5 comments about Schaum's Outline of Vector Analysis.

1. I bought this book many years ago and soon I felt it extraordinary. My idea has not changed along years. Clear, comprehensive, readable, even pleasant. You can really learn vector analysis step by step without a teacher. And you learn to use what you learn. All topics about vectors are explored, included differential operators and some differential geometry. It covers also tensor analysis (the last two chapter are on curvilinear coodinates and tensor). In my opinion there is a little more than a mere introduction to this subject. When I began to study tensors, I did't find a book that is completely satisfaying for a beginner. I turned out to my old Spiegel and the light was. Read first the last two chapters of Spiegel when you begin with tensors: you will understand basics concepts and you will avoid troubles. I feel to owe a debt of gratitude to this book and its Author. A true didactical masterpiece.



2. Hooray! Spiegel does a wonderful job of summarizing Vector Analysis simply and to the point. His definitions and explanations are concise and down-to-earth. Keep in mind this is an outline, and the format remains that way. But this is an extremely effective resource for this subject-- well done, IMO.
   
   The examples are often proofs, but are also a comprehensive overview of applications and standard problems. One criticism: sometimes, Spiegel introduces 'new' concepts (e.g. Jacobians) in the problems without defining them in the outline text. So you have to go through the sample problems (with answers!) to get all the stuff that's in the text. Also, if this is your first exposure to Vector Analysis, the problems are just problems, without a lot of background explanation. Much is self-explanatory, but once in a while, especially without previous Vector Analysis exposure, I can see where it would be a bit overwhelming to just jump into it. There isn't a lot of context for some of the non-proof problems. I've read/studied other books on the subject, so I'm not completely new to the field (but I am certainly no expert, either!)
   
   The last chapter on Tensor Analysis covers a ton of material in one lengthy chapter. A separate source on this complex subject would be a better way of approaching this area. Still, the definitions remains quite straight-forward and to the point, and the sample problems provide a nice overview. Call it a good quick-reference.



3. This book is worth a whole lot more than the paltry sum they're charging. You really can't go wrong with any mathematics or physics material authored by Murray Spiegel but this text is in a class by itself. Even though it's a Schaum's "Outline", you'll find that it's actually a first rate textbook. I'd say it's an outstanding learning tool given the fact that I found myself actually enjoying working through it!



4. The book offers a good introduction to vector analysis for the undergraduate student. Quite simple, lot of practical examples. It is a good supplement to a more theoretical textbook. Also the price is fine.



5. Different schools of thought have different checks and balanaces. These checks and balances take the forms of rules and norms with their own judgements of right and wrong. Probably the human mind can only take so many rules and norms at any one time; each school of thought somehow subconsciously understands this.
   
   Still, time and the wisdom that comes with it should make what I am saying obvious to all. And perhaps my point is indeed obvious to Prof. Spiegel. If so, he should note in his book somehow. Either in the discussion or in the problems.
   
   My main point and problem with this presentation on Vector Analysis is that the definition of vector is graphically inadequate. Pictorally speaking, position, separation, and displacement vectors have features that many other vectors don't. Such vectors must be treated somewhat differently than velocity, acceleration, and force vectors. Now velocity and acceleration vectors may have different features and need to be treated differently, but my point has already been made in identifying the existence of unique features of location vectors.
   
   Murray R. Spiegel has proven himself again and again in book after book as a great master of many topics as mathematical subjects. From Complex Variables to Vector Analysis.
   
   Still, he makes no mention that mathematicians take great liberties when they define concepts. And vector as "a quantity with magnitude and direction" or, worse, as "a vertical column or horizontal row of numbers"
   are exact examples of such liberties and their problematic consequences.
   
   Bottom Line: Great presentation of the symbols and the symbolic logic of vectors. Conceptually, Graphically, and Physically, speaking the analysis (presentation) is quite weak and quite misleading.

No comments about Intermediate Algebra.

1 comments about Elementary Algebra.

1. Thank you for the great book.
   You cannot get a 5 STAR because it could have been a little cheaper.
   regards,
   Luiz

5 comments about A Mathematician's Apology (Canto).

1. As Hardy himself makes clear in the beginning, he would never have written such a book if his mathematical powers had not failed him in old age. I do feel like this book is more an apology for not being a mathematician anymore than for having been one. As for all true loves, the time for judging and summings things up comes only when the joyful days of passion are over. I was hoping this book would give me an inspired first person view of what is higher mathematics and what is like to be a real mathematician. I found that it is not a good book for that, it doesn' t even try it. What it accomplishes instead is giving a precise, objective, cruel, marhematically clear picture of the drive, the ambition, the passion for excellence in any activity, be it a sport or a science that makes the life of the ones who dedicate their life to it so more pure and meaningful. It also poses some tough, fundamental questions regarding how much of your life one can dedicate to one single "abstract" passion without having to go trough some really bitter times and regrets in old age. My personal answer is that what really counts, in the end, is how much you loved and, what was sorely missing in Hardy's life, how much you express that love. But for some people, gifted and cursed at the same time, that is still not enough.



2. One of the most scholarly books that has been written in the 20th century, G.H. Hardy's thrilling memoir tells a story that other people are too afraid to discuss. Hardy's depressing transition from mathematical genius to near vegetable is a telling example of the archtypical fear of cerebral atrophy that resides among even the most resilient and foolhardy among us. This concise "novel" reads fluidly and especailly so for when written by a mathematician and serves to enlighten the world of the multi-talented nature of a world class mathematician. All in all this book is a rare find and should be read by people of all ages: whether a young aspiring mathematician or an old decrepit intellectual.



3. This short book has long been one of my favorites. Hardy's philosophical musings may depress some but they ring so very true. Hardy is quite honest about life, art, mathematics, and his failing abilities. For example, his statement, that a very small minority of us are really good at what we do may sound depressing today. But the fact is true.
   
   I can recall when words such as super, excellent, awesome etc. were used judiciously and very rarely to describe truly significant achievement. Today, doing one's job, albeit poorly, is described as excellent.
   
   What I most like about Hardy's book is it's honesty and respect for the reader. A suggestion. Read the book proper BEFORE wading through C.P. Snow's forward. After about the second read tackle the forward.
   
   A must have.



4. Hardy was a giant among early 20th century mathematicians. It is difficult to overstate his importance. He was one of the first to show that mathematics is as much art as science without having to have interpretation (such as Dunham's "Journey Through Genius...").
   
   This is what makes this book so poignant. Hardy realizes that he no longer is Hardy. In today's mathematics world that may not have been the case given the immediate communications possible between humans which may have kept him going. However, it may have been that he was suffering from the onset of dementia or Alzheimer's - it is difficult to tell given his admissions of not being up to the task - regardless, this book is overwhelmingly sad.
   
   Anyone who cares about math should read this and thank Hardy for his contributions - plus they should have a copy of "A Course in Pure Mathematics".



5. I learned about this book while reading another book, "Prime Obsession" and it awoke my curiosity mainly for two reasons: because it was a interesting subject, an apology for being a mathematician, trying to explain the purpose and usufulness of mathematics, and because I wanted to know more about Hardy's life, since I knew a few things about the nice story of this mathematician and Ramanujan. This is a brief book, there is a foreword that serve as a brief biography before enjoying Hardy thoughts, which by the way really grab your attention, even you learn a few lessons of simple mathematics proofs that try to show the beauty of it. I consider this book valuable for everyone.

2 comments about Calculus: Early Vectors.

1. As far as the actual value of this book as apposed to choosing another, I have no frame of reference to make a judgement. It appears to cover most topics of Calculus..



2. This is without a doubt the worst textbook I have ever owned. Okay, so it's calculus. It's a hard subject, and people do need to understand that; I know I do. However, this book goes to the unnecessary limits to ensure that anyone who is trying to learn calculus without the aide of a Mathematics Professor will surely fair, and waste countless hours trying to learn the notation that is used in the book, but never used in lecture or in the application courses (such as Engineering and Physics).
   
   The language used in this book talks with a tone of "theory", and never speaks in "teacher". It's amazing how my professor can go over the material in class, and it'll make perfect sense; solving the problems are... not a problem. However, learning a section without the professor is simply a nightmare.
   
   If you really want to learn vectors before learning the "actual calculus", I recommend purchasing an introductory physics text, and learning from there. Perhaps this is good book; if you eat, breathe and sleep theory talk. Otherwise, try to find another calculus book...

5 comments about Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition).

1. I bought Chartrand's book to teach myself how to
   understand and to do proofs. I worked every exercise
   in the text. Now taking some upper level proof based
   courses, after being out of school for 20 years, I am
   finding that I am more comfortable with proofs than
   most of the people in my classes. The main thing that
   helped me was the clear communication of the methods
   and the ample opportunities to test out my knowledge.
   The only thing I that would have helped me more is that
   most problems at the end of the chapters do not provide
   explanation. I had to trust my knowledge, which is not
   always a good idea. Still, the authors do a good
   job of conveying the concepts and I do very much like
   chapter zero. I am a school teacher and I show that
   chapter to my secondary students. Oh,that chapter
   explains "good" mathematical writing style.



2. If you look at the "Customers Who Bought This Item Also Bought" section on this page you will see several highly rated books that cover similar topics. They all are priced approximately $100 less than this book because Addison-Wesley (the publisher) has decided to market _Mathematical Proofs_ as a text-book rather than a book-book.
   
   This is tragic. The only people who will encounter this fantastic text are students with no choice but to suffer the rapacious fancies of textbook publishers.
   
   I was once such a student. Everything Penelope W. Yaqub "Fawzi M. Yaqub" says in her review is spot on. I have kept only three books on my personal shelf from my days as an undergraduate in mathematics. This slim volume is one of those.
   
   I recommend this book to anyone -- whether a student or hobbyist -- wanting to better their understanding of what mathematics is really about. It is also great training for thinking logically about all topics, from mathematics to current events
   
   I would have rated this 5 stars if the cover price were not so outrageous.



3. I own the first edition. Although it it has a high price compared to many other books that cover introductory proofs, it is a purchase that I have never regretted. My personal favorite chapter is #3. For me it was the breakthrough chapter. For those that have not read the book, the authors take the simple idea of even and odd integers, and use them to present the basic nuts and bolts of proofs, a real eye opening chapter!
   
   OK, I went ahead and bought the second edition... If you want to save about $40 on a new purchase, get this book from Pearson International Publishing. They will not see you a book in the USA or Canada, but you can buy it from an international book seller (EG: find one in the UK). If even at discount the price is too high, get the book from your library. If they do not have it, use the interlibrary loan service.
   
   I do want to say my praise of this book should not be taken as a condemnation of other books by other authors. Again, use your library to see the various approaches are to learning to do proofs in mathematics. Also look at logic and proofs in the philosophy section of your library.
   
   j.



4. This book pretty much changed my life. My only regret is I didn't find it earlier. What different choices would I have made if I were comfortable with mathematical proofs in high school or early college? I recommend this book to anyone who has an interest in understanding mathematics but for whatever reason never learned or were never taught it by their teachers in school - I'm certain I was never taught these ideas. This book is great for self study and the material should be accessible to most high school students.
   
   The book starts off with basic ideas about sets and some logic. The real "Aha!" moment for me was the explanation of implication and biconditional in chapter 2 and how they're used in direct proofs in chapter 3. The examples about even/odd numbers are perfect for someone feeling their way thru new ideas.
   
   After reading this book I went back to college as an adult and obtained a BS in mathematics. It's foolish to dwell on what might have been, but one can only imagine.



5. very, very, good book for those who are taking Proofs and want to learn how to proof some problems in math......

1 comments about Single Variable Essential Calculus: Early Transcendentals.

1. it is a nice book. but be careful when you order: it contains only from chapter 1 to chapter 9.

1 comments about Applied Calculus.

1. This is a fantastic book. Explanations are clear, and there are plenty of relevant word problems. Makes a difficult course easy if you're willing to put the time into it.

No comments about Elementary Algebra (2nd Edition) (Carson Developmental Mathematics Series).

No comments about Algebra 2, Student Edition.