Publication: ICFP '03: Proceedings of the eighth ACM SIGPLAN international conference on Functional programmingAugust 2003 Pages 79–86https://doi.org/10.1145/944705.944713
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A three-year study collected information bearing on the question of whether studying mathematics improves programming skills. An analysis of the data revealed significant differences in the programming effectiveness of two populations of students: (1) those who studied discrete mathematics through examples focused on reasoning about software and (2) those who studied the same mathematical topics illustrated with more traditional examples. Functional programming played a central role in the study because it provides a straightforward framework for the presentation of concepts such as predicate logic and proof by induction. Such topics can be covered in depth, staying almost entirely within the context of reasoning about software. The intricate complexities in logic that mutable variables carry with them need not arise, early on, to confuse novices struggling to understand new ideas. In addition, because functional languages provide useful and compact ways to express mathematical concepts, and because the choice of notation in mathematics courses is often at the discretion of the instructor (in contrast to the notational restrictions often fiercely guarded by the faculty in programming courses), discrete mathematics courses, as they are found in most computer science programs, provide an easy opportunity to enhance the education of students by exposing them to functional programming concepts.
Mar 13, 2018 The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics, includes new chapters on statements and proof, logical framework, natural numbers, and the integers, in addition to updated chapters from the previous edition. See more ideas about Discrete mathematics, Mathematics and Advanced mathematics. Nov 29, 2015 - Explore Vrazumikhin's board 'Discrete Mathematics', followed by 141 people on Pinterest. See more ideas about Discrete mathematics, Mathematics and Advanced mathematics.
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Software is discrete mathematics
Reviews
John S Fitzgerald
How to best train software engineering students in discrete mathematics is a source of continual debate. This paper advocates teaching mathematics through examples based on reasoning about software, rather than via more traditional 'math' examples. The paper introduces the Beseme project, which seeks to develop and assess teaching materials for discrete mathematics. The Beseme materials use functional programs covering areas ranging from list manipulation to tree balancing; mathematical reasoning skills are taught through proofs of program properties. The paper reports on the results of an experiment that gauged effectiveness by measuring student performance in a data structures course. Above-median students who had been taught using the Beseme materials achieved significantly better results than comparable students who had studied discrete mathematics in a traditional setting. The effect was not observed for below-median students. The paper provides arguments that the effect is due to the Beseme materials rather than instructors or innate talent. One might expect that students trained in discrete mathematics through the use of software examples as sophisticated as tree balancing might do better at data structures than those who had not. This raises a fundamental question: what constitutes successful training in discrete math__?__ This paper takes the view that discrete mathematics for computing is a utility subject, rather than a cultural inheritance in its own right. Some will find this too narrow a view, but the paper nevertheless provides some practical guidance for teachers struggling with student apathy in a subject that is often ignorantly portrayed as remote from 'real' computing science. Online Computing Reviews Service
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310 pagesDOI:10.1145/944705- General Chair:
- Colin Runciman,
- Program Chair:
- EISSN:1558-1160Issue’s Table of Contents
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View Digital EditionE-Book Review and Description:This book provides a 'palms-on' technique to educating Discrete Mathematics. Using software that is freely obtainable on Mac, PC & Unix platforms, the helpful language Haskell permits school college students to experiment with mathematical notations & concepts — a smart technique that provides school college students with on the spot options & permits lecturers to observe progress merely. This 2nd model accommodates additional supplies on the needs of formal methods to smart programming points. There are additional examples of induction proofs on small packages, & a new chapter displaying how a mathematical technique may be utilized to encourage AVL timber, a difficult data development. Designed for 1st & 2nd year undergraduates, the book can be correctly fitted to self-analysis. No prior info of helpful programming is required. Full with an instructor's info, by means of the web, this book is supposed as the primary educating textual content material for Discrete Mathematics packages, nevertheless will even current useful learning for Conversion Masters & Formal Methods packages.
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By using different techniques of page turn you could additionally enhance your eBook experience. You can try many ways to turn the pages of eBook to enhance your reading experience. Check out whether you can turn the page with some arrow keys or click a specific part of the screen, apart from using the mouse to handle everything. Favor to make us of arrow keys if you are leaning forwards. Try to use the mouse if you are comfy sitting back. Lesser the movement you need to make while reading the eBook better is going to be your reading experience.
Technical issues One issue on eBook readers with LCD screens is the fact that it will not take long before you strain your eyes from reading. To help prevent this, you can use the “white on black” feature of your iPad or similar attributes to other eBook readers. This will definitely help to make reading easier.
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