Linear Algebra - Concepts and Methods (Book + Solutions)

This book helps students to master the material of a standard US undergraduate first course in Linear Algebra.
The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is the book's audience: sophomores or juniors, usually with a background of at least one semester of calculus. The help that it gives to students comes from taking a developmental approach - this book's presentation emphasizes motivation and naturalness, using many examples.
The developmental approach is what most recommends this book so I will elaborate. Courses at the beginning of a mathematics program focus less on theory and more on calculating. Later courses ask for mathematical maturity: the ability to follow di˙erent types of arguments, a familiarity with the themes that underlie many mathematical investigations such as elementary set and function facts, and a capacity for some independent reading and thinking. Some programs have a separate course devoted to developing maturity but in any case a Linear Algebra course is an ideal spot to work on this transition. It comes early in a program so that progress made here pays o˙ later but it also comes late enough so that the classroom contains only students who are serious about mathematics.

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