Experiments In Undergraduate Mathematics A Mathematica Based Approach

Author : P Kent,Philip Ramsden,J Wood
Publisher : World Scientific
Page : 344 pages
File Size : 49,9 Mb
Release : 1996-10-08
Category : Mathematics
ISBN : 9781911298083

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Experiments In Undergraduate Mathematics: A Mathematica-based Approach by P Kent,Philip Ramsden,J Wood Pdf

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 : Phillip Kent
Publisher : World Scientific Publishing Company Incorporated
Page : 322 pages
File Size : 53,6 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 1860940285

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Experiments in Undergraduate Mathematics by Phillip Kent Pdf

Author : Celia Hoyles,Candia Morgan,Geoffrey Woodhouse
Publisher : Routledge
Page : 273 pages
File Size : 40,6 Mb
Release : 2002-01-04
Category : Education
ISBN : 9781135701079

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Rethinking the Mathematics Curriculum by Celia Hoyles,Candia Morgan,Geoffrey Woodhouse Pdf

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 : Sergei Abramovich
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 46,7 Mb
Release : 2014-05-08
Category : Education
ISBN : 9789401786225

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Computational Experiment Approach to Advanced Secondary Mathematics Curriculum by Sergei Abramovich Pdf

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 : Curtis C. McKnight
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 50,6 Mb
Release : 2000
Category : Education
ISBN : 9780821820162

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Mathematics Education Research: A Guide for the Research Mathematician by Curtis C. McKnight Pdf

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 : Mount Holyoke College
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 53,9 Mb
Release : 1997-03
Category : Mathematics
ISBN : 0387949224

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Laboratories in Mathematical Experimentation by Mount Holyoke College Pdf

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
Page : 318 pages
File Size : 54,6 Mb
Release : 2016-01-04
Category : Computers
ISBN : 9783319275857

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Mathematica®: A Problem-Centered Approach by Roozbeh Hazrat Pdf

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 : Anonim
Publisher : Unknown
Page : 1026 pages
File Size : 55,9 Mb
Release : 1997
Category : Mathematics
ISBN : CORNELL:31924074884572

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International Mathematical News by Anonim Pdf

Author : Gila Hanna,Laura Macchi,Karin Binder,Laura Martignon,Katharina Loibl
Publisher : Frontiers Media SA
Page : 552 pages
File Size : 48,9 Mb
Release : 2023-09-05
Category : Science
ISBN : 9782832529997

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Psychology and Mathematics Education by Gila Hanna,Laura Macchi,Karin Binder,Laura Martignon,Katharina Loibl Pdf

Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats. Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem. This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).

Author : Arthur James Wells
Publisher : Unknown
Page : 1778 pages
File Size : 44,8 Mb
Release : 1999
Category : Bibliography, National
ISBN : UOM:39015079755818

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The British National Bibliography by Arthur James Wells Pdf

Author : Falai Chen
Publisher : Unknown
Page : 228 pages
File Size : 52,5 Mb
Release : 2003
Category : Electronic books
ISBN : 9812795545

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Mathematics Experiments by Falai Chen Pdf

Author : Pamela E. Harris,Erik Insko,Aaron Wootton
Publisher : Springer Nature
Page : 324 pages
File Size : 48,9 Mb
Release : 2020-04-17
Category : Mathematics
ISBN : 9783030378530

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A Project-Based Guide to Undergraduate Research in Mathematics by Pamela E. Harris,Erik Insko,Aaron Wootton Pdf

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

Author : Rebecca Sanft,Anne Walter
Publisher : Academic Press
Page : 262 pages
File Size : 51,8 Mb
Release : 2020-03-30
Category : Science
ISBN : 9780128195963

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Exploring Mathematical Modeling in Biology Through Case Studies and Experimental Activities by Rebecca Sanft,Anne Walter Pdf

Exploring Mathematical Modeling in Biology through Case Studies and Experimental Activities provides supporting materials for courses taken by students majoring in mathematics, computer science or in the life sciences. The book's cases and lab exercises focus on hypothesis testing and model development in the context of real data. The supporting mathematical, coding and biological background permit readers to explore a problem, understand assumptions, and the meaning of their results. The experiential components provide hands-on learning both in the lab and on the computer. As a beginning text in modeling, readers will learn to value the approach and apply competencies in other settings. Included case studies focus on building a model to solve a particular biological problem from concept and translation into a mathematical form, to validating the parameters, testing the quality of the model and finally interpreting the outcome in biological terms. The book also shows how particular mathematical approaches are adapted to a variety of problems at multiple biological scales. Finally, the labs bring the biological problems and the practical issues of collecting data to actually test the model and/or adapting the mathematics to the data that can be collected. Presents a single volume on mathematics and biological examples, with data and wet lab experiences suitable for non-experts Contains three real-world biological case studies and one wet lab for application of the mathematical models Includes R code templates throughout the text, which are also available through an online repository, along with the necessary data files to complete all projects and labs

Author : Shangzhi Li
Publisher : World Scientific
Page : 234 pages
File Size : 40,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9812380507

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Mathematics Experiments by Shangzhi Li Pdf

Owing to the advent of computers, experiments are becoming an increasingly important part of mathematics. This book provides guidance to students doing experiments in mathematics. The aim is to stimulate interest in mathematics through examples and experiments. Each experiment in the book starts with an interesting problem. The students are expected to work with these problems on computers, try to find the solutions themselves, and experience the scientific exploration in the process. The problems which the authors have chosen cover a wide spectrum in mathematics, ranging from calculus, number theory, coding and probability to geometry and chaos. They are introduced in a simple way and yet show great depth. The discussions are thorough but not lengthy. This book is useful not only to mathematics students, but also to students in all areas of sciences who are interested in learning some of the mathematical tools. It provides a hands-on approach to the most fundamental issues in mathematics -- an approach which may help to revolutionize the teaching of mathematics.

Author : Anonim
Publisher : Unknown
Page : 168 pages
File Size : 51,5 Mb
Release : 2002
Category : Mathematics
ISBN : UCSC:32106016981554

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For the Learning of Mathematics by Anonim Pdf