Mathematics As A Laboratory Tool

The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students. The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems. The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology. The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus. The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools. Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.

Lab Math: A Handbook of Measurements, Calculations, and Other Quantitative Skills for Use at the Bench, 2nd edition, collects in one place the numbers and equations you rely on for your experiments and use to report your data-what they mean and how to use them-as well as easy-to-follow shortcuts for making the math easier. Written in an accessible and informal style, Lab Math describes basic mathematical principles and various tasks involving numbers, including how to calibrate lab equipment, how to make solutions, and the numbers involved in various methods for quantifying DNA, RNA, and proteins, and an all-new section on quantitative polymerase chain reaction. Basic statistical ideas and methods and the proper reporting of uncertainty are described in simple-to-understand language. Also included are reference tables, charts and "plug-and-chug" equation blanks for specific experimental procedures. Since the publication of the first edition in 2003, Lab Math has become an essential math reference and teaching resource for both on-the-spot practical information and background for understanding numerical tasks. Important additions in this second edition make Lab Math an even more useful tool for every laboratory.

The best laboratory math text on the market for almost 20 years, this title covers both the general principles of mathematics and specific equations, formulas, and calculations used for laboratory testing. It provides simple, easily understood explanations of calculations commonly used in clinical and biological laboratories. Contains more than 1000 practice problems.

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.

This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques / International Commission for the Study and Improvement of Mathematics Education.

This Open Access volume by the International Commission on Mathematical Instruction (ICMI) is an outcome of the ICMI Study 24 and gives a status-quo of school mathematics reform around the world and what we can learn from this movement. Each theme and section of the book offers descriptions and analyses of multiple case studies in different countries and contexts, along with opportunities to compare, contrast and learn from these diverse experiences. The volume provides a synthesis and meta-analysis of the different historical, geographical and global aspects of school mathematics reforms and explores in which way curricula are elaborated, proposed, changed, and reorganized. It offers a more informed and comprehensive analysis of the roles of different actors and of the many aspects influencing and shaping mathematics curriculum reforms that are taking or have taken place. It also explores the possibilities and means to tackle a curricular reform in the current scenario we live in and how to unfold future developments. This book will be of interest to practitioners and scholars with an interest in school mathematics curriculum reforms. It will also be a useful resource to those involved in school mathematics curriculum reform initiatives by providing current information about the curriculum changes that are taking place in respect of content, teacher education, educational materials, and a range of implementation challenges across diverse contexts.

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.

This book comprises the full selected Regular Lectures from the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 4700 experts from 100 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. These selected Regular Lectures present the work of fifty-one prominent mathematics educators from all over the globe. The Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.