SageMath, or Sage for short, is an open-source mathematical software system based on the Python language and developed by an international community comprising hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica, and MATLAB (R). To achieve this, Sage relies on many open-source programs, including GAP, Maxima, PARI, and various scientific libraries for Python, to which thousands of new functions have been added. Sage is freely available and is supported by all modern operating systems. Sage provides a wonderful scientific and graphical calculator for high school students, and it efficiently supports undergraduates in their computations in analysis, linear algebra, calculus, etc. For graduate students, researchers, and engineers in various mathematical specialties, Sage provides the most recent algorithms and tools, which is why several universities around the world already use Sage at the undergraduate level. Computational Mathematics with SageMath, written by researchers and by teachers at the high school, undergraduate, and graduate levels, focuses on the underlying mathematics necessary to use Sage efficiently and is illustrated with concrete examples. Part I is accessible to high school and undergraduate students and Parts II, III, and IV are suitable for graduate students, teachers, and researchers. This book is available under a Creative Commons license at sagebook.gforge.inria.fr.

This is a reproduction of a book published before 1923. This book may have occasional imperfectionssuch as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed worksworldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Germanistische Abhandlungen: Hermann Paul Zum 17. Marz 1902 Dargebracht Andreas Heusler, Emil Sulger-Gebing, Emil Koeppel, Friedrich von der Leyen, Johannes Hoops, Franz Muncker, Ludwig Sutterlin, Paul Zimmermann, Albert Thumb, Roman Woerner, Friedrich Panzer K.J. Trubner, 1902 Foreign Language Study; German; Foreign Language Study / German; Germanic philology; Language Arts & Disciplines / Linguistics

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.

This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.