Hefferon J. Linear Algebra

Saint Michael’s College, 2012. — 465 pages. Решебник к этой книге /file/1318288/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 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 as well as extensive and careful exercises.
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 different 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 and some do not. In either 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 off later but also comes late enough that students are serious about mathematics. The material is accessible, coherent, and elegant. There are a variety of argument styles, including direct proofs, proofs by contradiction, and proofs by induction. And, examples are plentiful.
Helping readers start the transition to being serious students of mathematics requires taking the mathematics seriously so all of the results here are proved. On the other hand, we cannot assume that students have already arrived and so in contrast with more advanced texts this book is filled with examples, often quite detailed.