Linear Algebra: Challenging Problems for Students (Johns Hopkins Studies in the Mathematical Sciences) [Hardcover]

Professor Fuzhen Zhang (Author)

Book Description

ISBN-10: 080185458X | ISBN-13: 978-0801854583 | Publication Date: August 22, 1996

"Working problems,"writes Fuzhen Zhang in the preface, "is a crucial part of learning mathematics. A good problem should be one through which one learns methods, uses techniques, and gains insights into the subject. The reader should find the collection of 200 problems in this book diverse, interesting, and challenging."

Linear Algebra: Challenging Problems for Students is a supplementary text for undergraduate and first-year graduate students majoring in mathematics, statistics, engineering, or related areas. The book will also be helpful for instructors teaching linear algebra and matrix theory. Based on the author's ten years' experience in teaching and research, it presents 200 problems of varying difficulty ranging from elementary to some which may baffle even professional mathematicians. Hints and solutions for all problems are found in the second half of the book.

Concise and clearly written, the problems in Linear Algebra are interesting, challenging, and up-to-date. This book will be of interest to students seeking to do further work in linear algebra on an independent basis, to those wishing to refresh their knowledge of the subject, and to those in seminar-style advanced linear algebra courses.

Editorial Reviews

Review

"Linear algebra is an increasingly important part of any curriculum in mathematics in our days... A well-organized problem book, like this, will surely be welcomed by students as well as by instructors... This is a very useful book." -- J. Szilasi, Zentralblatt fuer Mathematik

Review

"This book is full of interesting problems which are very useful to the student of linear algebra." -- Debraj Chakrabarti, University of Wisconsin

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Product Details

• Hardcover: 192 pages
• Publisher: The Johns Hopkins University Press (August 22, 1996)
• Language: English
• ISBN-10: 080185458X
• ISBN-13: 978-0801854583
• Product Dimensions: 9.5 x 6.5 x 0.8 inches
• Shipping Weight: 15.2 ounces
• Average Customer Review: 4.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #9,707,330 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

17 of 18 people found the following review helpful:

5.0 out of 5 stars An attractive supplement, August 15, 2000

By 

David Doster (New York, NY) - See all my reviews
(REAL NAME)   

This review is from: Linear Algebra: Challenging Problems for Students (Johns Hopkins Studies in the Mathematical Sciences) (Paperback)

Although the subtitle of the collection is "Challenging Problems for Students," a fair number of the problems are not difficult or tricky, but do a wonderful job of testing a student's understanding of the major concepts and techniques of elementary linear algebra. Not all of the problems are original, but they are all instructive and interesting. One of my favorites gives a product AB of a 3 x 2 and 2 x 3 matrix and asks for the product BA. The hints and solutions are clear and concise. I particularly appreciated the attractive layout of this text. Notation is chosen carefully, and everything from font size to spacing of text and the display of complex expressions seems to have been considered with utmost concern and respect for the reader. This book is a very good resource for both students and teachers of linear algebra.

7 of 7 people found the following review helpful:

4.0 out of 5 stars A good source of simple theoretical problems, December 8, 2005

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Linear Algebra: Challenging Problems for Students (Johns Hopkins Studies in the Mathematical Sciences) (Paperback)

Teachers of college mathematics are always long on stress and short on time. Exams come at regular intervals and finding the right problems to put on them is always a challenge. This is especially true for courses based on theory rather than algorithm execution. I have always found it easy to write exams in courses such as calculus, algebra and statistics, but find myself spending a lot of time creating the exams for courses such as linear and abstract algebra.
This book contains 200 problems and they are split into the following five categories:

1) Vector spaces
2) Determinants, inverses, rank and linear equations.
3) Matrices, linear transformations and eigenvalues.
4) Special matrices: Hadamard, Hermitian, Unitary, Normal and Permutation.
5) Inner product spaces.

While the problems are challenging, they are not unduly so and generally are within the range of what can be offered to your more talented students. Detailed hints to all of the problems are included.
If you are looking for problems to illustrate specific theoretical topics in linear algebra or need ideas for test problems, then this book is a resource that you should take a long look at. I am sure you will find something of value.

1 of 1 people found the following review helpful:

5.0 out of 5 stars great book for students, April 8, 2010

By 

Mark Lee (Atlanta, USA) - See all my reviews

Amazon Verified Purchase

This review is from: Linear Algebra: Challenging Problems for Students (Johns Hopkins Studies in the Mathematical Sciences) (Hardcover)

This expanded version contains a lot more practice problems plus review for basic linear algebra and matrix theory; it's an excellent book for math/stat majors and graduate students, especially for those who are to take "qualifying exams"...