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The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.
This book contributes to the field of mathematical problem solving by exploring current themes, trends and research perspectives. It does so by addressing five broad and related dimensions: problem solving heuristics, problem solving and technology, inquiry and problem posing in mathematics education, assessment of and through problem solving, and the problem solving environment. Mathematical problem solving has long been recognized as an important aspect of mathematics, teaching mathematics, and learning mathematics. It has influenced mathematics curricula around the world, with calls for the teaching of problem solving as well as the teaching of mathematics through problem solving. And as ...
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This book breaks through in the field of mathematical creativity and giftedness. It suggests directions for closing the gap between research in the field of mathematics education and research in the field of creativity and giftedness. It also outlines a research agenda for further research and development in the field. The book consists of a balanced set of chapters by mathematicians, mathematics educators, educational psychologists and educational researchers. The authors of different chapters accept dynamic conception of creativity and giftedness. The book provides analysis of cognitive, affective and social factors associated with the development of creativity in all students and with the...
"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for hig...
This book offers the first, comprehensive guide to planning and conducting intracranial EEG studies, and analyzing intracranial EEG data. The chapters address core questions in the field of intracranial EEG research. They are written by internationally recognized experts in the domain of intracranial EEG and acknowledge the heterogeneity of approaches in this field. The particular format of the book allows readers to find clear guidelines, hands-on expertise and invaluable background information for planning and conducting state-of-the-art intracranial EEG research projects. Besides offering a reference guide to newcomers in the field, it also provides scholarly information for the more expe...