Algorithmic And Experimental Methods In Algebra Geometry And Number Theory
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Algorithmic And Experimental Methods In Algebra Geometry And Number Theory
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Author : Gebhard Böckle
language : en
Publisher: Springer
Release Date : 2018-03-22
Algorithmic And Experimental Methods In Algebra Geometry And Number Theory written by Gebhard Böckle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-22 with Mathematics categories.
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
Algorithmic Algebraic Number Theory
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Author : M. Pohst
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-25
Algorithmic Algebraic Number Theory written by M. Pohst and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-25 with Mathematics categories.
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
Real Algebraic Geometry And Optimization
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Author : Thorsten Theobald
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-18
Real Algebraic Geometry And Optimization written by Thorsten Theobald and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Mathematics categories.
This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
The Computer Algebra System Oscar
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Author : Wolfram Decker
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
The Computer Algebra System Oscar written by Wolfram Decker and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.
This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.
Mathematical Software Icms 2024
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Author : Kevin Buzzard
language : en
Publisher: Springer Nature
Release Date : 2024-07-16
Mathematical Software Icms 2024 written by Kevin Buzzard and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-16 with Computers categories.
This book constitutes the proceedings of the 8th International Conference on Mathematical Software, ICMS 2024, held in Durham, UK, during July 22–25, 2024. The 37 full papers presented were carefully reviewed and selected from 46 submissions. The papers are organized in subject areas as follows: plenary lectures; number theory and related areas; novel formalisations of mathematics in lean; software for the applications of group theory to combinatorics; classical algebraic geometry & modern computer algebra: innovative software design and its applications; advancing computer algebra with massively parallel methods; computer algebra applications in the life sciences; machine learning within computer algebra systems; numerical software for special functions; mathematical research data; symbolic-numeric methods in algebraic geometry; Polyhedral geometry and combinatorics; general session.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Computer Algebra In Scientific Computing
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Author : François Boulier
language : en
Publisher: Springer Nature
Release Date : 2022-08-10
Computer Algebra In Scientific Computing written by François Boulier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-10 with Computers categories.
This book constitutes the proceedings of the 24th International Workshop on Computer Algebra in Scientific Computing, CASC 2022, which took place in Gebze, Turkey, in August 2022. The 20 full papers included in this book were carefully reviewed and selected from 32 submissions. They focus on the theory of symbolic computation and its implementation in computer algebra systems as well as all other areas of scientific computing with regard to their benefit from or use of computer algebra methods and software.
Women In Numbers Europe Iii
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Author : Alina Carmen Cojocaru
language : en
Publisher: Springer Nature
Release Date : 2022-02-01
Women In Numbers Europe Iii written by Alina Carmen Cojocaru and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-01 with Mathematics categories.
This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.
Essentials Of Tropical Combinatorics
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Author : Michael Joswig
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-08
Essentials Of Tropical Combinatorics written by Michael Joswig and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.
Mathematical Software Icms 2020
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Author : Anna Maria Bigatti
language : en
Publisher: Springer Nature
Release Date : 2020-07-07
Mathematical Software Icms 2020 written by Anna Maria Bigatti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Computers categories.
This book constitutes the proceedings of the 7th International Conference on Mathematical Software, ICMS 2020, held in Braunschweig, Germany, in July 2020. The 48 papers included in this volume were carefully reviewed and selected from 58 submissions. The program of the 2020 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a environment of mathematical software research, development and use.