Linear Algebra Problem Book

Dolciani Mathematical Expositions

by Paul R. Halmos

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.

Genres: Mathematics, Algebra, Textbooks

349 pages, Paperback

First published January 1, 1995

Reviews

[annalcoholic]

ma pire passion

[Viktor Velev]

Honestly, the best book if you really want to understand Linear Algebra. Halmos makes you learn the concepts by doing the math yourself, which is the only way to learn math! Supplementing this read with Halmos' Finite-dimensional vector spaces is highly recommended!

[Adam Lantos]

Wow, I was really surprised from the quality of the exercises! There are so many stuff that other books don't deal with that this book has problems on that it got me very excited!
Looking for something important that is not dealt or dealt in a poor manner in other books? Then check in this book, you will probably find it here!

[Chris Herdt]

Professor John Johnstone said this book, while containing just linear algebra problems and their solutions, is useful, as the solutions are well-explained.