Customer Reviews:
Incredibly Accessible.......2007-08-17
I used this book to teach myself linear algebra using a lesson plan developed by a teacher. A few things I found really helpful:
Lay constantly admonishes the reader to carefully study the text, by reading and re-reading. He understands that students learning linear algebra are likely to to be embarking on more abstract/advanced mathematics in the future--and he cares enough to teach good study skills as well as math. I've followed his advice, and found that with proper effort, I am able to teach myself.
Many of the questions are conceptual or True/False, which helps me to retain new concepts.
The study guide (sold separately, but very important if you're self-teaching) only includes answers to odd-numbered exercises. However, the answers are nicely detailed.
I especially appreciate that Lay refuses to flat-out offer answers to conceptual and True/False questions. Instead, there are hints and references to page numbers where helpful information can be found. This is important, not only because it (again) helps reinforce good study skills, but it encourages students to really try a problem before giving up and looking up the answer.
The introduction of new concepts is always followed by one or more examples, which helps to link theory to practice. In general, there are many examples that illustrate good problem-solving techniques. Proofs are detailed and well-justified, and there are some simple proofs that are left as problems in the book. These proofs are simple enough to not be terribly daunting to the student who is new to more abstract mathematical ideas.
For the student who would ask, "well what is it good for?" there are plenty of sections dedicated purely to applications of material learned in previous sections.
Detail-oriented methodical learners like myself should benefit from this book.
a good teacher helps..........2007-08-01
covers 75% of the detail and leaves the 25% up to you. it lacks clear explition is vector space secotion (row col vector nul basis etc). it seems like you do the first coumple of sections not understanding what you are getting at but when you get to chapter 6 or so the past stuff finaly makes sense. I found the book hard to understand when it was talking about maping, one to one on too. i suggest a TI-83 or higher and the solutions manual. The book also lacks pictures showing dimention row col nul basis etc.
Choose Another Book.......2007-07-30
The organization and the treatment given to most subjects are well below what one would expect for a Wikipedia entry on each respective topic.
Anyone who uses this book for any kind of self-study is unlikely to get more out of it more than a few examples on multiplying matrices, row reduction, and some poetry about eigen-spaces and vector spaces.
Take a look at ``Linear Algebra Done Right'' by Alxr.
meh............2007-05-14
This was the textbook that my school has been using for its first and second year Linear Algebra courses. I found it somewhat terse. It seems like it could be a great book for someone already familiar with linear algebra or the logic aspect of mathematics; I don't recommend it for anyone who is not very familiar with proofs. Fortunately, it doesn't lack examples of how to solve computation problems and solutions to the odd-numbered problems are provided in the back of the book. Unfortunately, when it comes to the proof problems, instead of just providing the reader with the answer like most other texts, the author will either mention a hint or refer the reader to the study guide (mine came with a disk which has to be installed on a computer), which could be a problem for readers not familiar with how to do proofs. Serving as a somewhat of a mediator between these two extremes are true/false questions which accompany each chapter in each section of the text. While those start out somewhat fun in the beginning, they can also get tiresome and repetive very quickly. The solutions to these, like the proofs, are not provided, but fortunately, all one has to do is read the text carefully in order to determine the appropriate response.
Shameful Plugs for Study Guide.......2006-03-25
Perhaps the most important questions at the end of each section are the true/false questions dealing with the concepts developed in the section. The computational problems are good for learning the algorithms but the true/false questions represent what you need to know.
After working through them and justifying your answers you turn to the back of the book and look for the correct solution but instead you find something like "Check your answers before referring to the study guide." Unfortunately the study guide is sold seperately so many people, including myself, choose not to buy it, nor should we have to. It makes the author seem like he cares more about selling book then teaching students.
I took Linear Algebra as an online course and there it is even more important that the material in the text is learned from the reading, as there is no physical lecture to supplement it. I would be more understanding if the author included just the answers in the text and left the justifications for the study guide, but to plug the study guide instead is just plain irresponsible.
Book Description
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.
Customer Reviews:
An outstanding introduction to Linear Algebra.......2007-08-09
This book provides a good companion for an introductory course in Linear Algebra. Mr. Lay's style is very clear, readable, and each concept logically builds on the last. My only concern is that, like another reviewer said there is the occasional gap between the exercises and the examples presented, which may require the assistance of the instructor. 4/5 Stars
A very good introduction to linear algebra.......2007-07-31
The highest quality of a book is the ability to teach yourself from it. Lay's book is very self-teachable because it is written in a non-pretentious, explanatory way, making sure you get the big picture while making sure you can do the little details. It reminds me of Griffiths books in physics.
It is a little proof light, so I can respect that a mathematician who is into analysis might find this book too easy. Problems aren't too hard but aren't too easy for the more conceptual questions.
And I appreciate that the problems are meant to test your ability to understand the material, not do mindless calculations that I know anyone can do. For example, some matrices will just start off already diagonalized for you in later chapters.
This is written from the perspective of a physicist. I thus say to my fellow scientists that this is a great book to gain a good understanding of the linear algebra. If you are an experimentalist who frankly wants to learn only what he needs to in order to get by, THEN THIS BOOK ISN'T FOR YOU. This book develops from scratch everything you need to know for undergraduate physics. Go read a Differential Equations book and learn as you go for the linear algebra. If you're a theorist, this is for you.
Good for the basics.......2007-07-11
I bought this book in June for a Linear Algebra course I will be starting in the fall. I've been looking through it and reading bits and pieces and from what I see I certainly like this guy's style. I've had completely unusable math books before but this is one of the few that I can use without the assistance of a teacher to at least begin to understand the basic concepts involved. Since I'll be taking the course as a high school student and not as a college student this book seems like it will do just fine to introduce concepts, and, from what I hear, the teacher who is taking over this course in the fall is excellent at explaining stuff so students understand it. Maybe after taking the course I'll change my mind, but for now Linear Algebra and Its Applications is one of the better math books I've ever used.
High Quality Linear Algebra Text! .......2007-01-21
This book is much better than what I feel some reviewers are giving it credit for. Perhaps they have had better exposure than I have to other materials for comparison, but I cannot say for sure.
What I can say is that this book, for me, nearly took the place of the instructor that I had for the course. The book is literally that good at explaining concepts to you and providing relevant examples. I'm not sure what some reviewers meant when they found a gap between the examples and the problems at the end of the chapters, but I did not have this problem anywhere that I can recall.
What I like most about this book, compared to most of the math books I've seen in my day (more than enough, I assure you) is the format of the writing and the exposition of the problems. There are clear, clear connections made between visual and mechanical aspects of the problem. When you are working a linear algebra problem from the book, you should have a good idea of visually what it looks like that you're doing, where columns and rows are positioned, what elements from each are multiplying by the other and what the end result should look like before you get there. I don't typically get this vivid connection between the abstract visualization of the problem and the actual mechanics in other books, but this one poured it on consistently and I really enjoyed that.
The writing style is also casual enough that you don't feel as if you're being led through chapter after chapter of rote and repetition. Instead, it feels like you're being led further and further toward your understanding of the subject and you really are learning something new along the way at each step.
Regardless of what others say, I think that if you have the financial means and the interest, you should definitely include this book in your repertoire of linear algebra references. It is a gem, a guide and an indispensable reference for the subject. There is no other linear algebra text like it.
An OK book.......2006-10-04
While its a very readable book I felt at times that the book leaved out some important details about certain topics. For example it gives an example and explains how to prove something yet gives no directions on how to disprove it, problems still require to do it. Another example later in the book is when it explains how to do something, shows an example, then mentions that some problems have multiple solutions but gives no directions on how to approach these kind of problems or how to make sure that you have all the solutions, you're on your own spending hours trying to put everything together.
Customer Reviews:
VERY different from most introductory calculus books--simply amazing!.......2006-09-23
This book, unlike most Calculus books out there, is meant to be read and understood. The way that Calculus is taught nowadays, people use books that are 90% problems, exercises, and examples, with an emphasis on computation. This book is 90% prose, and the emphasis is on cultivating a deep understanding. In addition, the book does away with the gap between "Calculus" and "Analysis", choosing to begin with a more mathematically mature perspective...but providing ample explanation for students who have not seen the material before.
This book is exceptional for self-study. I would recommend it to anyone learning calculus on their own, who actually wishes to understand it. This would make an excellent supplement to one of the standard Calculus textbooks, since it addresses just about all the classic weaknesses of these texts. I wish colleges would use this as a textbook, but alas, that would require a drastic restructuring of the curriculum.
This book may come across as "hard" to students, but this is only because it is structured in such a way that one cannot not get through it without understanding the material. Also, a student finishing this book will be ready to dive into more advanced analysis courses, whereas students using basic intro calculus textbooks will find themselves very poorly prepared for these things. The current calculus books with their emphasis on mechanical computation, allow students to get through without understanding the material, and that is why they come across as "clearer". In reality, they are much less clear than this book.
Great book but only if you want a deep treatment.......2005-09-14
This is one of the best math books I have ever used; Apostol does a great job of giving you intuition and telling you why the topics are important. The exposition is very clear.
However, this is not your usual Calculus I book. The level of approach is halfway between an intro to calc class where you learn HOW to calculate derivatives/integrals, and a real analysis class where you learn why derivatives and integrals are related and their axiomatic foundations.
Bottom line: this is a great book if you want to understand calculus deeply. It is a warmup for real analysis. However, there are probably better books if your only interest in calculus is for using it to solve engineering or physics problems.
Not for the faint of heart!!.......2005-09-03
Both this book and the second volume were used in my Honors Calculus classes, and let me tell you, it's not for the faint of heart!! The book is very good, but unless you're willing to get into it and really go at the problems and theorems, it's not going to do you much good. If this is your first calculus textbook, don't expect detailed explanations and pretty summaries of the chapter, since it doesn't have them; do expect lots of theorems and complicated proofs.
If you want a Calculus book, don't think twice - it's Apostol!.......2005-07-28
I would say that if you were only allowed to have two math books on your shelf, these books should be the two Apostol Calculus volumes. It's really hard to find texts which are both elegant and rigorous. Mr Apostol gives Calculus a so beautiful treatment that the book is suitable for both a serious study and a pleasant reading. The exercises are also great - you will have a lot of fun doing them.
The best math book I have ever read.......2005-04-21
This book is extremely well-written and leaves you with the feeling that it couldn't have been better. A tribute to this fact is that it is still in its second edition from 66 and, though it is rather old, has kept its quality.
It has a good number of exercises (usually between 15-30 per section/topic), which is less than most standard calculus book, but the difference is that the quality of the exercises here is much higher, and you will be surprised when some months later, when tackling some problem for another course, you will remember having done the exercise in Apostol. It also has answers to all the exercises (except for the ones which require a proof, rather than a number as a result). The problems range from easy to very hard, but usually there won't be more than two problems per section that one won't be able to do upon first reading and a little thinking.
The writing of the book is very good and rigorous, and it covers some topics that are not present in most calculus books. For example it has a small seciton on partial derivatives, it covers the weighted mean-value theorem for integrals and rearrangements of series. There are many other topics that don't usually fit in a calculus course, but the introduction of these when you are still learning it makes the connection between the topics much clearer. After having read the book from cover to cover, it has now become a very useful reference that never leaves my table. Also, because it is rigorous and has a broad number of topics, if you learn this and vol. II now you will save a lot of time later in more advanced courses such as analysis, differential equations, linear algebra and to a lesser extent even differential geometry and probability.
Because of its nonstandard approach, I think that this book is unsuitable for most people learning calculus for the first time (especially if you are taking a course and not just studying at your own pace). However, it (along with vol. II) is mandatory reading for anyone who wants to study math, in my opinion.
Average customer rating:
- Linear Algebra
- Excellent summary
- excellent detail
- Linear Algebra Review
- What a great help...
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Schaum's Outline of Linear Algebra
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ASIN: 0071362002 |
Book Description
This third edition of the successful outline in linear algebra--which sold more than 400,000 copies in its past two editions--has been thoroughly updated to increase its applicability to the fields in which linear algebra is now essential: computer science, engineering, mathematics, physics, and quantitative analysis. Revised coverage includes new problems relevant to computer science and a revised chapter on linear equations.
Customer Reviews:
Linear Algebra.......2007-09-25
This is the Higher level Linear Algebra book that covers the entire topic range. Helpful.
Excellent summary.......2007-05-03
I wanted to brush up on Eigenvalues for a compression algorithm and this was the perfect way to efficienctly recall everything from college. Very useful and succinct.
excellent detail.......2007-03-14
this text is very user friendly. the sample problems are completely worked out, so there is no guessing where the solution comes from. it's a great review book, and very easy to understand for a first time learner of linear algebra. although, i did find a few typos and insignificant errors. for example, when asked to find a parametric representation of the line passing through the point p(4,-2,3,1) in the direction of a vector u=[2,5,-7,8] , the equation for x2 is mistyped as x2=-2+2t. (2t where 5t should be)
Linear Algebra Review.......2007-01-04
I have found it to be an excellent addition to my library.
What a great help..........2006-11-15
I found the book to be a great asset in getting re-acquainted with Linear Algebra and vector calculus basics. Lots of example problems with solutions and some to work on your own.
Book Description
This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications.
Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices and their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra.
Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.
Customer Reviews:
Unhelpful in the extreme.......2007-09-14
Chapters 1, 2, and 4 are pretty well done up to a point. The explanations, examples, and problems are well written and can be followed without cross referencing other texts and pages on the web. You will learn the basics here without too much of a fuss.
Unfortunately, the book has a nasty habit of circular proofs. The author leaves out vital parts of the explanation in the text, referencing other parts of the text, which reference other parts of the text, and then ask you to solve the underlying proof yourself without explaining the fundamentals at all. The book also references FORWARD into chapters you have not gotten to yet in order to solve current proofs. This is not at all helpful. If your professor requires you to solve any of the proofs in any section you will be lost. Good luck.
Chapter 6 is an all-around disaster. Unless you have seen the material before, you will not get it here. The explanation at the beginning of the chapter cannot really be called an explanation. It is more of an obfuscation. The notation is not explained, it is assumed you know it or can figure it out on your own. The proofs in this chapter are a maze of unexplained concepts and hidden information.
Chapters 8 and 10 are more like the first chapters in usability, but the proofs are just as jumbled.
Intervening chapters from the ones I have described are applications of the material from previous chapters and are optional.
Buy another book (or two or three) as a supplement. You will need it.
One of the WORST textbooks I ever used.......2006-08-31
This book sucks at explaining, half the examples in this book just refer you to other examples/exercises that you have to complete yourself. HOW DOES THIS HELP IF YOU HAVE TO DO THE PROBLEM YOURSELF??!? Half the practice problems are theoretical questions that do not help you in understanding the concept whatsoever. The only thing it does is confuse and frustrate you more. Whoever uses this textbook to teach is obviously incompetent and/or has not looked it over at all.
A math book.......2003-07-17
This isn't the easiest linear text I've scene. This also isn't the hardest. The book has a ton of applications, which is good if you're an applied math, engineering, or science major. If your interests are in pure math the applications are still a nice little side note. The book's explanations are explained as clearly as possible without giving up any rigor. At first I didn't like the book, but after looking at several other linear textbooks I realized that these authors did a good job of explaining a difficult topic.
Best math book I've ever had.......2000-05-09
This book is a fabulous resource... explains things in as clear a way as Linear Algebra can be. If you want deeper understanding, many concepts are described in more depth, and most proofs are given in detail. It's not filled with cartoons and useless pictures like some textbooks, but clear, concise explanations of what turns out to be an interesting and fairly simple area of mathematics.
Book Description
This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.
Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms.
For statisticians and engineers.
Customer Reviews:
Excellent Book.......2007-10-02
I used the 3rd Ed. in UC Berkeley's MATH 110: Linear Algebra, then used the 4th while grading homework for the same class the next year. I think the book is fairly comprehensive (though by itself not enough to prepare one for grad school), and very well-written. The exercises at the end of each section span a wide range of difficulty. The book is self-contained, except for a few basic results from the calculus (one has to know the linearity properties of derivatives and definite integrals, i.e. derivative of linear combination is linear combination of derivatives and similarly for integrals), yet does sort of assume prior knowledge of linear algebra. At UC Berkeley students have already taken MATH 54: Linear Algebra & Differential Equations, which includes a brief treatment of vector spaces, linear transformations, eigenvalues, etc. I wouldn't say this book is "not for the faint of heart," as some reviewers put it. I think it's ideally suited--essential, in fact--for entering juniors majoring in the any of the mathematical sciences. If this book is your first exposure to linear algebra, then I highly, HIGHLY recommend chapters 12 and 13 of Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition), and chapters 1-5 of Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications.
An excellent book, but not for everybody.......2007-04-15
In the great game of textbook-writing, there is always the question of which textbook is "definitive", "comprehensive", yet also "accessible" and a "pleasant read". I will say that no textbook can possible exist that can cater to everybody. Such is the case with Friedberg's "Linear Algebra".
Rather than praising or complaining about the book, I will instead describe exactly how the book is written, and the reader can determine for himself/herself whether this is the book to buy.
The book is written "bottom-up". Instead of introducing a general concept, delving into detail, and then expanding again, in a sort of holistic approach, the book starts very rigorously. He begins with definitions and axioms. This includes definitions for the numbers "0" and "1" and their axiomatic properties.
Using these axioms and definitions, he proves basic theorems. He will then demonstrate several examples that relate to these theorems. In the exercises, he will ask you to prove corollaries to these theorems, or perhaps little theorems, that may help in later proofs. He will also introduce definitions and completely new types of problems in the exercises. Thus, the exercises are NOT supplementary - they are essential to the reading.
Subsequent chapters will repeat the process. He will introduce new definitions, possibly utilizing new knowledge from theorems proven in previous chapters. Then he will introduce and prove several lemmas and theorems. He will introduce a few examples for these theorems. Then exercises. Etc.
Most importantly, the author expects that the student learns through proofs. He expects that, by the very fact that you are able to prove something, you understand the material on a deeper, analytical level. If this is how you operate, this book is for you. If you can't understand a topic unless you see how it can be proven directly from what you already know, then this book is for you. However, it is rare to see concrete examples that are applications. Rather, the author presents everything in an all-encompassing, general manner, and leaves it to you sort out the details and specifics. This can be potentially unhelpful.
Overall, if the proof-based approach is what you're looking for, I haven't seen any book that presents the topic of Linear Algebra in such a concise fashion. Now I leave it to the reader to decide whether this is the book to buy.
Best book on 2nd course in linear algebra.......2006-12-20
If you are taking a second course in Linear Algebra then make sure your instructor use this book. Mine did I am glad she did. Also don't skip chapter 1 and 2 go over all the proofs and as many homework problems to reinforce the concepts. My first instructor didn't cover much from chapter 1 and 2 and I am glad I dropped the course however I hated this book because I didn't know those concepts from the first course in Linear Algebra. Mastering those two will open the way for chapter 5 and 6. We covered a little bit of 7 and I simply now love this book for the wonderful treatment of linear algebra. One of the best book around and after reading this compare any other book on linear algebra and you will know why this book is a bestseller in its category.
Overall Good Book.......2006-11-30
Before I bought this book for my course in linear algebra, I looked through these reviews and saw that this book would be concise and informative (and at times frustrating), so here is what I found.
You are using this for a second course in linear algebra but I have found that it also works for a first course in the subject. In my course we covered 6 of 7 chapters (touched on chap. 7) in a semester and I thought it was a good pace. While this book focuses on proofs, it provides some computational examples and does not assume you have already taken a course in linear algebra. If you want a book focused on applied lin al, look somewhere else, but if you want to know this stuff theoretically, this is a great book.
This book can be challenging at points but if you sit down and think, you will understand because the explanation is generally good. (An exception for me was the section on Dual Spaces). Also it can get annoying that the book does not mark vectors in any way (bold, arrow on top...) so in some places this can be a bit confusing. The only reason I am giving this 4 stars is because the book cuts a few corners like these.
Overall, I would recommend this book for either a real first course or a theoretical second course in linear algebra.
Great Book!.......2006-02-25
This book is great. I used it for a second course in linear algebra. I can really say that I understand the subject now, which I definitely couldn't before. The material is presented in a readable and yet rigorous and abstract fasion. My only problem with this book is that it leaves so many proofs to exercises and doesn't give the answers to most exercises.
Book Description
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.
The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.
* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon
NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems
Customer Reviews:
A new version of a classic book.......2007-02-21
I bought a copy of this new book and I have its old version with Hirsch and Smale as its only authors. Main differences between these books are some new chapters covering chaos and the exercises. Old version has better chapters dealing with linear algebra. I find this new version hard to read and it leaves many details to be filled by the reader. I would say that the new version is still a good choice for a second course in ODE or supplementary text for a graduate course. I gave it four stars.
Excellent Book.......2006-05-05
This is a great introduction to the next stage of differential equations after a first course. Devaney is a master of presenation, and makes everything seem easy. It is not as encyclopedic as some other books on this material, such as Arnold and Perko, but it is easier to read and still covers the most important advanced material.
good, not ideal.......2005-12-08
the two books by hirsch smale, one with devaney, seem like good books, but I am not crazy about either, at least from the few pages one can search online here.
the latter book with devaney just seems a dumbed down version of the earlier book by the two more famous authors. i expected that earlier book to be far better, but found to my regret that the two books actually share almost the same first page, and the main difference noticeable in the early going is that the 2 author work is poorly written, and the 3 author one is not written much better.
it is clearer but seems to be talking down to the reader in an annoying way. so neither is the absolute pleasure to read that the wonderfully written text of arnol'd is, or the classic of hurewicz. i would skip these books and get arnold and hurewicz instead.
New Edition.......2004-02-26
You should be aware that there are two similar books with similar titles by the same authors. The old edition is a hardcover all green book by Hirsch and Smale called:
"Differential Equations, Dynamical Systems and Linear Algebra"
The second with the lorenz attractors in yellow on the cover is by Hirsch, Smale and Devaney and is called:
"Differential Equations, Dynamical Systems and an Introduction to Chaos"
Now, that may be obvious to you, but it is important to note that because those are VERY different books (which I have both of right here). The 'old' one is a more theoretical text that mainly addresses linear systems and is organized more like a math monograph than a contemporary (i.e. with pictures and examples) textbook. It is difficult for most people. The newer version is COMPLETELY different and is written for a more diverse audience. It starts with linear systems but then goes into nonlinear systems and discrete systems. It is somewhat similar in character to Strogatz's Nonlinear Dynamics and Chaos. If you do not have a very strong abstract theoretical type of math background I would not recommend you start learning about differential equations from the "old" edition. You will find it very difficult. If you are used to a general abstract presentation of results you should be fine. For the NEW edition the level is very different. I would guess that courses in multi-variable calc, elementary diff eq, and linear algebra (if you understood them) would be sufficient preparation. Both books are excellent, just be clear on what you are looking for.
Book Description
Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.
Customer Reviews:
Great book!.......2007-10-08
I've used the third edition in conjunction with Professor Strang's excellent video lectures on the MIT OCW site. The combination of the two is absolutely superb. If you do the exercises at the end of each section you will learn linear algebra even if you never intended to!
Unsurpassed clarity - and this book just got better!.......2007-09-15
Professor Strang has taught Linear Algebra for many years to legions of one of the United States' top institution. So give him some credit, for starters...
This book is inimitable in its clarity and in how it yields so much insight. I have many books on Linear Algebra and I think this book is worth its weight in gold. I know of no other book that teaches the fundamental subspaces so well.
The book covers standard material in Linear Algebra (and then some) and has a strong matrix-oriented flavor (as opposed to a book giving an algebraic treatment - look for Valenza if you want that).
I don't understand what some of the complaining is about by some reviewers. The book is not abstract enough, not formal enough? No first treatment in Linear Algebra is or should be - that is Linear Algebra 2. Besides, matrices are pervasive in all fields of engineering, physics, applied math and other disciplines and later on the student will advance to even more complex issues (such as numerical linear algebra) and they simply cannot afford not to have seen the standard matrix treatment. In fact, that would be the reason it's so widely taught - because it's so useful. It's no use delving into abstract treatment if one doesn't understand the most basic facts about why it is that you can solve a system of linear equations.
Best of all, his lectures now can be seen on MIT's Open Courseware site.
I have used this book since the second edition. I believe this 4th edition is the best edition yet. Unlike some other books on the market, this new edition is a fully thought-through new edition (Strang has been restructuring his book throughout all editions, ever making this more clear and insightful). Not bloat at all. I wholeheartedly recommend it. In fact, I believe you might get hurt using some other books that are on the market that do a very lousy job on teaching this subject (such as Lay). This book is the gold standard.
Non Fiction.......2007-09-03
A somewhat dry but good text on the subject. An introduction to vector spaces, among other things. I just looked at fishpond and the price for a new hardcover is $300. Is this delivered by a strip-o-gram, or what? Unbelievable.
Anyway, it is good, but no way it is worth that sort of money given the subject and its age.
Excellent book.......2007-05-28
I stumbled across this book a few years ago when I was visiting someone in Pittsburgh. I woke up early, and having nothing else to do, I picked up Prof. Strang's book to read and I could not put it down. I am a mechanical engineer with an aversion towards mathematics - but Prof. Strang's conversation style completely won me over ( I refer to 2nd and 3rd editions of his book). Since then I have purchased three other books authored by him, and I have watched many of his videos on MIT's OCW website, and I have never felt let down.
No author can write a book that will be acceptable to every reader, and I find some of the criticism of his books exceedingly harsh. If you do not know how to multiply matrices, then this is not the book you want to start with, but once you know a little linear algebra, his video lectures and this book will give you a completely new perspective.
A solid explanation of linear algebra.......2007-02-21
First off, this book is not well-suited for students who have never seen a matrix and have not yet mastered the basic calculations of how to multiply and add matrices, or for those who have never seen Gaussian elimination. There are many other textbooks that do nothing but provide you with exercise after exercise of manual computations of inverses and determinants that are better suited to that purpose.
That said, for anyone taking a course in linear algebra who actually wants to know more than the rote mechanics of matrix multiplication and Gaussian elimination, this book provides a succint explanation of what matrices actually represent. And I've held onto the book as a reference now for many years (referring to the 3rd edition).
I came across it as a graduate student studying for doctoral qualifying examinations. Someone suggested that I check out Strang's book from the library as a supplement to my utterly confounding graduate school text. It was a godsend! I pored over Strang's book, doing computations on occasion, and taking copious notes of his thorough explanations of concepts like null space, row space, column space, and eigenvalues. After that, I had no problem passing my qualifying exam in linear algebra!
Product Description
This informally written text provides students with a clear introduction into the subject of linear algebra. Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary.
Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.
Customer Reviews:
And watch the FREE videos on the MIT site.......2007-08-09
It's hard to rate the textbook by itself, because I'm also watching the videos of the author's class on the MIT Open Courseware website. But no doubt, the two of these together are an unbeatable combination. The website videos are excellent. I do find the book somewhat hard to follow when I try to read it before watching the videos, but afterward, it's quite clear. So maybe I'd rate the book a 3 by itself, but a 5+ in combination with the FREE online videos. Strang is an outstanding lecturer.
What a terrible book!!!!!.......2007-02-25
I'm not one to be picky about an author's style of writing, but in the case of this book I have to be. It is COMPLETELY FALSE to call this book "introduction to linear algebra", what the title should be is "Gilbert Strang's ideas about linear algebra that no undergraduate in a first course in linear algebra will ever understand". Talk about inconsiderate instead of clearly explaining the steps involved in solving a problem, Strang will simple talk about some example of his personal interest that does nothing to solidify the main idea within the problem. How about the worked examples, he picks some arbitrary matrices and makes it so they can be solved in a single or very few steps that helps a lot when you want to know what's going on within the examples. Homework its freaking great to, the first question within each section is easy and than the second question and beyond is some kind of proof that you have no clue how to even approach because the author assumes you mastered the simple part in one question. I guess when you're a professor at MIT than you're automatically given the right to write terrible textbooks.
The engineer's classic........2006-07-26
People say that mathematical truths never change, and that's true enough. New concepts, applications, and techniques keep emerging, though, so math teaching needs to keep up with the times. Strang has done an outstanding job of keeping this book current and relevant.
It's not a mathematician's math book - this is aimed at people who need results and needs computational techniques more than they need crystalline theorems. That's why it's so helpful to see applications like Markov models, Kirchoff's laws, and Google's analyses of the web. It's also helpful to see examples worked in Mathematica and MATLAB, the tools of choice for desktop exploration of numerical systems. It's startlingly easy to come up with a 100x100 system of equations, and just nuts to try to solve it by hand.
Strang assumes some amount of calculus in this book, something that other books on linear algebra sometimes skip. That raises the bar for the readership, but also opens up topics like change-of-basis in function space, including Fourier analysis. It also allows differential equations to be addressed as linear systems. Even without calculus, though, a reader is exposed to the singular value decompostion, QR and other matrix decompositions, and considerations in performing the computations. I found a few oddities, such as the description of a matrix's condition number. That has great physical meaning when it's taken as the ratio of the matrix's highest and lowest eigenvalues, but Strang gives a definition that I found less intuitive.
Such oddities are rare, though. Even though this book covers many topics, its emphasis is on clear and applicable presentation. I recommend this to anyone studying linear algebra or who, like me, has to brush up on basics not used in many years.
//wiredweird
A wonderful book.......2006-05-24
As someone who already knows the basics of the subject, I guess I'm looking at things with the benefit of hindsight. However, I needed to shore up my own knowledge of Linear Algebra and thought I might as well turn to Strang for a refresher and a different approach.
The result is that I am truly pleased with this book. His writing is lively and engaging. Linear Algebra has a phenomenal tendency to get dry and Strang does an excellent job of turning the subject this way and that so that one can admire it from every angle. In particular, there are three major approaches in this book that make it stand out.
1. Strang places heavy emphasis on vectors, vector spaces and transformations. This is good preparation for future study in Linear Algebra. This will provide an intuitive understanding of linear operators on vector spaces later.
2. Another reviewer mentioned that the book utilises a discovery-based approach. While this might be a disadvantage when you're in a hurry, the approach prepares one well for learning more theoretically oriented subjects where self-guided discovery is imperative. In this sense, I think the discovery approach is far superior to others and prepares the reader well for future studies. The problems are really fun (although I personally think they are much too easy). Many of the questions require light-weight proofs without undue formalism (not really required at this level). These pseudo-proofs really do help build understanding of the subject. Maths-phobes will not even realise that they're fleshing out the subject themselves.
3. The didactic approach taken in the book is conversational and informal. When added to the freely available video lectures at the OCW site, given by Strang himself, you really have a perfect introduction to the subject of Linear Algebra. The lectures are superb and Strang is an excellent teacher. His enthusiasm and passion for the subject is obvious and infectious.
I really wish I had learned Linear Algebra from this book initially. The book does a good job of encouraging geometric intuition and visualisation. That said, I do not think the book is an ideal book for maths majors. The primary problems being too little exposure to abstraction and problems which are too easy. However, I do believe that the book can be used in conjunction with a more rigorous approach in cases where the latter gets just a touch too dry. There is time to develop the rigour in theoretical Algebra courses at a later stage, with the added benefit that the reader will have learned the experimental approach to learning taken in the book.
I suppose some will find Strang's excitement over Linear Algebra a bit of a pain, but personally I think this conveys the sheer joy of pursuing an intellectual endeavour. I've always bordered on disinterest with Linear Algebra and this has been very much dispelled. I like to be reminded why I chose to study mathematics in the first place sometimes. While I can see that this book isn't for everyone, I really enjoy it and recommend it highly.
Try it before you buy it?.......2006-03-14
I guess that's my best advice for anyone considering purchasing this book -- see if you can find a local copy first to examine. Pretty much everything you'd find in anyone else's linear algebra intro book is in his, so it's mainly a question of whether or not you like Strang's presentation of the material. Yes, he's kinda wordy, yes he probably gets a little overexcited at times and has too many exclamation points. However, you're going to spend a *lot* more time doing the problems than reading the text, so such reasons for disliking the book ring pretty hollow to me.
Other comments:
-- I *like* the fact that the book "reads like a novel;" it goes a long way towards providing motivation and insight relating to linear algebra, which a more "formal" (read: stuffy) book doesn't. It's clear to me that first and foremost Strang is trying to *teach*, whereas other books sometimes really make me wonder whether or not the author isn't just trying to demonstrate how clever they are.
-- I would agree with the "basically a good math book" reviewer who said it's not that great as a reference book and is light on advanced material. True enough, although given that it's "Introduction to Linear Algebra," I can't fault it for this.
-- On the other hand, Strang is teaching at a somewhat more abstract and advanced level than many intro linear algebra courses do (remember, this is used at MIT, and in many or perhpas even most cases the courses there simply are more challenging than the same course at other colleges). If you can wrap your mind around the abstraction and really understand what Strang's trying to commuincate, you'll end up with a better grasp of linear algebra than what most people have.
If you're in a working world situation and just "need some answers" without being force to learn where they come from (which Strang does tend to make you do), there are various "engineering mathematics" books that are probably a better buy if you're just after one book (I like Peter O'Neil's). I'd also suggest picking up a copy of a book like that if you're using Strang's book for self-study -- getting a couple of viewpoings on the same subject matter is enormously helpful when the first just isn't "clicking" for you.
Strang will occasionally state something like, "blah blah blah may seem difficult to understand now, but eventually it'll become quite obvious" -- and he's correct, at least if you go through his book and understand it. A good example of this is with least squares fitting -- the formulas for performing it really are "obvious" if you've been playing Strang's game all along; you really can just "write it down." I've yet to find that true with other books!
P.S. -- I definitely think that linear algebra wouldn't be a good career choice for the reviewer "bitlooter"!
Average customer rating:
- Great introduction to mathematical economics!
- A must read text book for any economics undergrad student
- A must read for graduate students in economics
- not so good
- The best math textbook for economist
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Fundamental Methods of Mathematical Economics
Alpha C Chiang
Manufacturer: McGraw-Hill/Irwin
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ASIN: 0070108137 |
Book Description
The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. the book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.
Customer Reviews:
Great introduction to mathematical economics!.......2007-07-18
I enjoy Chiang's writing style. I've been reading up on mathematical methods in preparation for a masters econ program, and feel very comfortable with the material thanks to this textbook. The international edition is a good bargain.
A must read text book for any economics undergrad student.......2006-04-02
I found it extremely easy to read and at the same time rigorous enough to settle the bases. The author knows very deeply the economics students needs of mathematical methods and achieves a precise and complete explanation of all notions I needed to know for my undergrad course. I strongly recommend it during the first or second year.
A must read for graduate students in economics.......2006-02-26
Alpha Chiang's text should serve as the foundation for all quantitive analysis done in economic theory. It is an invaluable teaching tool for graduate students in economics and will help them better understand the mathematical techniques that have become so necessary for economic modeling.
I am not a highly quantitative person myself, but I found Chiang's book comprehensible and a useful reference guide in my gradaute economics classes. Along with Hal Varian's "Microeconomic Theory" and Jan Kmenta's "Econometrics", I would say that Chiang's "Fundamentals of Mathematical Economics" should serve as sacred literature for any prospective graduate student in economics.
not so good.......2005-10-14
the text carries to excess the concept of "keeping the presentation as simple as possible". but in general you cannot understand or solve problems with a fifth grader's ability to abstract them.
especially the relunctance to use matrix notation makes some topics actually harder to understand once they become more complicated.
furthermore I find the structure quite confusing since the text amounts to a monotous blabla - clear definitions might be helpful and some rigor would keep the reader conscious instead of drifting off. after all the text is not so bad but I think we deserve something better. blume might be better.
The best math textbook for economist.......2005-09-30
That is why it used everywhere, in nearly all economic departments. I strongly recommend you buy this book. It really helped me in my undergrad, and it is helping in my graduate courses. If you want to buy another book to accompany this, get Simon and Blume book. One person (probably little masochistic) was saying that Chiang has so many examples, blah, blah, blah. Look, not everyone is a math genius, undergraduate student's need Chiang, it's even useful for graduates. Math is used quite too excessively in economics...showing off?
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