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This book is aimed at gifted and talented students in year 7, although it can also be used in the primary curriculum for highly able year 6 students. It consists of tightly focused sets of problems, with each set devoted to core ideas from the Framework but approached in a way that cultivatesmore profound mathematical thinking. The book is structured into a number of sections, which comes in three varieties: tasters, core, and extensions, thus recognising differentiation within the gifted spectrum. The materials can be used within ordinary lessons for top sets.
The Ausdehnungslehre of 1862 is Grassmann's most mature presentation of his "extension theory". The work was unique in capturing the full sweep of his mathematical achievements. Compared with Grassmann's first book, Lineale Ausdehnungslehre, this book contains an enormous amount of new material, including a detailed development of the inner product and its relation to the concept of angle, the "theory of functions" from the point of view of extension theory, and Grassmann's contribution to the Pfaff problem. In many ways, this book is the version of Grassmann's system most accessible to contemporary readers. This translation is based on the material in Grassmann's "Gesammelte Werke", published by B. G. Teubner (Stuttgart and Leipzig, Germany). It includes nearly all the Editorial Notes from that edition, but the "improved" proofs are relocated, and Grassmann's original proofs are restored to their proper places. The original Editorial Notes are augmented by Supplementary Notes, elucidating Grassmann's achievement in modern terms. This is the third in an informal sequence of works to be included within the History of Mathematics series, co-published by the AMS and the London Mathematical Society. Volumes in this subset are classical mathematical works that served as cornerstones for modern mathematical thought.
Designed to help classroom teachers provide enrichment for those students who quickly grasp the mathematical concepts being taught and are ready to move on to more challenging units. The units include challenging activities that will require higher level thinking and will broaden students' problem-solving skills.
Reproducible activities for students in year 6 who are capable of working approximately one year beyond their class level, and who need to be challenged and extended mathematically. Include checklists for teachers, reproducible activity worksheets under each mathematical strand, plus assessment worksheets.
The "Heinemann Mathematics" scheme has been developed by the authors of the primary course "SPMG", with the aim of building on established strengths to provide a structured development of children's mathematical knowledge and skills within the revised curricula.
The "Heinemann Mathematics" scheme has been developed by the authors of the primary course "SPMG", with the aim of building on established strengths to provide a structured development of children's mathematical knowledge and skills within the revised curricula.
New Senior Mathematics Extension 1 for Years 11 and 12 covers all aspects of the Extension 1 Mathematics course for Year 11&12. We've completely updated the series for today's classrooms, continuing the much-loved approach to deliver mathematical rigour with challenging student questions.
The purpose of this book is to help busy classroom teachers provide enrichment for those students who quickly grasp the mathematical concepts being taught and are ready to move on to more challenging material. The units include challenging activities that will require higher-level thinking and will broaden students' problem-solving skills. This book is a great resource for busy classroom teachers who need materials to extend learning opportunities for those students who quickly grasp the concepts covered in their grade level math curriculum. This book includes four units: geometry, fractions, graphing, and problem solving. The units provide hours of activities that will allow students to work independently or in small groups to extend their knowledge and apply their skills. Each unit includes 13 to 14 attractive, reproducible worksheets and an assignment sheet, making this an easy way for instructors to provide challenging, enriching experiences for capable math students. This can also be used for review and remediation with middle school students. For a less advanced version of math extension activities, see Math Extension Units Book 1—place value, problem solving, time and measurement, and money. For more math units geared toward the same goal, see Enrichment Activities for Math Books1, 2, and 3. Grades 4-5
Let [italic]H be a Hilbert space. Formally normal, normal, symmetric, selfadjoint, and semibounded subspaces of [italic]H2=[italic]H2[circled plus][italic]H are defined by means of the corresponding properties of the graphs of operators in H which are formally normal, normal, symmetric, selfadjoint, or semibounded, respectively. The author gives a complete description of all formally normal and normal subspace extensions in [italic]H2 of a given formally normal subspace [italic]N of [italic]H2. Those extensions which are graphs of operators are explicitly characterized. The symmetric and selfadjoint extensions of a given symmetric subspace are also classified; this result extends the well-known result of von Neumann characterizing the selfadjoint extensions of a (densely defined) symmetric operator. The construction of the "Friedrichs extension'' of a semibounded symmetric subspace is outlined. The existence of formally normal and symmetric extensions in a larger Hilbert space is also studied. A formally normal subspace need not have any normal subspace extension in a bigger subspace. But (as is known for operators), every symmetric subspace has selfadjoint extensions in suitable larger spaces; these extensions are completely characterized.