Products related to Mathematical:
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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 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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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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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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How do you calculate mathematical tasks in manufacturing technology?
In manufacturing technology, mathematical tasks are often calculated using various formulas and equations. These calculations can involve determining dimensions, tolerances, material properties, and other parameters necessary for designing and producing parts and products. Additionally, mathematical tasks in manufacturing technology may also involve using geometric and trigonometric principles to solve problems related to machining, tooling, and assembly. Computer-aided design (CAD) and computer-aided manufacturing (CAM) software are often used to perform these calculations and ensure accurate and efficient production processes.
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What are mathematical prisms?
Mathematical prisms are three-dimensional shapes that have two parallel and congruent polygonal bases connected by rectangular faces. The bases can be any polygon, such as a triangle, square, or pentagon. The height of the prism is the perpendicular distance between the two bases. The volume of a prism is calculated by multiplying the area of the base by the height.
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What are mathematical terms?
Mathematical terms are words or phrases used to describe mathematical concepts, operations, or relationships. They are used to communicate specific ideas or instructions in the language of mathematics. Examples of mathematical terms include "addition," "subtraction," "equation," "variable," "function," and "theorem." Understanding mathematical terms is essential for effectively solving mathematical problems and communicating mathematical ideas.
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What are mathematical formulas?
Mathematical formulas are concise and specific representations of mathematical relationships or rules. They are used to express mathematical concepts, calculations, and relationships between variables in a clear and systematic way. Formulas often consist of symbols, numbers, and mathematical operations, and are used to solve equations, make predictions, and perform calculations in various fields of mathematics and science. They provide a standardized and efficient way to communicate mathematical concepts and principles.
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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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Mathematical Analysis of Machine Learning Algorithms
The mathematical theory of machine learning not only explains the current algorithms but can also motivate principled approaches for the future.This self-contained textbook introduces students and researchers of AI to the main mathematical techniques used to analyze machine learning algorithms, with motivations and applications.Topics covered include the analysis of supervised learning algorithms in the iid setting, the analysis of neural networks (e.g. neural tangent kernel and mean-field analysis), and the analysis of machine learning algorithms in the sequential decision setting (e.g. online learning, bandit problems, and reinforcement learning).Students will learn the basic mathematical tools used in the theoretical analysis of these machine learning problems and how to apply them to the analysis of various concrete algorithms.This textbook is perfect for readers who have some background knowledge of basic machine learning methods, but want to gain sufficient technical knowledge to understand research papers in theoretical machine learning.
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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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Are mathematical functions bounded?
Mathematical functions can be bounded or unbounded, depending on their behavior. A function is said to be bounded if its output values are limited within a certain range. For example, the sine function is bounded between -1 and 1. However, functions like the natural logarithm or the quadratic function are unbounded, as their output values can grow without limit. Therefore, whether a mathematical function is bounded or not depends on its specific properties and behavior.
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What are mathematical functions?
Mathematical functions are relationships between a set of inputs and a set of outputs, where each input is related to exactly one output. They are typically represented by an equation or a rule that describes how the input values are transformed into output values. Functions are fundamental in mathematics and are used to model various real-world phenomena, analyze data, and solve problems in a systematic way. They can take many forms, such as linear, quadratic, exponential, trigonometric, and logarithmic functions.
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What is mathematical optimization?
Mathematical optimization is the process of finding the best solution to a problem from a set of possible solutions. It involves maximizing or minimizing a certain objective function while satisfying a set of constraints. This can be applied to a wide range of fields, including engineering, economics, and computer science, to help make better decisions and improve efficiency. Optimization problems can be solved using various mathematical techniques such as linear programming, nonlinear programming, and integer programming.
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What are mathematical equations?
Mathematical equations are expressions that show the relationship between two or more quantities using mathematical symbols and operations. They typically consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent and solve various mathematical problems and are an essential tool in fields such as physics, engineering, and economics. They can be simple or complex, and their solutions provide valuable information about the relationships between different quantities.
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