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Mathematical Circles : (Russian Experience)
'This is a sample of rich Russian mathematical culture written by professional mathematicians with great experience in working with high school students...Problems are on very simple levels, but building to more complex and advanced work...contains solutions to almost all problems; methodological notes for the teacher...developed for a peculiarly Russian institution (the mathematical circle), but easily adapted to American teachers' needs, both inside and outside the classroom' - from the Translator's notes.What kind of book is this?It is a book produced by a remarkable cultural circumstance in the former Soviet Union which fostered the creation of groups of students, teachers, and mathematicians called 'mathematical circles'.The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.This book is intended for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum.It is also a book of mathematical recreations and, at the same time, a book containing vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.The book is based on a unique experience gained by several generations of Russian educators and scholars.
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Mathematical Aspects of Deep Learning
In recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis.The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics.This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field.It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.
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Mathematical Engineering of Deep Learning
Mathematical Engineering of Deep Learning provides a complete and concise overview of deep learning using the language of mathematics.The book provides a self-contained background on machine learning and optimization algorithms and progresses through the key ideas of deep learning.These ideas and architectures include deep neural networks, convolutional models, recurrent models, long/short-term memory, the attention mechanism, transformers, variational auto-encoders, diffusion models, generative adversarial networks, reinforcement learning, and graph neural networks.Concepts are presented using simple mathematical equations together with a concise description of relevant tricks of the trade.The content is the foundation for state-of-the-art artificial intelligence applications, involving images, sound, large language models, and other domains.The focus is on the basic mathematical description of algorithms and methods and does not require computer programming.The presentation is also agnostic to neuroscientific relationships, historical perspectives, and theoretical research.The benefit of such a concise approach is that a mathematically equipped reader can quickly grasp the essence of deep learning. Key Features:A perfect summary of deep learning not tied to any computer language, or computational framework. An ideal handbook of deep learning for readers that feel comfortable with mathematical notation. An up-to-date description of the most influential deep learning ideas that have made an impact on vision, sound, natural language understanding, and scientific domains. The exposition is not tied to the historical development of the field or to neuroscience, allowing the reader to quickly grasp the essentials. Deep learning is easily described through the language of mathematics at a level accessible to many professionals.Readers from fields such as engineering, statistics, physics, pure mathematics, econometrics, operations research, quantitative management, quantitative biology, applied machine learning, or applied deep learning will quickly gain insights into the key mathematical engineering components of the field.
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Advanced Mathematical Thinking : A Special Issue of Mathematical Thinking and Learning
This is Volume 7, Issue 1 2005, a Special Issue of 'Mathematical Thinking and Learning' which looks at Advanced Mathematical Thinking. Opening with a brief history of attempts to characterize advanced mathematical thinking, beginning with the deliberations of the Advanced Mathematical Thinking Working Group of the International Group for the Psychology of Mathematics Education.The articles follow the recurring themes: (a) the distinction between identifying kinds of thinking that might be regarded as advanced at any grade level and taking as advanced any thinking about mathematical topics considered advanced; (b) the utility of characterizing such thinking for integrating the entire curriculum; (c) general tests, or criteria, for identifying advanced mathematical thinking; and (d) an emphasis on advancing mathematical practices.
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Kant's Mathematical World : Mathematics, Cognition, and Experience
Kant's Mathematical World aims to transform our understanding of Kant's philosophy of mathematics and his account of the mathematical character of the world.Daniel Sutherland reconstructs Kant's project of explaining both mathematical cognition and our cognition of the world in terms of our most basic cognitive capacities.He situates Kant in a long mathematical tradition with roots in Euclid's Elements, and thereby recovers the very different way of thinking about mathematics which existed prior to its 'arithmetization' in the nineteenth century.He shows that Kant thought of mathematics as a science of magnitudes and their measurement, and all objects of experience as extensive magnitudes whose real properties have intensive magnitudes, thus tying mathematics directly to the world.His book will appeal to anyone interested in Kant's critical philosophy -- either his account of the world of experience, or his philosophy of mathematics, or how the two inform each other.
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Deep Learning Architectures : A Mathematical Approach
This book describes how neural networks operate from the mathematical point of view.As a result, neural networks can be interpreted both as function universal approximators and information processors.The book bridges the gap between ideas and concepts of neural networks, which are used nowadays at an intuitive level, and the precise modern mathematical language, presenting the best practices of the former and enjoying the robustness and elegance of the latter. This book can be used in a graduate course in deep learning, with the first few parts being accessible to senior undergraduates. In addition, the book will be of wide interest to machine learning researchers who are interested in a theoretical understanding of the subject.
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Cryptographic Primitives in Blockchain Technology : A mathematical introduction
Many online applications, especially in the financial industries, are running on blockchain technologies in a decentralized manner, without the use of an authoritative entity or a trusted third party.Such systems are only secured by cryptographic protocols and a consensus mechanism.As blockchain-based solutions will continue to revolutionize online applications in a growing digital market in the future, one needs to identify the principal opportunities and potential risks.Hence, it is unavoidable to learn the mathematical and cryptographic procedures behind blockchain technology in order to understand how such systems work and where the weak points are. Cryptographic Primitives in Blockchain Technology provides an introduction to the mathematical and cryptographic concepts behind blockchain technologies and shows how they are applied in blockchain-based systems.This includes an introduction to the general blockchain technology approaches that are used to build the so-called immutable ledgers, which are based on cryptographic signature schemes. As future quantum computers will break some of the current cryptographic primitive approaches, Andreas Bolfing considers their security and presents the current research results that estimate the impact on blockchain-based systems if some of the cryptographic primitive break.Based on the example of Bitcoin, he shows that weak cryptographic primitives pose a possible danger for the ledger, which can be overcome through the use of the so-called post-quantum cryptographic approaches.
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Mathematical Tasks : The Bridge Between Teaching and Learning
If we want our pupils to develop fluency, understanding and the ability to solve complex problems, then it is vital that teachers develop the ability to select, adapt and design appropriate mathematical tasks. In 'Mathematical Tasks: The Bridge Between Teaching and Learning', Chris McGrane explores a range of practical approaches, strategies and principles behind the design and effective use of tasks in the mathematics classroom that lead to all pupils becoming successful learners. First-hand interviews with world class mathematics education experts and practicing teachers bring to life the ideas behind how tasks can act as a bridge between what the teacher wants the pupil to make sense of and what the pupil actually does makes sense of; tasks are how we enable pupils to enact mathematics - it is only by being mathematical that pupils can truly make connections across mathematical ideas and understand the bigger picture.This is a book for classroom teachers. Chris McGrane offers a range of practical examples for nurturing deep learning in mathematics that can be adapted and embedded in one's own classroom practice. This is also a book for those who are interested in the theory behind tasks. Chris and his interviewees examine the key role tasks play in shaping learning, teaching, curriculum and assessment. Suitable for teachers at all stages in their careers and teachers are encouraged to return to the book from time to time over the years to notice how their use of tasks in the classroom changes as they themselves develop.
Price: 17.00 £ | Shipping*: 3.99 £
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