Products related to Mathematics:
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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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Thinking about Mathematics : The Philosophy of Mathematics
This unique text by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections.The first describes questions and issues about mathematics that have motivated philosophers almost since the beginning of intellectual history.Part II is an historical survey, discussing the role of mathematics in such thinkers as Plato, Aristotle, Kant, and Mill.The third section covers the three major positions, and battle lines, throughout the twentieth century: that mathematics is logic (logicism), that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism).Finally, Part IV looks at contemporary positions and work which brings the reader up-to-date on the discipline.Thinking about Mathematics is accessible to those with little background in either mathematics or philosophy.It is aimed at students and professionals in mathematics who have little contact with academic philosophy and at philosophy students and other philosophers who forgot much of their mathematics.
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Theoretical Neuroscience : Understanding Cognition
This textbook is an introduction to Systems and Theoretical/Computational Neuroscience, with a particular emphasis on cognition.It consists of three parts: Part I covers fundamental concepts and mathematical models in computational neuroscience, along with cutting-edge topics.Part II explores the building blocks of cognition, including working memory (how the brain maintains and manipulates information "online" without external input), decision making (how choices are made among multiple options under conditions of uncertainty and risk) and behavioral flexibility (how we direct attention and control actions).Part III is dedicated to frontier research, covering models of large-scale multi-regional brain systems, Computational Psychiatry and the interface with Artificial Intelligence.The author highlights the perspective of neural circuits as dynamical systems, and emphasizes a cross-level mechanistic understanding of the brain and mind, from genes and cell types to collective neural populations and behavior.Overall, this textbook provides an opportunity for readers to become well versed in this highly interdisciplinary field of the twenty-first century. Key FeaturesRooted in the most recent advances in experimental studies of basic cognitive functionsIntroduces neurobiological and mathematical concepts so that the book is self-containedHeavily illustrated with high-quality figures that help to illuminate neurobiological concepts, present experimental findings and explain mathematical modelsConcludes with a list of core cognitive behavior tasks, ten take-home messages and three open questions for future researchComputer model codes are available via GitHub for hands-on practice
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Theoretical Neuroscience : Understanding Cognition
This textbook is an introduction to Systems and Theoretical/Computational Neuroscience, with a particular emphasis on cognition.It consists of three parts: Part I covers fundamental concepts and mathematical models in computational neuroscience, along with cutting-edge topics.Part II explores the building blocks of cognition, including working memory (how the brain maintains and manipulates information "online" without external input), decision making (how choices are made among multiple options under conditions of uncertainty and risk) and behavioral flexibility (how we direct attention and control actions).Part III is dedicated to frontier research, covering models of large-scale multi-regional brain systems, Computational Psychiatry and the interface with Artificial Intelligence.The author highlights the perspective of neural circuits as dynamical systems, and emphasizes a cross-level mechanistic understanding of the brain and mind, from genes and cell types to collective neural populations and behavior.Overall, this textbook provides an opportunity for readers to become well versed in this highly interdisciplinary field of the twenty-first century. Key FeaturesRooted in the most recent advances in experimental studies of basic cognitive functionsIntroduces neurobiological and mathematical concepts so that the book is self-containedHeavily illustrated with high-quality figures that help to illuminate neurobiological concepts, present experimental findings and explain mathematical modelsConcludes with a list of core cognitive behavior tasks, ten take-home messages and three open questions for future researchComputer model codes are available via GitHub for hands-on practice
Price: 210.00 £ | Shipping*: 0.00 £
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How can one connect events in mathematics?
Events in mathematics can be connected through logical reasoning and the application of mathematical principles. By identifying patterns, relationships, and dependencies between different mathematical events, one can establish connections and draw conclusions. Additionally, the use of mathematical models and representations can help to visualize and understand the connections between events in mathematics. Furthermore, the use of mathematical notation and language can help to express the relationships and connections between different mathematical events.
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Business mathematics or pure mathematics?
It ultimately depends on your career goals and interests. Business mathematics focuses on practical applications in business and finance, such as accounting, economics, and statistics. Pure mathematics, on the other hand, delves into theoretical concepts and abstract reasoning, with applications in fields like physics, engineering, and computer science. If you are interested in pursuing a career in business or finance, business mathematics may be more relevant. However, if you are passionate about theoretical concepts and problem-solving, pure mathematics may be a better fit for you.
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What type of mathematics is meant: commercial mathematics or technical mathematics?
The type of mathematics meant in this context is commercial mathematics. Commercial mathematics focuses on practical applications of mathematics in business and finance, such as calculating interest, profit and loss, and managing budgets. It is used in everyday business transactions and financial decision-making. Technical mathematics, on the other hand, is more focused on the theoretical and abstract aspects of mathematics, often used in fields such as engineering, physics, and computer science.
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Economic mathematics, business informatics, or teaching mathematics?
The choice between economic mathematics, business informatics, or teaching mathematics ultimately depends on your interests and career goals. Economic mathematics combines mathematical techniques with economic theory to analyze and solve complex economic problems. Business informatics focuses on using information technology to improve business processes and decision-making. Teaching mathematics involves educating others on mathematical concepts and skills. Consider your strengths, interests, and long-term career aspirations to make an informed decision on which path to pursue.
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Combinatorial Mathematics
This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics.The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments.Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science.Optional more advanced material also makes it valuable as a research reference.Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material.It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty.Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language.The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.
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Discrete Mathematics
Biggs' Discrete Mathematics has been a best-selling textbook since the first and revised editions were published in 1986 and 1990, respectively.This second edition has been developed in response to undergraduate course changes and changes in students' needs.New to this edition are chapters on statements and proof, logical framework, and natural numbers and the integers, in addition to updated chapters from the previous edition.The new chapters are presented at a level suitable for mathematics and computer science students seeking a first approach to this broad and highly relevant topic.Each chapter contains newly developed tailored exercises, and miscellaneous exercises are presented throughout, providing the student with over 1000 individual tailored exercises.This edition is accompanied by a website www.oup.com/mathematics/discretemath containing hints and solutions to all exercises presented in the text, providing an invaluable resource for students and lecturers alike.The book is carefully structured, coherent and comprehensive, and is the ideal text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory, coding theory and abstract algebra.
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Engineering Mathematics
Engineering Mathematics is the unparalleled undergraduate textbook for students of electrical, electronic, communications and systems engineering. Tried and tested over many years, this widely used textbook is now in its 5th edition, having been fully updated and revised. This new edition includes an even greater emphasis on the application of mathematics within a range of engineering contexts. It features detailed explanation of why a technique is important to engineers. In addition, it provides essential guidance in how to use mathematics to solve engineering problems.This approach ensures a deep and practical understanding of the role of mathematics in modern engineering.
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Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics : Perspectives from Cognitive Neuroscience
Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics provides an essential bridge between scientific research and practical interventions with children.It unpacks what we know about the possible cognitive causation of mathematical difficulties in order to improve teaching and therefore learning.Each chapter considers a specific domain of children’s numerical development: counting and the understanding of numbers, understanding of the base-10 system, arithmetic, word problem solving, and understanding rational numbers.The accessible guidance includes a literature review on each topic, surveying how each process develops in children, the difficulties encountered at that level by some pupils, and the intervention studies that have been published.It guides the reader step-by-step through practical guidelines of how to assess these processes and how to build an intervention to help children master them.Illustrated throughout with examples of materials used in the effective interventions described, this essential guide offers deep understanding and effective strategies for developmental and educational psychologists, special educational needs and/or disabilities coordinators, and teachers working with children experiencing mathematical difficulties.
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Why mathematics?
Mathematics is a fundamental tool for understanding the world around us. It provides a framework for solving problems, making predictions, and analyzing data. Additionally, mathematics is essential for many fields such as science, engineering, economics, and computer science. It also helps develop critical thinking and problem-solving skills that are valuable in everyday life. Overall, mathematics is important because it helps us make sense of the world and empowers us to make informed decisions.
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Is the mathematics in a mathematics degree the most difficult mathematics there is?
The mathematics in a mathematics degree is certainly challenging, but it may not necessarily be the most difficult mathematics there is. The difficulty of mathematics can vary depending on the specific area of study, the individual's aptitude and background, and the level of abstraction and complexity involved. Advanced topics in pure mathematics, theoretical physics, and certain areas of applied mathematics can be extremely challenging and may surpass the difficulty level of undergraduate mathematics courses. Additionally, the difficulty of mathematics is subjective and can vary from person to person.
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Should I study business mathematics or pure mathematics?
The decision to study business mathematics or pure mathematics depends on your career goals and interests. If you are interested in pursuing a career in business, finance, economics, or any field that requires practical applications of mathematics, then studying business mathematics would be more beneficial. On the other hand, if you have a passion for theoretical mathematics and are interested in pursuing a career in academia, research, or pure mathematics, then studying pure mathematics would be the better choice. Consider your long-term goals and interests to make an informed decision.
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How does studying mathematics differ from mathematics in school?
Studying mathematics goes beyond the curriculum taught in school. It involves delving deeper into the theoretical and practical aspects of the subject, exploring advanced topics, and applying mathematical concepts to real-world problems. In school, the focus is often on learning specific formulas and solving standard problems, whereas studying mathematics involves critical thinking, problem-solving, and a deeper understanding of the underlying principles. Additionally, studying mathematics allows for more flexibility and the opportunity to pursue specialized areas of interest within the field.
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