testing and integer factorization , finding solutions to diophantine equations , and explicit methods in arithmetic geometry.Reply