Mathematics

Functions of a complex variable: theory and practice by George F. Carrier

By George F. Carrier

Services of a posh variable are used to resolve purposes in a number of branches of arithmetic, technology, and engineering. services of a posh Variable: thought and approach is a ebook in a unique class of influential classics since it relies at the authors’ broad event in modeling advanced occasions and offering analytic suggestions. The publication makes to be had to readers a complete variety of those analytical recommendations established upon advanced variable concept. talent in those ideas calls for perform. The authors offer many workouts, incorporating them into the physique of the textual content. through finishing a considerable variety of those routines, the reader will extra absolutely take advantage of this ebook. according to graduate classes in utilized arithmetic, features of a fancy Variable: concept and approach is meant for utilized mathematicians, scientists, engineers, and senior or graduate-level scholars who've complicated wisdom in calculus and have an interest in such topics as complicated variable idea, functionality conception, mathematical tools, complex engineering arithmetic, and mathematical physics.

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THE CONTENT PRINCIPLE Assessment should reflect the mathematics that is most important for students to learn. The content principle has profound implications for designing, developing, and scoring mathematics assessments as well as reporting their results. Some form of the content principle may have always implicitly guided assessment development, but in the past the notion of content has been construed in the narrow topic-coverage sense. Now content must be viewed much more broadly, incorporating the processes of mathematical thinking, the habits of mathematical problem solving, and an array of mathematical topics and applications, and this view must be made explicit.

Html9/4/2008 10:44:32 PM next page > page_47 < previous page page_47 next page > Page 47 tional change. If an assessment represents a significant but small fraction of important mathematical knowledge and performance, then the same assessment should not be used over and over again. Repeated use could inappropriately narrow the curriculum. Developing New Assessment Tasks Several desired characteristics of assessment tasks can be deduced from the content principle and should guide the development of new assessment tasks.

19 Further complicating the problem is that many classesincluding those labeled college prepdo not provide the mathematics education needed by today's students. Just gaining access to such classes is not enough. All students must learn important mathematics in these classes. 20 Yet most young children like mathematics and see it as something they are capable of doing. Indeed, most children enter school with quite sophisticated theories about how numbers are used in their world. In elementary school, however, mathematics begins to look different to them.

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