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Innovation in Music: Technology and Creativity
Innovation in Music: Technology and Creativity is a groundbreaking collection bringing together contributions from instructors, researchers, and professionals.Split into two sections, covering composition and performance, and technology and innovation, this volume offers truly international perspectives on ever-evolving practices. Including chapters on audience interaction, dynamic music methods, AI, and live electronic performances, this is recommended reading for professionals, students, and researchers looking for global insights into the fields of music production, music business, and music technology.
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Mathematics and Computation : A Theory Revolutionizing Technology and Science
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophyMathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation.With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges.He explains the ideas and motivations leading to key models, notions, and results.In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences.Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics.He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society.For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields.Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyondHigh-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific disciplineHistorical accounts of the evolution and motivations of central concepts and modelsA broad view of the theory of computation's influence on science, technology, and societyExtensive bibliography
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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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How does integration work in mathematics?
Integration in mathematics is a process of finding the integral of a function. It involves finding the area under a curve or the accumulation of quantities over a given interval. Integration is the reverse process of differentiation, and it helps in solving problems related to finding areas, volumes, and other physical quantities. By using integration, we can calculate the total change or total amount of a quantity over a given range.
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What are integration rules in mathematics?
Integration rules in mathematics are a set of formulas and techniques used to find the integral of a function. These rules include the power rule, which states that the integral of x^n is (1/(n+1))x^(n+1), and the constant multiple rule, which allows constants to be factored out of the integral. Other important integration rules include the sum and difference rules, the substitution rule, and the integration by parts rule. These rules are essential for solving definite and indefinite integrals and are fundamental in calculus.
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How does partial integration work in mathematics?
Partial integration, also known as integration by parts, is a technique used in calculus to evaluate the integral of a product of two functions. It is based on the product rule for differentiation and involves choosing one function to differentiate and the other to integrate. By applying the formula for partial integration, the original integral can be transformed into a simpler form that is easier to evaluate. This technique is particularly useful for integrating functions that are the product of two different types of functions, such as polynomials and exponentials.
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How do differentiation and integration work in mathematics?
Differentiation and integration are two fundamental operations in calculus. Differentiation involves finding the rate of change of a function at a specific point, or the slope of the tangent line to the function's graph at that point. Integration, on the other hand, involves finding the accumulation of a quantity over a given interval, or the area under the curve of a function. In essence, differentiation and integration are inverse operations of each other, with differentiation finding the rate of change and integration finding the accumulation. Together, they form the basis of calculus and are used to solve a wide range of mathematical problems in various fields.
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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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What is a question regarding integration in mathematics?
One question regarding integration in mathematics could be: "How can we use integration to find the area under a curve or the total accumulated quantity of a changing quantity over a given interval?" This question relates to the fundamental concept of integration, which involves finding the accumulation of quantities over a continuous range and is a key tool in calculus for solving problems related to area, volume, and other physical quantities.
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What is the relationship between differentiation and integration in mathematics?
Differentiation and integration are two fundamental operations in calculus that are closely related. Differentiation is the process of finding the rate at which a function is changing at a given point, while integration is the process of finding the accumulation of a function over a given interval. The relationship between the two operations is described by the Fundamental Theorem of Calculus, which states that differentiation and integration are inverse operations of each other. In other words, differentiation "undoes" integration, and integration "undoes" differentiation.
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Can you give an introduction to the mathematics of integration?
Integration is a fundamental concept in calculus that involves finding the accumulation of quantities over a continuous interval. It is the reverse process of differentiation and is used to find the area under a curve, the volume of a solid, and the average value of a function, among other applications. The process of integration involves finding an antiderivative of a function, which is a function whose derivative is the original function. The definite integral represents the accumulation of the function over a specific interval, while the indefinite integral represents the family of antiderivatives of the function. Integration is a powerful tool in mathematics and is used in various fields such as physics, engineering, and economics.
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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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