Tag: Arithmetic

March 25, 2023

Conjectures in Arithmetic Algebraic Geometry A Survey

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Free Download Conjectures in Arithmetic Algebraic Geometry: A Survey by Wilfred W. J. Hulsbergen
English | PDF | 1992 | 246 Pages | ISBN : 3528064331 | 11.1 MB
In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat’s Last Theorem one is naturally led to intro- duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat’s Last Theorem for a large class of exponents. Before Kummer, Dirich- let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions.

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March 6, 2023

Open Problems in Arithmetic Algebraic Geometry

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Free Download [various contributors], "Open Problems in Arithmetic Algebraic Geometry "
English | ISBN: 1571463739 | 2019 | 344 pages | PDF | 57 MB
This book originated in the idea that open problems act as crystallization points in mathematical research. Mathematical books usually deal with fully developed theories. But here we present work at an earlier stage-when challenging questions can give new directions to mathematical research.

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March 4, 2023

Approximate Arithmetic Circuit Architectures for FPGA-based Systems

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Free Download Approximate Arithmetic Circuit Architectures for FPGA-based Systems
English | 2023 | ISBN: 3031212932 | 190 Pages | PDF EPUB (True) | 35 MB
This book presents various novel architectures for FPGA-optimized accurate and approximate operators, their detailed accuracy and performance analysis, various techniques to model the behavior of approximate operators, and thorough application-level analysis to evaluate the impact of approximations on the final output quality and performance metrics. As multiplication is one of the most commonly used and computationally expensive operations in various error-resilient applications such as digital signal and image processing and machine learning algorithms, this book particularly focuses on this operation. The book starts by elaborating on the various sources of error resilience and opportunities available for approximations on various layers of the computation stack. It then provides a detailed description of the state-of-the-art approximate computing-related works and highlights their limitations.

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February 1, 2023

Algebra, Arithmetic, Numbers and Numeration A Mathematics Book for High Schools and Colleges

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Algebra, Arithmetic, Numbers and Numeration: A Mathematics Book for High Schools and Colleges by Kingsley Augustine
English | 2018 | ISBN: N/A | ASIN: B077H9TR12 | 190 pages | PDF | 1.64 Mb
This book which is suitable for students in high schools and students in colleges. It also serves as a useful tool for students who are preparing for entrance examinations into colleges and universities. The step by step explanations presented in the worked examples are easy to understand since care was taken to sufficiently explain salient points. Numerous exercises at the end of each chapter are intended to test students’ understanding of the topic. Therefore students are presented with an effective means of self-assessment whereby they can determine their individual strengths and revision needs. The topics covered in this eBook include:Linear equation and equations with fractionsNumber basesStandard forms and approximationsLaws of indicesLaws and theories of logarithmsModular arithmeticChange of subject of formulaeVariationWord problems involving fractionsSimple interestCompound interestProportional divisionAverage and mixture, rateFraction Decimal PercentageRatio.

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