Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010218872 | QA184.5 H35 1995 | Open Access Book | Book | Searching... |
On Order
Summary
Summary
Can one learn linear algebra solely by solving problems? Paul Halmos thinks so, and you will too once you read this book. The Linear Algebra Problem Book is an ideal text for a course in linear algebra. It takes the student step by step from the basic axioms of a field through the notion of vector spaces, on to advanced concepts such as inner product spaces and normality. All of this occurs by way of a series of 164 problems, each with hints and, at the back of the book, full solutions. This book is a marvelous example of how to teach and learn mathematics by 'doing' mathematics. It will work well for classes taught in small groups and can also be used for self-study. After working their way through the book, students will understand not only the theorems of linear algebra, but also some of the questions which were asked which enabled the theorems to be discovered in the first place. They will gain confidence in their problem solving abilities and be better prepared to understand more advanced courses. As the author explains, 'I don't think I understand a subject until I know the questions ... I wrote this book to organize those questions, problems, in my own mind.' Try this book with your students and they too will be able to organize and understand the questions of linear algebra.
Reviews 1
Choice Review
Halmos's A Hilbert Space Problem Book (1st ed., CH, Mar'68; 2nd ed., 1982) is a classic of learning-by-doing mathematical exposition at the graduate level. Here, he uses the same formula for the benefit of undergraduate linear algebra students. The book's core consists of 163 problems organized by topic along the lines of the author's Finite-Dimensional Vector Spaces (2nd ed., 1958; reprinted 1974). Problems are said to range in difficulty from "accessible to any interested grade school students" to "might stump even a professional expert (at least for a minute or two)." Though not meant to stand by itself as a textbook, considerable crafty explication has been rolled into the problem statements. Between the problems and the solutions come the hints and the one-liners that manage to turn on the lights without spoiling the fun; one imagines they were the hardest part of the book to write. For those who need them, the solutions are clear and copious; for those who do not, they nevertheless offer gems of unexpected insight. Were it possible for the experience of apprenticeship to a master of mathematics to be packaged between the covers of a book, this would be it. No teacher of linear algebra should neglect to consult it. Highly recommended for all libraries. All levels. D. V. Feldman; University of New Hampshire
Table of Contents
| 1 Scalars |
| 2 Vectors |
| 3 Bases |
| 4 Transformations |
| 5 Duality |
| 6 Similarity |
| 7 Canonical forms |
| 8 Inner product spaces |
| 9 Normality |
| 10 Hints and solutions |
