Linear Algebra Problem Book (Dolciani Mathematical Expositions)

Rating:
Summary: Start out with one of the best
Review: 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.

Rating:
Summary: Start out with one of the best
Review: 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.

Rating:
Summary: Clear, interesting, easy to follow.
Review: 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.