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This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
This set of grade 5 math resources covers multiplication and division word problems; perimeter and area; addition and subtraction of whole numbers and decimals; circles, polygons, and angles; addition and subtraction with fractions; volume, capacity, and weight; multiplication and division with whole numbers and decimals; algebra, functions, and graphs; multiplication and division with fractions; patterns and transformations; ratio, proportion, and percent; three-dimensional figures.
This unique comprehensive curriculum encourages students to learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively increasing their understanding. "MathScape: Seeing and Thinking Mathematically" was developed by Education Development Center, Inc. with funding from the National Science Foundation. It is one of four middle school mathematics programs to receive a satisfactory rating from the American Association for the Advancement of Science (AAAS).
Containing hundreds of images and dozens of maps, All American History is a complete year s curriculum for students in grades 5-8 when combined with the Student Activity Book and Teacher s Guide. It is also adaptable for younger and older students. The first volume covers Exploration through 1840. There are 32 weekly lessons, and each lesson contains three sections examining the atmosphere in which the event occurred, the event itself, and the impact this event had on the future of America. Designed to be engaging and written in a comfortable style, All American History reads like a good book-bringing America s story to life piece by piece."