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.

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.

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.

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

Mathematics and Computation

Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434

Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

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.

Introduction to Programming Using Java

Author: David Eck
Publisher: Orange Grove Text Plus
ISBN: 9781616100476
Category :
Languages : en
Pages : 0

Book Description
This is a free, on-line textbook on introductory programming using Java. This book is directed mainly towards beginning programmers, although it might also be useful for experienced programmers who want to learn more about Java. It is an introductory text and does not provide complete coverage of the Java language. The text is a PDF and is suitable for printing or on-screen reading. It contains internal links for navigation and external links to source code files, exercise solutions, and other resources. Contents: 1) Overview: The Mental Landscape. 2) Programming in the Small I: Names and Things. 3) Programming in the Small II: Control. 4) Programming in the Large I: Subroutines. 5) Programming in the Large II: Objects and Classes. 6) Introduction to GUI Programming. 7) Arrays. 8) Correctness and Robustness. 9) Linked Data Structures and Recursion. 10) Generic Programming and Collection Classes. 11) Files and Networking. 12) Advanced GUI Programming. Appendices: Source Code for All Examples in this Book, and News and Errata.

C++ Crash Course

Author: Josh Lospinoso
Publisher: No Starch Press
ISBN: 1593278888
Category : Computers
Languages : en
Pages : 793

Book Description
A fast-paced, thorough introduction to modern C++ written for experienced programmers. After reading C++ Crash Course, you'll be proficient in the core language concepts, the C++ Standard Library, and the Boost Libraries. C++ is one of the most widely used languages for real-world software. In the hands of a knowledgeable programmer, C++ can produce small, efficient, and readable code that any programmer would be proud of. Designed for intermediate to advanced programmers, C++ Crash Course cuts through the weeds to get you straight to the core of C++17, the most modern revision of the ISO standard. Part 1 covers the core of the C++ language, where you'll learn about everything from types and functions, to the object life cycle and expressions. Part 2 introduces you to the C++ Standard Library and Boost Libraries, where you'll learn about all of the high-quality, fully-featured facilities available to you. You'll cover special utility classes, data structures, and algorithms, and learn how to manipulate file systems and build high-performance programs that communicate over networks. You'll learn all the major features of modern C++, including: Fundamental types, reference types, and user-defined types The object lifecycle including storage duration, memory management, exceptions, call stacks, and the RAII paradigm Compile-time polymorphism with templates and run-time polymorphism with virtual classes Advanced expressions, statements, and functions Smart pointers, data structures, dates and times, numerics, and probability/statistics facilities Containers, iterators, strings, and algorithms Streams and files, concurrency, networking, and application development With well over 500 code samples and nearly 100 exercises, C++ Crash Course is sure to help you build a strong C++ foundation.

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.