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eBook Linear Algebra Problem Book (Dolciani Mathematical Expositions) download

by Paul R. Halmos

eBook Linear Algebra Problem Book (Dolciani Mathematical Expositions) download ISBN: 0883853221
Author: Paul R. Halmos
Publisher: The Mathematical Association of America (January 1, 1995)
Language: English
Pages: 349
ePub: 1803 kb
Fb2: 1586 kb
Rating: 4.4
Other formats: lit mbr lrf mobi
Category: Math Sciences
Subcategory: Mathematics

This is an absolutely excellent book. I came at it before I had ever taken a linear class. It frequently refers back to the wrong problem number, and there are typos in the mathematics that could cause problems if you aren't keeping track of what is happening

This is an absolutely excellent book. The book develops the subject in a way that it seems a natural progression. It frequently refers back to the wrong problem number, and there are typos in the mathematics that could cause problems if you aren't keeping track of what is happening.

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.

LINEAR ALGEBRA PROBLEM BOOK Paul R. Halmos. The DOLCIANI MATHEMATICAL EXPOSITIONS series of the Mathematical Association of America was established through a generous gift to the Association from Mary P. Dolciani, Professor of Mathematics at Hunter College of the City Uni- versity of New York.

Linear Algebra Problem Book, Dolciani Mathematical Expositions, Mathematical Association of America. Halmos, Paul R. "Invariants of certain stochastic transformations: The mathematical theory of gambling systems. Duke Mathematical Journal 5, no. 2 (1939): 461–478. Logic as Algebra, Dolciani Mathematical Expositions No. 21, Mathematical Association of America. posthumous, with Steven Givant), Introduction to Boolean Algebras, Springer. Albers, Donald J. (1982).

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

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.

Linear Algebra Problem Book book. Paul Halmos thinks so, and you will too once you read this book. Linear Algebra Problem Book (Dolciani Mathematical Expositions). 0883853221 (ISBN13: 9780883853221).

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebra—and nowadays that means every user of mathematics. It can be used as the basis of either an official course or a program of private study

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebra—and nowadays that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get.

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

The Linear Algebra Problem Book is an ideal text for a course in linear algebra. 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.

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.
Comments: (7)
Iaiastta
I bought this for an Advanced Linear Algebra class for which our instructor assigned no textbook. While I enjoyed the problems, had fun reading it, and felt it contributed to my understanding of the material, I wouldn't recommend it as the sole resource for a student taking the class. Buy a textbook, but also buy this as a supplement. Both of the textbooks I bought had few worked examples, so I taught myself a lot from this book. However, I also didn't understand the point of a few of Halmos's problems until after reading the corresponding section in the textbook. This may be due to my status as a first year graduate student, 7 years after finishing my undergraduate degree. Recent graduates continuing on into graduate study may find they can easily work the problems. I had to do a lot of review. In short, this is dessert. Make sure you purchase your main course (textbook) to get the most nutrition out of your meal.
Irostamore
I don't disagree with the praise of the other reviewers, but I would like to mention two errors that might help others who already own or will purchase this book.
On page 239, in the line of equations at the top of the page, the last symbol should be "e sub i", not "e sub j".
Also on the same line, in the double summation between the second and third = signs, the last symbol should be "e sub i", not "gamma sub j"
Gabar
It is good book, but it is not as perfect as one may think. I guess it has so high rating due to "popularity" of the author in mathematics. So let us face the truth:

PROS:
- There are a lot of problems, and more than half of them are very good. So this list of problems is the only reason to have this book in your library.
- ~33% is great - one should read it

CONS:
- a lot of typos
- a lot of proofs are missing (intentionally or not).
- a lot of proofs are not complete.
- sometimes Halmos instead of solving a problem, solve ANOTHER problem, very close to original but NOT equivalent.

His book on finite dimensional vector space is much better and honest compared to this one.
Overall it is ok, but it is not perfect in any sense.
Zahisan
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.
Breder
This book might just be the best book for self study ever written. The exposition is minimal, covering basic definitions and only a few examples, whenever necessary. The problems are challenging and illuminating. I love the fact that there is a hints section, as well as thorough solutions to each problems. And when I say thorough, I mean REALLY thorough. The first chapter is an excellent introduction to/review of some basic modern algebra (groups, fields) and from there the book dives into linear algebra.

This book is not nearly as thorough as Halmos's Finite-Dimensional Vector Spaces, or even the classic Linear Algebra Done Right, by Sheldon Axler. However, this book might be more instructive than both of them combined.

Highly recommended to anyone interested in linear algebra and who enjoys solving problems.
Kanrad
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!