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Author: P Kent Publisher: World Scientific ISBN: 1911298089 Category : Mathematics Languages : en Pages : 344
Book Description
All students need to master a variety of mathematical tools and concepts at the start of their university career. This distinctive book helps students learn these by doing. The approach is interactive, using experiments, performed in the symbolic algebra package Mathematica, to impart the fundamentals of many of the topics students encounter. A clear exposition of the topic accompanies every experiment.The modular style of the book allows students to study each topic independently. The sheer power of computer algebra software lets students develop and test their own conjectures, obtaining quick and instructive results. The software modules accompanying this course includes many custom functions designed to facilitate learning and testing process.Students who have some familiarity with the material will find their understanding refreshed and deepened through this approach. The exposure to modern computer algebra software will also benefit students in their subsequent studies, research, and professional careers.This classroom-tested book covers Calculus; Complex Numbers; Vectors and Matrices; Functions and Graphs; Trigonometry; and Series. It should therefore also be of use to many secondary school and high school students.Requires: Mathematica 2.2 or later (to be purchased separately); notebook interface. Software modules for this book are available with the hardback edition and via the Internet, or directly from the authors. For further details of the book, including licensing information for certain UK higher education institutions, visit the book's WWW site at metric.ma.ic.ac.uk/
Author: P Kent Publisher: World Scientific ISBN: 1911298089 Category : Mathematics Languages : en Pages : 344
Book Description
All students need to master a variety of mathematical tools and concepts at the start of their university career. This distinctive book helps students learn these by doing. The approach is interactive, using experiments, performed in the symbolic algebra package Mathematica, to impart the fundamentals of many of the topics students encounter. A clear exposition of the topic accompanies every experiment.The modular style of the book allows students to study each topic independently. The sheer power of computer algebra software lets students develop and test their own conjectures, obtaining quick and instructive results. The software modules accompanying this course includes many custom functions designed to facilitate learning and testing process.Students who have some familiarity with the material will find their understanding refreshed and deepened through this approach. The exposure to modern computer algebra software will also benefit students in their subsequent studies, research, and professional careers.This classroom-tested book covers Calculus; Complex Numbers; Vectors and Matrices; Functions and Graphs; Trigonometry; and Series. It should therefore also be of use to many secondary school and high school students.Requires: Mathematica 2.2 or later (to be purchased separately); notebook interface. Software modules for this book are available with the hardback edition and via the Internet, or directly from the authors. For further details of the book, including licensing information for certain UK higher education institutions, visit the book's WWW site at metric.ma.ic.ac.uk/
Author: Sergei Abramovich Publisher: Springer Science & Business Media ISBN: 9401786224 Category : Education Languages : en Pages : 333
Book Description
This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, the book addresses a call for the preparation of teachers capable of utilizing modern technology tools for the modeling-based teaching of mathematics with a focus on methods conducive to the improvement of the whole STEM education at the secondary level. By the same token, using the book’s pedagogy and its mathematical content in a pre-college classroom can assist teachers in introducing students to the ideas that develop the foundation of engineering profession.
Author: Mount Holyoke College Publisher: Springer Science & Business Media ISBN: 9780387949222 Category : Mathematics Languages : en Pages : 308
Book Description
The text is composed of a set of sixteen laboratory investigations which allow the student to explore rich and diverse ideas and concepts in mathematics. The approach is hands-on, experimental, an approach that is very much in the spirit of modern pedagogy. The course is typically offered in one semester, at the sophomore (second year) level of college. It requires completion of one year of calculus. The course provides a transition to the study of higher, abstract mathematics. The text is written independent of any software. Supplements will be available on the projects' web site.
Author: Roozbeh Hazrat Publisher: Springer ISBN: 3319275852 Category : Computers Languages : en Pages : 337
Book Description
This textbook introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked-out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool. This new edition has been extensively revised and updated, and includes new chapters with problems and worked examples.
Author: Curtis C. McKnight Publisher: American Mathematical Soc. ISBN: 0821820168 Category : Education Languages : en Pages : 120
Book Description
Mathematics education research in undergraduate mathematics has increased significantly in the last decade and shows no signs of abating in the near future. Thus far, this research has often been associated with innovations in curriculum such as calculus reform, statistics education, and the use of computational and graphing technology in instruction. Mathematics education research, carefully conducted, is something far more fundamental and widely useful than might be implied by its use by the advocates of innovation in undergraduate mathematics education. Most simply, mathematics education research is inquiry by carefully developed research methods aimed at providing evidence about the nature and relationships of many mathematics learning and teaching phenomena. It seeks to clarify the phenomena, illuminate them, explain how they are related to other phenomena, and explain how this may be related to undergraduate mathematics course organization and teaching. This book-the collaborative effort of a research mathematician, mathematics education researchers who work in a research mathematics department and a professional librarian-introduces research mathematicians to education research. The work presents a non-jargon introduction for educational research, surveys the more commonly used research methods, along with their rationales and assumptions, and provides background and careful discussions to help research mathematicians read or listen to education research more critically. This guide is of practical interest to university-based research mathematicians, as it introduces the methodology of quantitative and qualitative research in education; provides critical guidelines for assessing the reliability and validity of mathematics education research; and explains how to use online database resources to locate education research. The book will also be valuable to graduate students in mathematics who are planning academic careers, and to mathematics department chairs and their deans.
Author: V. I. Arnold Publisher: American Mathematical Soc. ISBN: 0821894161 Category : Mathematics Languages : en Pages : 170
Book Description
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Author: Celia Hoyles Publisher: Routledge ISBN: 1135701075 Category : Education Languages : en Pages : 273
Book Description
At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.
Author: Jochen Voss Publisher: John Wiley & Sons ISBN: 1118728025 Category : Mathematics Languages : en Pages : 322
Book Description
A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course.
Author: P Kent
Author: P Kent
Author: Phillip Kent
Author: Sergei Abramovich
Author: Mount Holyoke College
Author: 
Author: Roozbeh Hazrat
Author: Curtis C. McKnight
Author: V. I. Arnold 
Author: Celia Hoyles
Author: Jochen Voss