Thinking Mathematics Foundations
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Thinking Mathematics Foundations
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Author :
language : en
Publisher:
Release Date : 1993
Thinking Mathematics Foundations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The Foundations Of Mathematics
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Author : Ian Stewart
language : en
Publisher: Oxford University Press
Release Date : 2015
The Foundations Of Mathematics written by Ian Stewart and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Juvenile Nonfiction categories.
The transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas. This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of 'nonstandard analysis', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.
Guide To Teaching Data Science
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Author : Orit Hazzan
language : en
Publisher: Springer Nature
Release Date : 2023-03-20
Guide To Teaching Data Science written by Orit Hazzan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-20 with Computers categories.
Data science is a new field that touches on almost every domain of our lives, and thus it is taught in a variety of environments. Accordingly, the book is suitable for teachers and lecturers in all educational frameworks: K-12, academia and industry. This book aims at closing a significant gap in the literature on the pedagogy of data science. While there are many articles and white papers dealing with the curriculum of data science (i.e., what to teach?), the pedagogical aspect of the field (i.e., how to teach?) is almost neglected. At the same time, the importance of the pedagogical aspects of data science increases as more and more programs are currently open to a variety of people. This book provides a variety of pedagogical discussions and specific teaching methods and frameworks, as well as includes exercises, and guidelines related to many data science concepts (e.g., data thinking and the data science workflow), main machine learning algorithms and concepts (e.g., KNN, SVM, Neural Networks, performance metrics, confusion matrix, and biases) and data science professional topics (e.g., ethics, skills and research approach). Professor Orit Hazzan is a faculty member at the Technion’s Department of Education in Science and Technology since October 2000. Her research focuses on computer science, software engineering and data science education. Within this framework, she studies the cognitive and social processes on the individual, the team and the organization levels, in all kinds of organizations. Dr. Koby Mike is a Ph.D. graduate from the Technion's Department of Education in Science and Technology under the supervision of Professor Orit Hazzan. He continued his post-doc research on data science education at the Bar-Ilan University, and obtained a B.Sc. and an M.Sc. in Electrical Engineering from Tel Aviv University.
Mathematical Foundations Of Advanced Informatics
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Author : Bernhard Steffen
language : en
Publisher: Springer
Release Date : 2018-03-20
Mathematical Foundations Of Advanced Informatics written by Bernhard Steffen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Computers categories.
The books in this trilogy capture the foundational core of advanced informatics. The authors make the foundations accessible, enabling students to become effective problem solvers. This first volume establishes the inductive approach as a fundamental principle for system and domain analysis. After a brief introduction to the elementary mathematical structures, such as sets, propositional logic, relations, and functions, the authors focus on the separation between syntax (representation) and semantics (meaning), and on the advantages of the consistent and persistent use of inductive definitions. They identify compositionality as a feature that not only acts as a foundation for algebraic proofs but also as a key for more general scalability of modeling and analysis. A core principle throughout is invariance, which the authors consider a key for the mastery of change, whether in the form of extensions, transformations, or abstractions. This textbook is suitable for undergraduate and graduate courses in computer science and for self-study. Most chapters contain exercises and the content has been class-tested over many years in various universities.
The Mathematical Foundation Of Multi Space Learning Theory
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Author : Tai Wang
language : en
Publisher: Taylor & Francis
Release Date : 2024-03-12
The Mathematical Foundation Of Multi Space Learning Theory written by Tai Wang and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-12 with Education categories.
This book explores the measurement of learning effectiveness and the optimization of knowledge retention by modeling the learning process and building the mathematical foundation of multi-space learning theory. Multi-space learning is defined in this book as a micro-process of human learning that can take place in more than one space, with the goal of effective learning and knowledge retention. This book models the learning process as a temporal sequence of concept learning, drawing on established principles and empirical evidence. It also introduces the matroid to strengthen the mathematical foundation of multi-space learning theory and applies the theory to vocabulary and mathematics learning, respectively. The results show that, for vocabulary learning, the method can be used to estimate the effectiveness of a single learning strategy, to detect the mutual interference that might exist between learning strategies, and to predict the optimal combination of strategies. In mathematical learning, it was found that timing is crucial in both first learning and second learning in scheduling optimization to maximize the intersection effective interval. The title will be of interest to researchers and students in a wide range of areas, including educational technology, learning sciences, mathematical applications, and mathematical psychology.
Mathematical Foundations Of Systems Analysis
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Author : Robert H. Kupperman
language : en
Publisher:
Release Date : 1969
Mathematical Foundations Of Systems Analysis written by Robert H. Kupperman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with System analysis categories.
Primary text for first-year graduate or advanced undergraduate courses in business decision theory, economics, industrial engineering, etc.
Rigor In The 6 12 Math And Science Classroom
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Author : Barbara R. Blackburn
language : en
Publisher: Routledge
Release Date : 2018-11-08
Rigor In The 6 12 Math And Science Classroom written by Barbara R. Blackburn and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-08 with Education categories.
Learn how to incorporate rigorous activities in your math or science classroom and help students reach higher levels of learning. Expert educators and consultants Barbara R. Blackburn and Abbigail Armstrong offer a practical framework for understanding rigor and provide specialized examples for middle and high school math and science teachers. Topics covered include: Creating a rigorous environment High expectations Support and scaffolding Demonstration of learning Assessing student progress Collaborating with colleagues The book comes with classroom-ready tools, offered in the book and as free eResources on our website at www.routledge.com/9781138302716.
Teaching Mathematics Creatively
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Author : Linda Pound
language : en
Publisher: Routledge
Release Date : 2021-09-30
Teaching Mathematics Creatively written by Linda Pound and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-30 with Education categories.
This revised and updated third edition offers a range of strategies, activities and ideas to bring mathematics to life in the primary classroom. Taking an innovative and playful approach to maths teaching, this book promotes creativity as a key element of practice and offers ideas to help your students develop knowledge, understanding and enjoyment of the subject. In the creative classroom, mathematics becomes a tool to build confidence, develop problem solving skills and motivate children. The fresh approaches explored in this book include a range of activities such as storytelling, music and construction, elevating maths learning beyond subject knowledge itself to enable students to see mathematics in a new way. Key chapters of this book explore: • Learning maths outdoors - make more noise, make more mess or work on a larger scale • Everyday maths - making sense of the numbers, patterns, shapes and measures children see around them • Music and maths – the role of rhythm in learning, and music and pattern in maths Stimulating, accessible and underpinned by the latest research and theory, this is essential reading for trainee and practising teachers who wish to embed creative approaches to maths teaching in their classroom.
Logos And Alogon
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Author : Arkady Plotnitsky
language : en
Publisher: Springer Nature
Release Date : 2023-01-16
Logos And Alogon written by Arkady Plotnitsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-16 with Mathematics categories.
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.
Geometry In History
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Author : S. G. Dani
language : en
Publisher: Springer Nature
Release Date : 2019-10-18
Geometry In History written by S. G. Dani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-18 with Mathematics categories.
This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.