Mathematics As A Tool
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Mathematics As A Tool
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Author : Johannes Lenhard
language : en
Publisher: Springer
Release Date : 2017-04-04
Mathematics As A Tool written by Johannes Lenhard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-04 with Science categories.
This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge. The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.
Tools And Mathematics
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Author : John Monaghan
language : en
Publisher: Springer
Release Date : 2016-04-18
Tools And Mathematics written by John Monaghan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Education categories.
This book is an exploration of tools and mathematics and issues in mathematics education related to tool use. The book has five parts. The first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The fourth part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future: task and tool design and new forms of activity via connectivity and computer games.
Symbolizing Modeling And Tool Use In Mathematics Education
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Author : K.P Gravemeijer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Symbolizing Modeling And Tool Use In Mathematics Education written by K.P Gravemeijer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Education categories.
The almost universal rejection of the notion of symbols as `carriers of meaning' has created the need to find an alternative for the use of models as embodiments of mathematical concepts. By taking its point of departure as a concern for the way students actually use tools and symbols, and for what these signify for them, this book explores the option of building on symbolizing, modelling and tool use as personally meaningful activities of students. This theme is approached from different angles and different perspectives. One dimension is that of setting, varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction. Another dimension is the theoretical framework of the researcher, varying from constructivism, to activity theory, cognitive-psychology and instructional-design theory. This book will appeal to a wide audience, varying from researchers, instructional designers, educators, and graduate students.
Mathematical Modelling
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Author : D. N. P. Murthy
language : en
Publisher: Pergamon
Release Date : 1990
Mathematical Modelling written by D. N. P. Murthy and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematical models categories.
Mathematical Concepts
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Author : Jürgen Jost
language : en
Publisher: Springer
Release Date : 2015-09-10
Mathematical Concepts written by Jürgen Jost and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-10 with Mathematics categories.
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning.
Tools Of The Trade
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Tools Of The Trade written by Paul J. Sally (Jr.) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics." "Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as self-study projects for students, or for Inquiry Based Learning activities presented by the students."--BOOK JACKET.
Mathematics A Simple Tool For Geologists
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Author : D. Waltham
language : en
Publisher: Routledge
Release Date : 2013-08-21
Mathematics A Simple Tool For Geologists written by D. Waltham and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-21 with Science categories.
Uses geological examples to illustrate mathematical ideas. Contains a large number of worked examples, and problems for students to attempt themselves. Answers to all the questions are given at the end of the book.
Mathematics And Tools For Financial Engineering
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Author : Petros A. Ioannou
language : en
Publisher: SIAM
Release Date : 2021-09-07
Mathematics And Tools For Financial Engineering written by Petros A. Ioannou and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.
This book presents an overview of fundamental concepts in mathematics and how they are applied to basic financial engineering problems, with the goal of teaching students to use mathematics and engineering tools to understand and solve financial problems. Part I covers mathematical preliminaries (set theory, linear algebra, sequences and series, real functions and analysis, numerical approximations and computations, basic optimization theory, and stochastic processes), and Part II addresses financial topics ranging from low- to high-risk investments (interest rates and value of money, bonds, dynamic asset modeling, portfolio theory and optimization, option pricing, and the concept of hedging). Based on lectures for a master’s program in financial engineering given by the author over 12 years at the University of Southern California, Mathematics and Tools for Financial Engineering contains numerous examples and problems, establishes a strong general mathematics background and engineering modeling techniques in a pedagogical fashion, and covers numerical techniques with applications to solving financial problems using different software tools. This textbook is intended for graduate and advanced undergraduate students in finance or financial engineering and is useful to readers with no prior knowledge in finance who want to understand some basic mathematical tools and theories associated with financial engineering. It is also appropriate as an overview of many mathematical concepts and engineering tools relevant to courses on numerical analysis, modeling and data science, numerical optimization, and approximation theory.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Mathematics As A Tool
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Author : Johannes Lenhard
language : en
Publisher: Springer
Release Date : 2017-04-10
Mathematics As A Tool written by Johannes Lenhard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Science categories.
This book puts forward a new role for mathematics in the natural sciences. In the traditional understanding, a strong viewpoint is advocated, on the one hand, according to which mathematics is used for truthfully expressing laws of nature and thus for rendering the rational structure of the world. In a weaker understanding, many deny that these fundamental laws are of an essentially mathematical character, and suggest that mathematics is merely a convenient tool for systematizing observational knowledge. The position developed in this volume combines features of both the strong and the weak viewpoint. In accordance with the former, mathematics is assigned an active and even shaping role in the sciences, but at the same time, employing mathematics as a tool is taken to be independent from the possible mathematical structure of the objects under consideration. Hence the tool perspective is contextual rather than ontological. Furthermore, tool-use has to respect conditions like suitability, efficacy, optimality, and others. There is a spectrum of means that will normally differ in how well they serve particular purposes. The tool perspective underlines the inevitably provisional validity of mathematics: any tool can be adjusted, improved, or lose its adequacy upon changing practical conditions.