From Mathematics to Generic Programming

Author: Alexander A. Stepanov
Publisher: Addison-Wesley Professional
ISBN: 0133491781
Category : Computers
Languages : en
Pages : 311

Book Description
In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful. If you’re a reasonably proficient programmer who can think logically, you have all the background you’ll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem. As you read this book, you’ll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You’ll also gain deep insight into the value of mathematics to programming—insight that will prove invaluable no matter what programming languages and paradigms you use. You will learn about How to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiency Ancient paradoxes, beautiful theorems, and the productive tension between continuous and discrete A simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on it Powerful mathematical approaches to abstraction How abstract algebra provides the idea at the heart of generic programming Axioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structures Surprising subtleties of simple programming tasks and what you can learn from them How practical implementations can exploit theoretical knowledge

Elements of Programming

Author: Alexander Stepanov
Publisher: Lulu.com
ISBN: 0578222140
Category : Computers
Languages : en
Pages : 282

Book Description
Elements of Programming provides a different understanding of programming than is presented elsewhere. Its major premise is that practical programming, like other areas of science and engineering, must be based on a solid mathematical foundation. This book shows that algorithms implemented in a real programming language, such as C++, can operate in the most general mathematical setting. For example, the fast exponentiation algorithm is defined to work with any associative operation. Using abstract algorithms leads to efficient, reliable, secure, and economical software.

Programming with Types

Author: Vlad Riscutia
Publisher: Simon and Schuster
ISBN: 1638350264
Category : Computers
Languages : en
Pages : 531

Book Description
Summary Programming with Types teaches you to design safe, resilient, correct software that’s easy to maintain and understand by taking advantage of the power of strong type systems. Designed to provide practical, instantly useful techniques for working developers, this clearly written tutorial introduces you to using type systems to support everyday programming tasks. About the technology Common bugs often result from mismatched data types. By precisely naming and controlling which data are allowable in a calculation, a strong type system can eliminate whole classes of errors and ensure data integrity throughout an application. As a developer, skillfully using types in your everyday practice leads to better code and saves time tracking down tricky data-related errors. About the book Programming with Types teaches type-based techniques for writing software that’s safe, correct, easy to maintain, and practically self-documenting. Designed for working developers, this clearly written tutorial sticks with the practical benefits of type systems for everyday programming tasks. Following real-world examples coded in TypeScript, you’ll build your skills from primitive types up to more-advanced concepts like functors and monads. What's inside Building data structures with primitive types, arrays, and references How types affect functions, inheritance, and composition Object-oriented programming with types Applying generics and higher-kinded types About the reader You’ll need experience with a mainstream programming language like TypeScript, Java, JavaScript, C#, or C++. About the author Vlad Riscutia is a principal software engineer at Microsoft. He has headed up several major software projects and mentors up-and-coming software engineers.

A Programmer's Introduction to Mathematics

Author: Jeremy Kun
Publisher:
ISBN:
Category :
Languages : en
Pages : 400

Book Description
A Programmer's Introduction to Mathematics uses your familiarity with ideas from programming and software to teach mathematics. You'll learn about the central objects and theorems of mathematics, including graphs, calculus, linear algebra, eigenvalues, optimization, and more. You'll also be immersed in the often unspoken cultural attitudes of mathematics, learning both how to read and write proofs while understanding why mathematics is the way it is. Between each technical chapter is an essay describing a different aspect of mathematical culture, and discussions of the insights and meta-insights that constitute mathematical intuition. As you learn, we'll use new mathematical ideas to create wondrous programs, from cryptographic schemes to neural networks to hyperbolic tessellations. Each chapter also contains a set of exercises that have you actively explore mathematical topics on your own. In short, this book will teach you to engage with mathematics. A Programmer's Introduction to Mathematics is written by Jeremy Kun, who has been writing about math and programming for 10 years on his blog "Math Intersect Programming." As of 2020, he works in datacenter optimization at Google.The second edition includes revisions to most chapters, some reorganized content and rewritten proofs, and the addition of three appendices.

Generic Programming and the STL

Author: Matthew H. Austern
Publisher: Addison-Wesley Professional
ISBN:
Category : Computers
Languages : en
Pages : 584

Book Description
Introduces programmers to the generic programming paradigm and to the C++ Standard Template Library and its use as an extensible framework for generic and interoperable components. Explains ideas underlying generic programming and shows how to create algorithms decoupled from the types and data structures they operate on, and how to write more efficient code that can be used and reused across platforms. Assumes familiarity with C++ and algorithms. Annotation copyrighted by Book News, Inc., Portland, OR

Datatype-Generic Programming

Author: Roland Backhouse
Publisher: Springer Science & Business Media
ISBN: 3540767851
Category : Computers
Languages : en
Pages : 379

Book Description
This tutorial book presents six carefully revised lectures given at the Spring School on Datatype-Generic Programming, SSDGP 2006. This was held in Nottingham, UK, in April 2006. It was colocated with the Symposium on Trends in Functional Programming (TFP 2006), and the Conference of the Types Project (TYPES 2006). All the lectures have been subjected to thorough internal review by the editors and contributors, supported by independent external reviews.

Introduction to Scientific Programming with Python

Author: Joakim Sundnes
Publisher:
ISBN: 3030503569
Category : Computer programming
Languages : en
Pages : 157

Book Description
This open access book offers an initial introduction to programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming. The book uses relevant examples from mathematics and the natural sciences to present programming as a practical toolbox that can quickly enable readers to write their own programs for data processing and mathematical modeling. These tools include file reading, plotting, simple text analysis, and using NumPy for numerical computations, which are fundamental building blocks of all programs in data science and computational science. At the same time, readers are introduced to the fundamental concepts of programming, including variables, functions, loops, classes, and object-oriented programming. Accordingly, the book provides a sound basis for further computer science and programming studies.

Programming for Computations - Python

Author: Svein Linge
Publisher: Springer
ISBN: 3319324284
Category : Computers
Languages : en
Pages : 244

Book Description
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.

Basic Category Theory for Computer Scientists

Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262326450
Category : Computers
Languages : en
Pages : 117

Book Description
Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Generative Programming

Author: Krzysztof Czarnecki
Publisher:
ISBN: 9780210309773
Category : Generative programming (Computer science)
Languages : en
Pages : 832

Book Description