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Number theory

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Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters.

Number theory --- getallenleer

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Random Number Generators, Principles and Practices has been written for programmers, hardware engineers, and sophisticated hobbyists interested in understanding random numbers generators and gaining the tools necessary to work with random number generators with confidence and knowledge. Using an approach that employs clear diagrams and running code examples rather than excessive mathematics, random number related topics such as entropy estimation, entropy extraction, entropy sources, PRNGs, randomness testing, distribution generation, and many others are exposed and demystified. If you have ever Wondered how to test if data is really random Needed to measure the randomness of data in real time as it is generated Wondered how to get randomness into your programs Wondered whether or not a random number generator is trustworthy Wanted to be able to choose between random number generator solutions Needed to turn uniform random data into a different distribution Needed to ensure the random numbers from your computer will work for your cryptographic application Wanted to combine more than one random number generator to increase reliability or security Wanted to get random numbers in a floating point format Needed to verify that a random number generator meets the requirements of a published standard like SP800-90 or AIS 31 Needed to choose between an LCG, PCG or XorShift algorithm Then this might be the book for you.

Random number generators. --- Generators, Random number --- Electronic digital computers

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The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.

Number theory --- Mathematics --- wiskunde --- getallenleer

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This is the [9220328]tensive biography of the in[9221258]l German mathematician, Peter Gustav Lejeune Dirichlet (1805 – 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This uni[9220744]roach is exempli[9220232]a paper that effectively launched the [9240719] analytic number theory. The same orientation pervaded his teaching, which had a profound in[9222376]on the work of many mathematicians of subsequent generations. Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet’s life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal not only to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.

Number theory --- Mathematics --- wiskunde --- getallenleer