2 comments about Dr. Math Presents More Geometry: Learning Geometry is Easy! Just Ask Dr. Math..

1. This is an interesting book to read through and gives clears information on the logic of proving or using various theorems. Information is separated into chapters on circles, triangles, quadrilaterals, etc. How much you will enjoy this book is probably dependent on how you want to use it. If you have a specific question you need help answering, it may not be of use to you unless you have time to skim through the appropriate chapter, and then you may or may not be lucky and find it. It is not intended to be a text and doesn't necessarily progress in that structured, complete form. It is a fun,math "read" with nice diagrams and clear explanations.



2. Will be using to assist students in HS Geometry as well as passing their state graduation exam.

2 comments about Pipe Fitter's Math Guide.

1. Very boring book. Only very basic pipefitting formulas and math. Good for first timers.



2. I stumbled across this book about 10 years ago in a trade publication. At that time craft training was imperiled by the decline of the trade unions in our area and I was searching for a tool to help bolster training for young and inexperienced employees. I strongly disagree with the previous review that states this book is very boring. Over the last ten years I have bought about 30 copies of the book. Basic math principles as they apply to the pipefitting trade are laid out very well and easy to understand. Also, the author does a really good job of laying out step by step, the proper way to use a scientific calculator when working trade math formulas.

5 comments about Trigonometry the Easy Way.

1. This book was not that helpful to me. I have had trigonometry before and purchased this book as a refresher. There are very few examples throughout the text, which makes it very difficult to solve the exercises at the end of each chapter.



2. This is by far the worst workbook I have ever encountered. I would give this piece of crapp "negative infinity stars" just to express my anger, if it were possible. I have spent a month and a half of my summer studying for trig using this book which ended up as a waste of effort and, most importantly, time. The summer is the only time where can I boost my brain and get ahead of everybody, and even sometimes become smarter than the teachers (hee!hee!).
   The thing that annoys me the most was the blasted organization of this book. The stupid fairy tale was the entire gist than learning trig. Each chapter was focused on a dilemma faced by the king and his servants, and hardly anything about trig. It took me 3-4 days just to interpret each chapter due to these: the lack of examples, the lack of practice following the lesson before the new stuffs are taught (I call it "try it"), the tone is for a 8 year old (hey, wow! a 8 year is learning trig), and learning the materials can be a toil since the informations are, rather than stated directly like most workbooks, implied in the story, meaning you will waste time rereading the stupidstory again and again trying to comprehend it. Another thing, you have to understand the story in order to actually learn trig in T.E.W (who said that!).
   Mr. Douglas A. Downing has written a pain in the head. Why does he have to teach us trig by the usage of a gay fairy tale. He could have taken an easier turn by just teaching trig directly to us instead of deriving ways to make the story relevant to trig, then we are more into the story (a reason why I didn't purchase Calculus the Easy Way). You have to give him credit for being creative but all his works just turned out to be B.S. Maybe he was on crack. One thing is for certain, I will never purchase anything with the name Douglas A. Downing on it.



3. Like many other reviewers, I found the attempt to imbed trig into a fairy tale very unamusing at best. The math concepts covered were hard to keep straight, since you had to keep re-reading the crappy story to refresh your memory. I can't imagine that anyone could really learn trig (or anything) with this kind of approach. And the author shouldn't have even attempted to write it...not without some serious background work in creative writing anyway.



4. Ok, so I'm an archaeologist, just finished my masters degree in archaeology. However, I specialize in 3D visualization. My master's thesis was on 3D laser scanning of fossil casts. Anyway, I don't have a background in computer science or math, but because of this book I was able to pickup enough trig to write a 3D graphics program and finish my masters. I'm no rocket scientist, and I hate borring math books. So say what you want about this book's corny storyline, at least it's not a list of formulas and numbers. I recommend this book.



5. This is a great resource for teachers who want to teach the difficult concept of trigonometry in a simple, steady fashion - through the use of story telling.
   
   I like it over the textbook approach.

1 comments about 501 Math Word Problems, 2nd Edition (501 Math Word Problems).

1. Overall I think this is a quality product, that packs a lot of bang for its price of $12.95. I'm using it to prepare for the GRE later this year, and have found it to be great at stoking your learned math skills as well as introducing new concepts. Very straightforward, comes with the answers to each question answered and explained in depth at the end of the section. It also comes with a free Online practice center which you can use as many times as you want with similiar problems in the book. The online site offers free detailed answer explanations, diagnostic reports of where you stand, and instant scoring. It covers the basic math skills up through Algebra and Geometry most colleges and graduates schools are looking for. I wouldn't suggest it for a math intensive review for Engineering or Physics, much too simple for that, geared more for the social sciences. The only drawback is that I have found some answer errors in the text, so beware, and double check the answers by working through each problem.

5 comments about Geometrical Methods of Mathematical Physics.

1. This book presents the basic concepts of differential geometry in a clear, concise manner using modern notation. Schutz's writing style is very readable and there is a considerable breadth of coverage. In areas where one might wish for greater depth, Schutz provides excellent references. My only regret is that the physical applications chapters weren't longer. An excellent starter book and a good quick reference if you continue in differential geometry, GR or field theory.



2. This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.



3. I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
   Eventhough its not the worst book out there its not the best either.My advise,buy a better book.



4. Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.



5. Advanced mathematics, such as differential geometry and topology, plays an important role in many areas of physics. This excellent book covers one of these topics, differential geometry. This is a topic essential for understanding general relativity and gauge theory. There are several good books aimed at physicists that cover differential geometry. While some of these have a broader scope than this book, nevertheless this book is my favorite one for differential geometry.
   
   The topics covered include those necessary for reading advanced treatments of general relativity (such as Wald or Misner/Thorne/Wheeler). These include manifolds, fiber bundles, tangent/cotangent bundles, forms, Lie derivatives, Killing vectors and Lie groups.
   
   Following this basic material a chapter covering some applications to physics, one example is electromagnetism. Up to this point the consideration of manifolds had been fairly general. In the final chapter the implications of adding a connection, and then a metric, are considered.
   
   Why do I think this book is so good? It's not the breadth of material covered, this book is very focused on a limited range of material. It's the quality of the presentation for what it does cover. The development follows a logical order, the writing is exceptionally clear and the diagrams are very useful since Schutz explains them so well.

5 comments about Discovering Geometry: An Inductive Approach.

1. OMG! This book was so complicated to understand. They expect you to know everything. Because of this mindless crap, I failed Geometry and had to take the regular one. And the worst part is that they don't include enough examples to explain how to work the problem. I wouldn't recommend this God forsaken piece of crap to anyone who wants to do good in Geometry.



2. This book was the bane of my existence throughout 9th Grade Geometry. Having had a year of a real math book this year I am finally able to realize just how stupid the book was. It treats the student like he or she is about two years old, does not provide the information necessary for exam review, and is far too colloquial in general. In addition, it has no answers in the back, just "Hints" in the back of the book that either do nothing at all to help or solve the problem completely without explanation. It also says "SHAME ON YOU" if one looks at the hints without first trying the problem. Personally, I don't enjoy being chastized by a math book, especially one with such a bad approach to Geometry,



3. This is by far the worst text book i have ever seen or had to use. Unless you are an expert at geometry or have a great teacher this book will be useless to you. It gives no anwsers to the odd problems and there is no glossary. Because of this i dont know if my answers are right or wrong. I usually try to find the way to solve problems myself but since this book gives no examples on how to do anything i cant. I feel sorry for any other person who is like myself, and is forced to use this sorry exuse for a text book.



4. I am an eighth grader taking Geometry, so it is obviously advanced. However, this book is not helpful AT ALL in learning. It is so frustrating to not even have a glossary in the back to find definitions, and the book does a very bad job of explaining tough concepts. If you are a teacher, please try a different book.



5. This geometry book is clearly written, has interesting visuals, usea excellent teaching strategies, and is simply the best book available. High school students at various levels seem to respond well to the textbook. I know math teachers who think this book is far superior to any other.
   
   I wish they'd had geometry books like this one when I was in school!

5 comments about Topology from the Differentiable Viewpoint.

1. In all practicality, for general math students this book is nice for the library, but by no means is it essential. In fact, it's not worth the $25 in most cases. There are so many outstanding Math texts / topics out there, it is doubtful and political that Milnor's Differential Viewpoint deserves its popularity.
   
   I found this book helpful as supplementary reading for Calculus on Manifolds, so I am a minority student. (Majority student = Linear Algebra Done Right.) Spivak's book motivated the need to look carefully at the first few sections of Milnor's book. The definitions in Milnor coincide perfectly with Spivak.
   
   I left Milnor's book with a good intuition about the inverse function theorem, manifolds, and the rank theorem. I also gave a small study to Sard's Theorem, but I had no need to venture into what apparently was the meat of the book...
   
   It is arguable that the Inverse Function Theorem, Manifolds, and the Rank Theorem alone warrant buying this book, despite it only represents the first 2 sections of it, and is far from the total purpose of the book. Nonetheless, that's all I wanted to gain at the time I was reading it.
   
   On the other hand, if you really are a Differential Topology student (small minority), you are the one who wouldn't need the review because you would know what you are trying to get from the book.
   
   On the other hand, students who buy this book who don't know why will probably do nothing more than collect dust with it.
   
   
   
   
   
   
   



2. This book packs a lot of interesting material into a small volume. E.g., I picked up another book recently that started talking about cobordisms right off the bat; despite my having a couple of shelves full of well-known Dover, Springer, Cambridge UP etc. books on topology, differential geometry, mathematical physics, etc., Milnor's tiny book was the only one I found that could help me understand what cobordisms are right away. The book also uses many illustrations to help understanding.
   
   I demote this to 4 stars only because Princeton UP's price is a bit high; many years ago I was lucky enough to find a used copy of the old U. Virginia edition, and paid much less.



3. 
   Despite the lovely subject matter covered in this book, it more importanty gives one a taste of Mathematics as an intellectual discipline. It in outline shows how a mathematical theory - in this case Differential Topology - is constructed and consquently what mathematicians actually do and think about.
   Anyone who would like to appreciate Mathematics as a field of study rather than just learn some math should open this book.
   
   Better still, the prerequisite is only multivariate calculus!I have long thought this book should be the third year of calculus rather than differential equations or complex analysis.
   
   Additionally, for the novice it is the only entry I know of into the mysteries of high dimensional geometry, that amazing almost unbelieveable accomplishment of the human mind.
   
   There is a Star Trek episode in which a blind woman wears a dress of sensors which enable her to know more about her environment than a person can know from seeing. She knows exact distances and dimensions, can detect minute movements, can process the complete spectrum of light. In some sense she sees better. Modern topology and geometry are like that sensor dress for seeing higher dimensions. While we can not visualize the sphere in 5 dimensions, we know more about it from these mathematical theories than a five dimensionally sighted being ever could.
   
   Today, mathematics is often considered to be just a practical tool - like a spread sheet - or a toaster oven. We forget its power to widen our imagination, to frame the unimaginable. This book reminds us of this and shows why Mathematics is the Queen of Sciences.
   
   
   



4. I would suggest to use this book as a companion to more serious books on topology. Weighing in at a mere 51 pages, this book accomplishes what it needs to: a brief, succinct introduction to topology mostly based on the work of Brouwer. There is a nice mixture of topics, ranging from Sard's theorem to Poincare-Hopf theorem. The proofs and ideas are not fully rigorous or developed, but that would be quite a bit to expect from such a short exposition.



5. Milnor's "Topology from the Differentiable Viewpoint" is a brief sketch of differential topology, well written, as are all books by Milnor, with clear, concise explanations. For students who wish to learn the subject, it should be read as a companion to a more substantive text, such as Guillemin & Pollack's Differential Topology or Hirsch's Differential Topology, as too much of the material is left out for this to be adequate as a textbook. OTOH, it does make for good bedtime reading.
   
   While this book is highly regarded among mathematicians, it is not without its faults, namely,
   - it fails to cover many topics of importance, such as tranversality (only mentioned in an exercise), embeddings, differential forms, integration, Morse theory, and the intersection form;
   - it only cites some theorems without proving them, or it leaves the proofs to the reader;
   - it offers proofs of many theorems that are really only sketches without all the details;
   - manifolds are only defined as subsets of Euclidean spaces;
   - there is only 1 collection of 17 problems at the end of the book, which are used to introduce important concepts; and
   - it probably moves too quickly for true beginners, packing a lot into only 51 pages.
   
   So don't buy this as your only, or even first, book on differential topology. Oddly, many of the faults that I listed above are simultaneously strengths, in that it can be read very quickly, with relatively little effort and a high rate of retention. Milnor really emphasizes the topology of the subject, giving applications such as the fundamental theorem of algebra, Brouwer's fixed point theorem, the hairy ball theorem, the Poincare-Hopf theorem, and Hopf's theorem. Most of the book focuses on degree theory, but there is also a nice introduction to framed cobordism, which is rare for an elementary book. Guillemin & Pollcak's book was based in large part of this one, and could be read together, with G&P giving more elementary explanations and additional topics, while Milnor's book provides a proof of the Sard theorem and the Pontrjagin-Thom construction. The exercises, though not particularly difficult, do provide a good opportunity to practice proving theorems in the subject, as there are no hints for them, as one would find in many other differential topology books, and they are not separated by chapter.

1 comments about College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics).

1. Thank you Dover!! This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book contains all the classical theorems with full proofs, including many theorems that belong to the so called triangle geometry that was developed in the last quarter of the nineteenth century. Due to geometry software the subject is becoming popular again. The book also contains a treasure of exercises, but no solutions which can be a nuisance (but than you should consider buying an other text). If you prepare for a mathematical contest or if you are interested in a complete overview of the classical plane geometry (for instance after reading Ross Honsberger's "Episodes"), this is your book.
   
   The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry.

3 comments about Teach Yourself Calculus.

1. Hundreds of Calculus texts claim to teach this rich field of mathematics easily or well. Most texts send students running out of class. As an educator, my goal is to explain all of the fundamental techniques of Calculus, with their proofs, in a manner and pace that a tenth grade inner-city student can comprehend. I believe this is quite feasible using this book as a comprehensive guide if the teacher loves math, uses the text, and loves the students. The self-tests are cogent and progress gradually in complexity - keeping pace with the growing power of the chapters. This is the first book I reach for when a Geometry or Algebra student asks me "Do you think I could ever take Calculus?" You bet! Hugh Neill's masterful "Teach Yourself Calculus". I recommend it without reservation. N. Montero, MD



2. I was looking for a little book of calculus I could carry around with me, my textbook from school is just too big. I knew that such a book wouldn't cover every single topic in calculus, but if it covered the major stuff and had good presentation, I would be pleased, since the rest could be filled in using online resources, etc.
   I saw this book at the bookstore, and thought it looked pretty decent, it was only $13, so I bought it. I'm glad I did, the introduction to e and natural logarithms is the best I've seen. The author is able to explain concepts in the most clear and concise manner, such as is rarely seen.
   This book is the best little book of calculus I've seen.



3. I have not yet finished the book; I do think it is clearly written.
   
   I would have awarded four stars but due to some incorrect answers that cause one to waste time trying to find where the reader (me) made a mistake, a penality of one star is assessed.
   
   There is nothing more frustrating.

No comments about Geometry, Student Edition.