Kategoria BISAC: Mathematics >> Study & Teaching

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on - but not restricted to - those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite the substantial amount of curriculum development activity over the last 15 years and growing scholarly interest in their use, the book represents the first compilation of research on teachers and mathematics curriculum materials and the first...

This book now in its second revised and extended edition is a self-contained exposition of the theory of compact right semigroupsfor discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.

The acclaimed author ofA Tour of the CalculusandThe Infinite Ascentoffers an enlightening and enthralling tour of the basics of mathematics, and reveals a world of fascination in fundamental mathematical ideas.
One, Two, Threeis David Berlinski s captivating exploration of the foundation of mathematics, its fundamental ideas, and why they matter. By unraveling the complex answers to these most elementary questions What is a number? How do addition, subtraction, and other functions actually work? What are geometry and logic? Berlinski reveals the intricacy behind...

This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes.

This textbook presents a number of the most important numerical methods for finding eigenvalues and eigenvectors of matrices. The authors discuss the central ideas underlying the different algorithms and introduce the theoretical concepts required to analyze their behaviour. Several programming examples allow the reader to experience the behaviour of the different algorithms first-hand. The book addresses students and lecturers of mathematics and engineering who are interested in the fundamental ideas of modern numerical methods and want to learn how to apply and extend these ideas to...

Stochastic processes occur in a large number of fields in sciences and engineering, so they need to be understood by applied mathematicians, engineers and scientists alike. This work is ideal for a first course introducing the reader gently to the subject matter of stochastic processes. It uses Brownian motion since this is a stochastic process which is central to many applications and which allows for a treatment without too many technicalities. All chapters are modular and are written in a style where the lecturer can "pick and mix" topics. A "dependence chart" will guide the reader when...

Mathematics Education and Technology-Rethinking the Terrain revisits the important 1985 ICMI Study on the influence of computers and informatics on mathematics and its teaching. The focus of this book, resulting from the seventeenth Study led by ICMI, is the use of digital technologies in mathematics teaching and learning in countries across the world. Specifically, it focuses on cultural diversity and how this diversity impinges on the use of digital technologies in mathematics teaching and learning. Within this focus, themes such as mathematics and mathematical practices;...

This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern...

What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available...