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Computational Mathematics with SageMath

P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas

Author : P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas
Publisher : SIAM
Page : 459 pages
File Size : 47,9 Mb
Release : 2018-12-10
Category : Science
ISBN : 9781611975451

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Computational Mathematics with SageMath by P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas Pdf

This fantastic and deep book about how to use Sage for learning and doing mathematics at all levels perfectly complements the existing Sage documentation. It is filled with many carefully thought through examples and exercises, and great care has been taken to put computational functionality into proper mathematical context. Flip to almost any random page in this amazing book, and you will learn how to play with and visualize some beautiful part of mathematics. --- William A. Stein, CEO, SageMath, and professor of mathematics, University of Washington 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. 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.

Sage for Undergraduates

Gregory V. Bard

Author : Gregory V. Bard
Publisher : American Mathematical Soc.
Page : 3520 pages
File Size : 49,6 Mb
Release : 2015-02-16
Category : Mathematics
ISBN : 9781470411114

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Sage for Undergraduates by Gregory V. Bard Pdf

As the open-source and free competitor to expensive software like MapleTM, Mathematica®, Magma, and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (single-variable integral calculus) or higher-level course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling. The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors.

Numerical Analysis Using Sage

George A. Anastassiou,Razvan A. Mezei

Author : George A. Anastassiou,Razvan A. Mezei
Publisher : Springer
Page : 314 pages
File Size : 48,6 Mb
Release : 2015-04-11
Category : Mathematics
ISBN : 9783319167398

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Numerical Analysis Using Sage by George A. Anastassiou,Razvan A. Mezei Pdf

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application. Answers may be verified using Sage. The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®. Sage is open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a plus. Moreover, the code can be written using any web browser and is therefore useful with Laptops, Tablets, iPhones, Smartphones, etc. All Sage code that is presented in the text is openly available on SpringerLink.com.

Computational Mathematics with SageMath

P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thiéry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas

Author : P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thiéry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas
Publisher : SIAM
Page : 464 pages
File Size : 50,8 Mb
Release : 2018-12-10
Category : Science
ISBN : 9781611975468

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Computational Mathematics with SageMath by P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thiéry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas Pdf

“This fantastic and deep book about how to use Sage for learning and doing mathematics at all levels perfectly complements the existing Sage documentation. It is filled with many carefully thought through examples and exercises, and great care has been taken to put computational functionality into proper mathematical context. Flip to almost any random page in this amazing book, and you will learn how to play with and visualize some beautiful part of mathematics.” --- William A. Stein, CEO, SageMath, and professor of mathematics, University of Washington 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®. 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.

Programming for Computations - Python

Svein Linge,Hans Petter Langtangen

Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Page : 244 pages
File Size : 44,7 Mb
Release : 2016-07-25
Category : Computers
ISBN : 9783319324289

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Programming for Computations - Python by Svein Linge,Hans Petter Langtangen Pdf

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Prime Numbers and the Riemann Hypothesis

Barry Mazur,William Stein

Author : Barry Mazur,William Stein
Publisher : Cambridge University Press
Page : 155 pages
File Size : 51,9 Mb
Release : 2016-04-11
Category : Mathematics
ISBN : 9781107101920

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Prime Numbers and the Riemann Hypothesis by Barry Mazur,William Stein Pdf

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

Sage Beginner's Guide

Craig Finch

Author : Craig Finch
Publisher : Packt Publishing Ltd
Page : 620 pages
File Size : 42,9 Mb
Release : 2011-05-11
Category : Computers
ISBN : 9781849514477

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Sage Beginner's Guide by Craig Finch Pdf

Annotation Your work demands results, and you don't have time for tedious, repetitive mathematical tasks. Sage is a free, open-source software package that automates symbolic and numerical calculations with the power of the Python programming language, so you can focus on the analytical and creative aspects of your work or studies. Sage Beginner's Guide shows you how to do calculations with Sage. Each concept is illustrated with a complete example that you can use as a starting point for your own work. You will learn how to use many of the functions that are built in to Sage, and how to use Python to write sophisticated programs that utilize the power of Sage. This book starts by showing you how to download and install Sage, and introduces the command-line interface and the graphical notebook interface. It also includes an introduction to Python so you can start programming in Sage. Every major concept is illustrated with a practical example. After learning the fundamentals of variables and functions in Sage, you will learn how to symbolically simplify expressions, solve equations, perform integrals and derivatives, and manipulate vectors and matrices. You will learn how Sage can produce numerous kinds of plots and graphics. The book will demonstrate numerical methods in Sage, and explain how to use object-oriented programming to improve your code. Sage Beginner's Guide will give you the tools you need to unlock the full potential of Sage for simplifying and automating mathematical computing. Effectively use Sage to eliminate tedious algebra, speed up numerical calculations, implement algorithms and data structures, and illustrate your work with publication-quality plots and graphics.

Modular Forms, a Computational Approach

William A. Stein

Author : William A. Stein
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 42,9 Mb
Release : 2007-02-13
Category : Mathematics
ISBN : 9780821839607

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Modular Forms, a Computational Approach by William A. Stein Pdf

This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Number-Crunching

Paul J. Nahin

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 406 pages
File Size : 51,8 Mb
Release : 2011-08-08
Category : Mathematics
ISBN : 9781400839582

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Number-Crunching by Paul J. Nahin Pdf

More stimulating mathematics puzzles from bestselling author Paul Nahin How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

A Computational Introduction to Number Theory and Algebra

Victor Shoup

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 41,5 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Programming for Computations - MATLAB/Octave

Svein Linge,Hans Petter Langtangen

Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Page : 228 pages
File Size : 40,6 Mb
Release : 2016-08-01
Category : Computers
ISBN : 9783319324524

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Programming for Computations - MATLAB/Octave by Svein Linge,Hans Petter Langtangen Pdf

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

The Calabi–Yau Landscape

Yang-Hui He

Author : Yang-Hui He
Publisher : Springer Nature
Page : 214 pages
File Size : 40,5 Mb
Release : 2021-07-31
Category : Mathematics
ISBN : 9783030775629

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The Calabi–Yau Landscape by Yang-Hui He Pdf

Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.

A Course in Cryptography

Heiko Knospe

Author : Heiko Knospe
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 40,9 Mb
Release : 2019-09-27
Category : Ciphers
ISBN : 9781470450557

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A Course in Cryptography by Heiko Knospe Pdf

This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.

An Introduction to SAGE Programming

Razvan A. Mezei

Author : Razvan A. Mezei
Publisher : John Wiley & Sons
Page : 243 pages
File Size : 43,9 Mb
Release : 2015-12-29
Category : Mathematics
ISBN : 9781119122784

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An Introduction to SAGE Programming by Razvan A. Mezei Pdf

Features a simplified presentation of numerical methods by introducing and implementing SAGE programs An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods emphasizes how to implement numerical methods using SAGE Math and SAGE Interacts and also addresses the fundamentals of computer programming, including if statements, loops, functions, and interacts. The book also provides a unique introduction to SAGE and its computer algebra system capabilities; discusses second and higher order equations and estimate limits; and determines derivatives, integrals, and summations. Providing critical resources for developing successful interactive SAGE numerical computations, the book is accessible without delving into the mathematical rigor of numerical methods. The author illustrates the benefits of utilizing the SAGE language for calculus and the numerical analysis of various methods such as bisection methods, numerical integration, Taylor’s expansions, and Newton’s iterations. Providing an introduction to the terminology and concepts involved, An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods also features: An introduction to computer programming using SAGE Many practical examples throughout to illustrate the application of SAGE Interacts for various numerical methods Discussions on how to use SAGE Interacts and SAGE Cloud in order to create mathematical demonstrations Numerous homework problems and exercises that allow readers to practice their programming skillset A companion website that includes related SAGE programming code and select solutions to the homework problems and exercises An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods is an ideal reference for applied mathematicians who need to employ SAGE for the study of numerical methods and analysis. The book is also an appropriate supplemental textbook for upper-undergraduate and graduate-level courses in numerical methods.

Introduction to Number Theory

Anthony Vazzana,Martin Erickson,David Garth

Author : Anthony Vazzana,Martin Erickson,David Garth
Publisher : CRC Press
Page : 530 pages
File Size : 50,6 Mb
Release : 2007-10-30
Category : Computers
ISBN : 9781584889380

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Introduction to Number Theory by Anthony Vazzana,Martin Erickson,David Garth Pdf

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi

Computational Mathematics With Sagemath

Computational Mathematics with SageMath by P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thi?ry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas Pdf

Sage for Undergraduates by Gregory V. Bard Pdf

Numerical Analysis Using Sage by George A. Anastassiou,Razvan A. Mezei Pdf

Computational Mathematics with SageMath by P. Zimmermann,A. Casamayou,N. Cohen,G. Connan,T. Dumont,L. Fousse,F. Maltey,M. Meulien,M. Mezzarobba,C. Pernet,N. M. Thiéry,E. Bray,J. Cremona,M. Forets,A. Ghitza,H. Thomas Pdf

Programming for Computations - Python by Svein Linge,Hans Petter Langtangen Pdf

Prime Numbers and the Riemann Hypothesis by Barry Mazur,William Stein Pdf

Sage Beginner's Guide by Craig Finch Pdf

Modular Forms, a Computational Approach by William A. Stein Pdf

Number-Crunching by Paul J. Nahin Pdf

A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

Programming for Computations - MATLAB/Octave by Svein Linge,Hans Petter Langtangen Pdf

The Calabi–Yau Landscape by Yang-Hui He Pdf

A Course in Cryptography by Heiko Knospe Pdf

An Introduction to SAGE Programming by Razvan A. Mezei Pdf

Introduction to Number Theory by Anthony Vazzana,Martin Erickson,David Garth Pdf

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