Linear Algebra Problem Book (Dolciani Mathematical Expositions) [Paperback]

Paul R. Halmos (Author)

Book Description

ISBN-10: 0883853221 | ISBN-13: 978-0883853221 | Publication Date: September 5, 1996

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.

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

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.

Product Details

• Paperback: 350 pages
• Publisher: The Mathematical Association of America (September 5, 1996)
• Language: English
• ISBN-10: 0883853221
• ISBN-13: 978-0883853221
• Product Dimensions: 9.1 x 6.1 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #322,286 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

41 of 41 people found the following review helpful:

5.0 out of 5 stars Start out with one of the best, June 13, 2001

By 

Dougabug "dougabug" (Orangevale, CA United States) - See all my reviews

This review is from: Linear Algebra Problem Book (Dolciani Mathematical Expositions) (Paperback)

Halmos is one of the great mathematical expositors of the 20th Century, and his book "Finite Dimensional Vector Spaces" stands as the definitive introduction to the subject for budding mathematicians. This book, "Linear Algebra Problem Book", is perhaps best described as an engaging and semi-informal invitation and complement to that original work, which grew out of lectures given by the legendary John von Neumann. In contrast to typical treatments of linear algebra, "Finite Dimensional Vector Spaces" is abstract (introduces determinants through alternating forms), rigorous, concise, and demands a certain level of mathematical maturity. This book, "Linear Algebra" is exactly the opposite. Starting from very little assumed background, it all but gives away the store, written in plain language, anticipating students' questions and misconceptions, and leading them to a deeper understanding of mathematics through the Socratic method. This is not a problem book in the Schaum's outline sense; there is no drill or rote calculations. Every question is carefully chosen to illustrate a point or expose a potential misunderstanding in the student's knowledge or to exercise the student's intuition and ability to make connections. The answers are given as detailed explanations, integral to the exposition, which go far beyond merely answering the questions posed, raising deeper implications and questions. This is an excellent book for beginning students of higher mathematics, and a very user friendly guide to Halmos' classic text.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Great book!, February 22, 2006

By 

Physicsmind "Physicswish" (CA United States) - See all my reviews

This review is from: Linear Algebra Problem Book (Dolciani Mathematical Expositions) (Paperback)

I agree with the following reviewer in that Halmos' books are always entertaining and inviting! Fun to read, concise yet clear! The book contains most of the elementary yet important problems in an undergrad course with solutions in the back. It's very helpful working through all these problem because it will tremendous enhance your understanding of the subject. Also, if you want a hardcore problem oriented approach to linear algebra, check out Proskuryakov's Problems in Linear Algebra. Some of the problems in the book are Putnam like. Virtually any type of Putnam taste problems in Linear Algebra can be found in Proskuryakov. But this one, contrast to Halmos', is the least entertaining--that's why it is called HARDCORE PROBLEM APPROACH! You would be a great linear algebra problem solving machine working through both books!

10 of 12 people found the following review helpful:

5.0 out of 5 stars Clear, interesting, easy to follow., April 29, 1999

By A Customer

This review is from: Linear Algebra Problem Book (Dolciani Mathematical Expositions) (Paperback)

I'm no mathematician but, I own a number of linear algebra and abstract algebra books and this book makes them all pale in comparison. I really enjoyed working through it. Maybe a bit pedantic for more advanced types but, if you want to get a handle on the concepts this is the book.