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These homework texts provide an opportunity for shared activities between parent and child. They provide two activities a week, a variety of formal written practice, and informal shared practical activities. The activities focus on key number skills, and there is advice for parents.
Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.
Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.
This World Bank report is a rich compilation of information on teaching learning materials (TLM) in Africa based on the extensive and multi-faceted experience of the author's work in the education sector in Africa. The study examines a wide range of issues around TLM provision including curriculum, literacy and numeracy, language of instruction policy, procurement and distribution challenges, TLM development and production and their availability, management and usage in schools. It also looks at the role of information and communication technology (ICT) based TLMs and their availability. The study recognizes that improved TLM system management is a critical component in achieving affordable and sustainable TLM provision for all students. This study, which draws from more than 40 Anglophone, Francophone, Lusophone, and Arabic-speaking countries will be particularly useful for policymakers, development partners, and other stakeholders attempting to understand the wide range of issues surrounding the complexity of textbook provision in Sub Saharan Africa.
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
Praise for the first edition: 'This book should be of interest to anyone interested in sustainable development, and especially sustainability indicators. Bell and Morse easily succeed in exposing the fundamental paradoxes of these concepts and, more importantly, they offer us a way forward. Readers ... will find their practical recommendations for those attempting to do sustainability analysis in the field most welcome, which is also the book's greatest strength.' Local Environment: The International Journal of Justice and Sustainability 'This book makes a valuable contribution to the theory and practice of using indicators for sustainability. It introduces systems ideas and a range of tools and techniques that have the potential to broaden and deepen our understanding of a whole range of complex situations. Well worth a closer look.' Christine Blackmore, Open University 'This is a book that explores new ways of thinking about how to measure sustainability... It offers stimulating food for thought for environmental educators and researchers.' Environmental Education Research 'This book tells me, as an SI 'practitioner', where I have been and why, and more importantly how I should be thinking in order to effectively present to and empower the local community in the years ahead.' David Ellis, Principal Pollution Monitoring Officer, Norwich City Council 'A practical guide to the development of sustainability indicators which offers a systemic and participative way to use them at local scale. Our preliminary results are highly positive and the approach is applicable in many contexts.' Elisabeth Coudert, Programme Officer Prospective and Regional Development, Blue Plan The groundbreaking first edition of Sustainability Indicators reviewed the development and value of sustainability indicators and discussed the advantage of taking a holistic and qualitative approach rather than focusing on strictly quantitative measures. In the new edition the authors bring the literature up to date and show that the basic requirement for a systemic approach is now well grounded in the evidence. They examine the origins and development of Systemic Sustainability Analysis (SSA) as a theoretical approach to sustainability which has been developed in practice in a number of countries on an array of projects since the first edition. They look at how SSA has evolved into the practical approaches of Systemic Prospective Sustainability Analysis (SPSA) and IMAGINE, and, in particular, how a wide range of participatory methodologies have been adopted over the years. They also provide an assessment of the strengths and weaknesses of projects that undertake work in the general field of sustainable development.
"The History of Mathematics: An Introduction," Sixth Edition, is written for the one- or two-semester math history course taken by juniors or seniors, and covers the history behind the topics typically covered in an undergraduate math curriculum or in elementary schools or high schools. Elegantly written in David Burton's imitable prose, this classic text provides rich historical context to the mathematics that undergrad math and math education majors encounter every day. Burton illuminates the people, stories, and social context behind mathematics'greatest historical advances while maintaining appropriate focus on the mathematical concepts themselves. Its wealth of information, mathematical and historical accuracy, and renowned presentation make The History of Mathematics: An Introduction, Sixth Edition a valuable resource that teachers and students will want as part of a permanent library.
Consciousness is widely perceived as one of the most fundamental, interesting and difficult problems of our time. However, we still know next to nothing about the relationship between consciousness and the brain and we can only speculate about the consciousness of animals and machines. Human and Machine Consciousness presents a new foundation for the scientific study of consciousness. It sets out a bold interpretation of consciousness that neutralizes the philosophical problems and explains how we can make scientific predictions about the consciousness of animals, brain-damaged patients and machines. Gamez interprets the scientific study of consciousness as a search for mathematical theories that map between measurements of consciousness and measurements of the physical world. We can use artificial intelligence to discover these theories and they could make accurate predictions about the consciousness of humans, animals and artificial systems. Human and Machine Consciousness also provides original insights into unusual conscious experiences, such as hallucinations, religious experiences and out-of-body states, and demonstrates how ‘designer’ states of consciousness could be created in the future. Gamez explains difficult concepts in a clear way that closely engages with scientific research. His punchy, concise prose is packed with vivid examples, making it suitable for the educated general reader as well as philosophers and scientists. Problems are brought to life in colourful illustrations and a helpful summary is given at the end of each chapter. The endnotes provide detailed discussions of individual points and full references to the scientific and philosophical literature.