Products related to Mathematics:
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Teaching Mathematics Using Interactive Mapping
Teaching Mathematics Using Interactive Mapping offers novel ways to learn basic math topics such as simple relational measures or measuring hierarchies through customized interactive mapping activities.These activities focus on interactive web-based Geographic Information System (GIS) and are relevant to today’s problems and challenges.Written in a guided, hands-on, understandable manner, all activities are designed to build practical and problem-solving skills that rest on mathematical principles and move students from thinking about maps as references that focus solely on "where is" something, to analytical tools, focusing primarily on the "whys of where." Success with this transition through interaction permits most readers to master mathematical concepts and GIS tools. FEATURESOffers custom-designed geographical activities to fit with specific mathematical topicsHelps students become comfortable using mathematics in a variety of professionsProvides an innovative, engaging, and practical set of activities to ease readers through typically difficult, often elementary, mathematical topics: fractions, the distributive law, and much moreUses web-based GIS maps, apps, and other tools and data that can be accessed on any device, anywhere, at any time, requiring no prior GIS backgroundWritten by experienced teachers and researchers with lifelong experience in teaching mathematics, geography, and spatial analysisFeatures an accompanying Solution Guide, available on the book's product page, that is beneficial for instructors, students, and other readers as an aid to gauging progress. This textbook applies to undergraduate and graduate students in universities and community colleges including those in basic mathematics courses, as well as upper-level undergraduate and graduate students taking courses in geographic information systems, remote sensing, photogrammetry, geography, geodesy, information science, engineering, and geology.Professionals interested in learning techniques and technologies for collecting, analyzing, managing, processing, and visualizing geospatial datasets will also benefit from this book as they refresh their knowledge in mathematics.
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Concept Mapping as an Assessment Tool for Conceptual Understanding in Mathematics
This book investigates the practicability and effectiveness of the concept map as a tool for assessing students’ conceptual understanding in mathematics. The author first introduces concept mapping and then employs it to investigate students’ conceptual understanding of four different mathematical topics.Alongside traditional scoring methods, she adopts Social Network Analysis, a new technique, to interpret student-constructed concept maps, which reveals fresh insights into the graphic features of the concept map and into how students connect mathematical concepts.By comparing two traditional school tests with the concept map, she examines its concurrent validity and discusses its strengths and drawbacks from the viewpoint of assessing conceptual understanding.With self-designed questionnaires, interviews, and open-ended writing tasks, she also investigates students and teachers’ attitudes toward concept mapping and describes the implications these findings may have for concept mapping’s use in school and for further research on the topic. Scholars and postgraduate students of mathematics education and teachers interested in concept mapping or assessing conceptual understanding in classroom settings will find this book an informative, inspiring, and overall valuable addition to their libraries.
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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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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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What is a mapping in mathematics?
In mathematics, a mapping refers to a relation between two sets, where each element in the first set is associated with exactly one element in the second set. This association is often represented by a rule or function that assigns each input value to a unique output value. Mappings are used to describe how elements from one set are transformed or related to elements in another set, and they are fundamental to many areas of mathematics, including algebra, calculus, and geometry. In essence, a mapping is a way of describing how elements from one set correspond to elements in another set.
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What is a derivative mapping in mathematics?
In mathematics, a derivative mapping is a function that assigns to each point in the domain of a given function its derivative at that point. It is a way of representing how the function changes at each point in its domain. The derivative mapping is often used to study the rate of change of a function, determine critical points, and analyze the behavior of the function at specific points. It is a fundamental concept in calculus and plays a crucial role in various mathematical applications.
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What is a mapping rule in mathematics?
A mapping rule in mathematics is a set of instructions that defines how elements from one set are paired with elements from another set. It specifies the relationship between the elements of the two sets, often using a formula or a set of conditions. Mapping rules are used to describe functions, transformations, and other mathematical operations that relate one set of values to another. They are essential for understanding the connections between different mathematical concepts and for solving problems in various areas of mathematics.
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What is spatial visualization ability?
Spatial visualization ability refers to the capacity to mentally manipulate and comprehend spatial relationships between objects. Individuals with strong spatial visualization skills can easily visualize and understand how objects relate to each other in space, such as rotating or manipulating shapes in their mind. This ability is crucial in various fields such as engineering, architecture, and mathematics, as it allows individuals to solve complex problems and understand spatial concepts more effectively. Improving spatial visualization ability can enhance problem-solving skills and overall cognitive performance.
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Vedic Mathematics
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Basic Mathematics
This is a text in basic mathematics with multiple uses for either high school or college level courses.Readers will get a firm foundation in basic principles of mathematics which are necessary to know in order to go ahead in calculus, linear algebra or other topics.The subject matter is clearly covered and the author develops concepts so the reader can see how one subject matter can relate and grow into another.
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Construction Mathematics
Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths.Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises.End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in Construction.Additional coverage of the core unit Mathematics in Construction and the Built Environment from BTEC National Construction, Civil Engineering and Building Services courses makes this an essential revision aid for students who do not have Level 2 mathematics experience before commencing their BTEC National studies.This is also the ideal primer for any reader who wishes to refresh their mathematics knowledge before going into a construction HNC or BSc.
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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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Is spatial visualization important for engineers?
Yes, spatial visualization is important for engineers as it allows them to mentally manipulate and understand complex 3D objects and structures. Engineers often need to design and analyze various components and systems, and spatial visualization skills help them to conceptualize and communicate their ideas effectively. Whether it's designing a new product, creating blueprints for a building, or solving complex problems, spatial visualization is a crucial skill that allows engineers to think critically and innovate in their field.
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Why is spatial perception so important for mathematics?
Spatial perception is important for mathematics because it helps individuals visualize and manipulate geometric shapes, understand spatial relationships, and solve problems involving spatial reasoning. This ability is crucial for tasks such as geometry, trigonometry, and calculus, where visualizing shapes and their transformations is essential. Spatial perception also aids in understanding concepts like symmetry, congruence, and similarity, which are foundational in mathematics. Overall, spatial perception enhances one's ability to comprehend and apply mathematical concepts in a more intuitive and efficient manner.
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Can one improve their spatial visualization skills?
Yes, it is possible to improve spatial visualization skills through practice and training. Engaging in activities such as puzzles, building models, and playing spatial reasoning games can help develop these skills. Additionally, practicing mental rotation exercises and regularly challenging oneself with spatial tasks can also contribute to improvement. With consistent effort and dedication, individuals can enhance their spatial visualization abilities over time.
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What are problems with spatial visualization skills?
Some problems with spatial visualization skills include difficulty in understanding and interpreting maps, graphs, and diagrams. Individuals with poor spatial visualization skills may struggle with tasks such as navigating through unfamiliar environments, understanding 3D objects, and mentally rotating objects. This can impact their performance in subjects such as math, science, and engineering, as well as in everyday activities such as driving and assembling furniture. Additionally, poor spatial visualization skills can lead to frustration and decreased confidence in one's abilities.
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