Computational and Algorithmic Linear Algebra and n-Dimensional Geometry

A sophomore level book on linear algebra and n-dimensional geometry with the aim of developing in college entering undergraduates skills in algorithms, computational methods, and mathematical modeling.

**Tag(s):**
Linear Algebra

**Publication date**: 31 Dec 2001

**ISBN-10**:
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**ISBN-13**:
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**Paperback**:
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**Views**: 11,224

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**Post time**: 10 Apr 2008 12:44:03

Computational and Algorithmic Linear Algebra and n-Dimensional Geometry

A sophomore level book on linear algebra and n-dimensional geometry with the aim of developing in college entering undergraduates skills in algorithms, computational methods, and mathematical modeling.

Excertps from the Introduction:

There are many outstanding books on linear algebra, but most of them have their focus on undergraduates in mathematics departments. They concentrate on developing theorem-proving skills in the readers, and not so much on helping them develop mathematical modeling, computational, and algorithmic skills. Students who miss a few classes, particularly those already not doing well in the class, often find it very difficult to catch up with the help of such text books. The net result after about half the term is an unhealthy situation in which only the top half of the class is comfortably following the teachers lectures, with the rest falling more and more behind.

Also, with mounting pressure to pack more and more material into undergraduate mathematics courses, it is highly unlikely that more class time can be found to allocate to linear algebra. So, an important component of a solution strategy to this problem is to see whether students can be helped to learn these concepts to a large extent from their own efforts.

Our focus is to help the students develop the mathematical modeling, computational, and algorithmic skills that they need to bring linear algebra tools and facts to solving real world problems. Proofs of simple results are given without being specially labeled as proofs. Proofs of more complex facts are left out, for the reader to look up in any of the traditional textbooks on the subject, some of which are listed in the bibliography.

There are many outstanding books on linear algebra, but most of them have their focus on undergraduates in mathematics departments. They concentrate on developing theorem-proving skills in the readers, and not so much on helping them develop mathematical modeling, computational, and algorithmic skills. Students who miss a few classes, particularly those already not doing well in the class, often find it very difficult to catch up with the help of such text books. The net result after about half the term is an unhealthy situation in which only the top half of the class is comfortably following the teachers lectures, with the rest falling more and more behind.

Also, with mounting pressure to pack more and more material into undergraduate mathematics courses, it is highly unlikely that more class time can be found to allocate to linear algebra. So, an important component of a solution strategy to this problem is to see whether students can be helped to learn these concepts to a large extent from their own efforts.

Our focus is to help the students develop the mathematical modeling, computational, and algorithmic skills that they need to bring linear algebra tools and facts to solving real world problems. Proofs of simple results are given without being specially labeled as proofs. Proofs of more complex facts are left out, for the reader to look up in any of the traditional textbooks on the subject, some of which are listed in the bibliography.

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