Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
- Amazon Sales Rank: #20087 in Books
- Published on: 2005-09-01
- Original language: English
- Number of items: 1
- Binding: Hardcover
- 576 pages
About the Author
David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.
As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter.
A top-notch educator, Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or Unviersity Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.
I am just finishing up an introductory Linear Algebra course using this book. I am a mechanical engineering student, and not a math major, so keep that in mind when reading this review.
I personally really liked Lay's approach and writing style. The first chapter is a basic overview of linear algebra and helps you develop a strong background for the following chapters.
I particularly like Lay's method of highlighting important theorems and definitions. He uses a light blue background for theroems and key ideas and a greenish type color for definitions. Very helpful for studying and you don't have to dig through the text to find the main topics. There is also a glossary, something that seems kind of rare in math textbooks.
I liked the practice problems before each problem set, they were kind of like examples, except the solution was on a different page. Also, row operations in this text always work out nicely, which means I didn't struggle with difficult computations that need not be difficult and cloud the concept I was trying to learn.
I didn't feel like there was enough problems. There was about 10-20 problems computational problems, some true/false questions, and about 10-15 or so questions that either asked you to prove things or were applied problems. I wish there was twice the amount of problems.
The invertible matrix theorem should of been summarized in its entirety somewhere. Its scattered across 6 sections in 5 different chapters.
Alright so this was a long winded review, but hopefully you found it helpful.I feel the book is really good for engineering students and applied math majors. Pure theoretical math majors, I could see how you might not like this book. The text doesn't seem that abstract and you aren't buried in proofs, but I believe Lay has geared his text more towards applied mathematics than pure math anyways. I was able to learn most of the material on my own as my professor (as in most math and science classes) was really bad. I feel that this book is good for self-study or as a saving grace from a poor professor.
Ver little help on tough concepts
This book is an overview of Linear Algebra rather than a comprehensive study. The problems that really dwell deep into the concepts are left unanswered even when the problem is odd. You go to the back of the book and the answer isn't there; instead, it tells you to go to the STUDY GUIDE for the answer. Here's the clincher. You buy a $30 study guide, and then you flip to the correct section and the ANSWER ISN'T THERE. This is a BAD SALES SCHEME. The author claims that giving students answers inhibits critical thinking, but it's clear that he really intends for unwary students to buy his study guide so he can get money without exerting minimum mental effort. I strongly discourage people from buying this book. You'd be better off asking for help on the internet blogs.
underwhelmed / Updated? I don't think so
i'm not going to write 3 paragraphs about how much i love math, and what my fricking sat score was and how many A's i have as most nerds do when they review a math book. i am a math nerd too, but i'll keep the discussion to why i dislike the book (which will be short too, as i need to get back to studying it!)
1. i found there to be a nagging disconnect between the material covered and the exercises. i don't mind difficult problems, but at least appreciate some help from text. if i just wanted to figure it all out on my own i wouldn't have bought the book.
2. the study guide is not very useful. it provides solutions to every other odd problem. true / false answers just refer you back to the book and tell you to check your answers.
3. the text's answers to true/false problems tell you to think about it, then consult the study guide. see 2 above.
basically, i enjoy the material, my prof is great, the book is a big disappointment. if it wasn't for my prof's enthusiasm for the subject i'd be frustrated and not select any additional linear algebra electives. luckily, i do look forward to additional courses as the material is extremely useful in industry, i'm an applied math person.
finally, i searched for another text to supplement my studies and settled on Matrix Analysis and Applied Linear Algebra by Meyer, and look forward to its arrival. my second choice was: Linear Algebra : A Modern Introduction (with CD-ROM) by Poole, and it was a close second. both texts are highly recommended and very focused on applied subject matter. both have well developed websites, ect... but Meyer's text was published by SIAM with a stong focus on how the material is being used in practice. it also comes with a searchable, printable version of the text (and possibly study guide) on the cd.
if you want a balanced view before you buy this text. go to the 3rd ed, not the 3rd ed updated, and read some of the negative reviews in addition to the good ones. my experience was similar to many of those negagive reviews. disappointment and frustration with a very popular text. good luck.
Updated? I don't think so
In my opinion, this borders on the outrageous. I don't know if it is the author or the publisher, but someone should be ashamed to be taking such advantage of students. like shooting fish in a barrel and calling yourself a great marksman.
What is updated about this text? In my understanding, nothing! Update apparently means new chapters have been added to the publisher's website. most instructor's don't seem to know of this, so they don't use them, and they unwittingly order the newest edition. most students don't know either and needlessly fork over $120 for nothing new.
With vulture marketing practices like this I can't imagine why students would buy international texts.
if you are required to buy this text, check if you prof plans to use the "updated" chapters. if not, save some $ and go find a 3rd edition to use for your class.