This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
This book is intended to help students preparing parcitipate in Mathematical Olympiads for juniors. The book presents the tests used to select the Romanian Team for Junior Balkan Mathematical Olympiad.
Bulgarian Mathematical Competitons 2003 - 2006. This book includes problems and solutions for Winter Mathematical Competiton, Spring Mathematical Competiton, National Olympiad and Team Selection Test from 2003 -2006.
The content of California Pre-Algebra offers complete coverage of California’s Grade 7 Mathematics Content Standards. Mathematics standards from previous grades are reviewed to help understand Grade 7 standards. Activities are provided to develop Grade 7 concepts. Each lesson has ample skill practice so that students can master the important mathematical processes taught in Grade 7. California Pre-Algebra also teaches valuable techniques for solving purely mathematical as well as real-world problems. Throughout each chapter students will engage in error analysis and mathematical reasoning to build critical thinking skills and to construct logical arguments. California Pre-Algebra thus provides a balance between basic skills, conceptual understanding, and problem solving – all supported by mathematical reasoning.
The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.
