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Kunihiko Kodaira's influence in mathematics has been fundamental and international, and his efforts have helped lay the foundations of modern complex analysis. These three volumes contain Kodaira's written contributions, published in a large number of journals and books between 1937 and 1971. The volumes cover chronologically the major periods of Kodaira's mathematical concentration and reflect his collaboration with other prominent theoreticians. Thus they begin with early works that discuss the application of Hilbert space methods to differential equations, and the use of elementary solutions to prove regularity theorems for strongly elliptic systems of partial differential equations. Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).
Mathematics and Science education have both grown in fertile directions in different geographic regions. Yet, the mainstream discourse in international handbooks does not lend voice to developments in cognition, curriculum, teacher development, assessment, policy and implementation of mathematics and science in many countries. Paradoxically, in spite of advances in information technology and the “flat earth” syndrome, old distinctions and biases between different groups of researcher’s persist. In addition limited accessibility to conferences and journals also contribute to this problem. The International Sourcebooks in Mathematics and Science Education focus on under-represented regions of the world and provides a platform for researchers to showcase their research and development in areas within mathematics and science education. The First Sourcebook on Asian Research in Mathematics Education: China, Korea, Singapore, Japan, Malaysia and India provides the first synthesized treatment of mathematics education that has both developed and is now prominently emerging in the Asian and South Asian world. The book is organized in sections coordinated by leaders in mathematics education in these countries and editorial teams for each country affiliated with them. The purpose of unique sourcebook is to both consolidate and survey the established body of research in these countries with findings that have influenced ongoing research agendas and informed practices in Europe, North America (and other countries) in addition to serving as a platform to showcase existing research that has shaped teacher education, curricula and policy in these Asian countries. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives.
This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair’s Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.