Linear Algebra Problem Book (Dolciani Mathematical Expositions) by Paul R. Halmos (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review ‘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.’ Choice Book Description Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions. Book Description 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. Read more

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