Discrete Mathematics and Mathematical Modelling in the Digital Era


Book Description

This book features carefully selected research papers presented during the 9th International Conference on Discrete Mathematics and Mathematical Modelling in the Digital Era (ICDMMMDE-2023). The conference, organised at the Department of Mathematics, The Gandhigram Rural Institute in Gandhigram, Tamil Nadu, India, took place from 23–25 March 2023. Serving as a dynamic platform, the event attracted emerging researchers, mathematicians, industrialists, scientists, and engineers from across the globe, fostering discussions on pertinent research topics. This volume showcases noteworthy contributions from esteemed researchers within the realm of discrete mathematics and mathematical modeling, meticulously subjected to a rigorous peer-review process for publication. The included papers delve into diverse subjects, including controllability, image processing, topology, graph theory, fuzzy delay differential equations, analysis, queuing theory, and applications in networks and biology. Theculmination of these contributions forms a comprehensive and authoritative resource for scholars and professionals alike.







Digital And The Real World, The: Computational Foundations Of Mathematics, Science, Technology, And Philosophy


Book Description

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).




Developing Deep Knowledge in Middle School Mathematics


Book Description

This textbook is for prospective teachers of middle school mathematics. It reflects on the authors’ experience in offering various mathematics education courses to prospective teachers in the US and Canada. In particular, the content can support one or more of 24-semester-hour courses recommended by the Conference Board of the Mathematical Sciences (2012) for the mathematical preparation of middle school teachers. The textbook integrates grade-appropriate content on all major topics in the middle school mathematics curriculum with international recommendations for teaching the content, making it relevant for a global readership. The textbook emphasizes the inherent connections between mathematics and real life, since many mathematical concepts and procedures stem from common sense, something that schoolchildren intuitively possess. This focus on teaching formal mathematics with reference to real life and common sense is essential to its pedagogical approach. In addition, the textbook stresses the importance of being able to use technology as an exploratory tool, and being familiar with its strengths and weaknesses. In keeping with this emphasis on the use of technology, both physical (manipulatives) and digital (commonly available educational software), it also explores e.g. the use of computer graphing software for digital fabrication. In closing, the textbook addresses the issue of creativity as a crucial aspect of education in the digital age in general, and in mathematics education in particular.




Mathematics and the Natural Sciences


Book Description

The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.




Developing Safety-Critical Software


Book Description

The amount of software used in safety-critical systems is increasing at a rapid rate. At the same time, software technology is changing, projects are pressed to develop software faster and more cheaply, and the software is being used in more critical ways. Developing Safety-Critical Software: A Practical Guide for Aviation Software and DO-178C Compliance equips you with the information you need to effectively and efficiently develop safety-critical, life-critical, and mission-critical software for aviation. The principles also apply to software for automotive, medical, nuclear, and other safety-critical domains. An international authority on safety-critical software, the author helped write DO-178C and the U.S. Federal Aviation Administration’s policy and guidance on safety-critical software. In this book, she draws on more than 20 years of experience as a certification authority, an avionics manufacturer, an aircraft integrator, and a software developer to present best practices, real-world examples, and concrete recommendations. The book includes: An overview of how software fits into the systems and safety processes Detailed examination of DO-178C and how to effectively apply the guidance Insight into the DO-178C-related documents on tool qualification (DO-330), model-based development (DO-331), object-oriented technology (DO-332), and formal methods (DO-333) Practical tips for the successful development of safety-critical software and certification Insightful coverage of some of the more challenging topics in safety-critical software development and verification, including real-time operating systems, partitioning, configuration data, software reuse, previously developed software, reverse engineering, and outsourcing and offshoring An invaluable reference for systems and software managers, developers, and quality assurance personnel, this book provides a wealth of information to help you develop, manage, and approve safety-critical software more confidently.




Advances in Mathematics for Industry 4.0


Book Description

Advances in Mathematics for Industry 4.0 examines key tools, techniques, strategies, and methods in engineering applications. By covering the latest knowledge in technology for engineering design and manufacture, chapters provide systematic and comprehensive coverage of key drivers in rapid economic development. Written by leading industry experts, chapter authors explore managing big data in processing information and helping in decision-making, including mathematical and optimization techniques for dealing with large amounts of data in short periods. - Focuses on recent research in mathematics applications for Industry 4.0 - Provides insights on international and transnational scales - Identifies mathematics knowledge gaps for Industry 4.0 - Describes fruitful areas for further research in industrial mathematics, including forthcoming international studies and research




Discrete Mathematics


Book Description

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.




Teaching and Learning in a Digital World


Book Description

This book gathers the Proceedings of the 20th International Conference on Interactive Collaborative Learning (ICL2017), held in Budapest, Hungary on 27–29 September 2017. The authors are currently witnessing a significant transformation in the development of education. The impact of globalisation on all areas of human life, the exponential acceleration of technological developments and global markets, and the need for flexibility and agility are essential and challenging elements of this process that have to be tackled in general, but especially in engineering education. To face these current real-world challenges, higher education has to find innovative ways to quickly respond to them. Since its inception in 1998, this conference has been devoted to new approaches in learning with a focus on collaborative learning. Today the ICL conferences offer a forum for exchange concerning relevant trends and research results, and for sharing practical experience gained while developing and testing elements of new technologies and pedagogies in the learning context.