Well written with good ideas but check your geometry
930050
Someone who understands geometry should have proof-read this book.  Check the 45 degree angles on the diagrams.  Otherwise, the graphics are great and the book is well written and easy to understand.  I'll have to wait until the snow is gone to try out the concepts.
1785344
This book is pleasant to browse, containing various lore about geometry, history, geography and the occult.  It is very attractive visually, containing many nice photographs and diagrams.  Unfortunately, given the important place of mathematics in the book, I am afraid to say that the author appears to know rather more about art and mysticism than he does about mathematics.  For example, on page 52 we read: "For modern mathematics irrational numbers are those that cannot be pinned down to a few digits.  They are, in fact, repeating decimals that go on forever."  In fact, of course, irrational numbers are characterized by having decimal expansions that do not repeat.  Also, on page 51, it is apparent that the author does not understand the construction of the mathematical curve known as the Conchoid of Nicomedes.  This is a pity, because it would have been very easy to give the correct description since the relevant diagram is already included on the page.
2354250
All in all, this book is very well written, especially if compared to other books in similar titles. Concepts are explained concisely and no extra irrelevant materials covered. That said, it still can be improved in two areas:
1. This book is very useful if you read it together with the companion wookbooks. The book I read was for weblogic, which, unfortunately, was kind of out dated. It took a while to get the first example up and running. After that, the rest is quite smooth.
2. The later part of the book, starting from chapter 12, seems to be done more in a rush. Even the writing style was kind of different from earlier chapters. Also there were quite some repetitions that probably could be omitted and replaced with more elaboration and examples of the topics.
4902460
Good suggestions but some information needs further study.  Easy to read and the plans he suggests are easy to follow.
608821
It's a very interesting book. It gives me a new view of math. Even though I attended Peking University (Chinese best university) to study math when I was 15 years old. I am sure if I could have read this book when I was in primary and high school, I would have been much more interested in Math and then may have gone to a quite different career path.

I would like to give this book a five star if it doesn't contain some obvious mistakes. I have read about one third of this book so far and find two mistakes. A critical one in the appendix to prove that the sum of 1 over all primary number is divergent. It would be greatly appreciated if the author can fix those mistakes in the next version. Also, If the author would like to know the details of the mistakes I have discovered, please feel free to contact me at l.wen@griffith.edu.au

Anyway, it is a nice and inspiring book to read.
261323
This is an excellent review of the math of pursuit and escape paths. I have not read the book completely, but I concentrated my reading on a couple of problems I was mostly interested in: The Lady in the Lake problem, and the Lion-and-Man problem. These two problems are strictly connected, and have more immediate geometric explanations than the equations of the problems presented in the book. However, these alternative explanations are missing in the book; too bad because they add a lot to the understanding and intuition of the problems. In one case actually, (Lion-and-Man problem), I believe the outcome of the problem  is different from the one provided. This doesn't detract from this enjoyable book, which is well written, with very approachable, step-by-step math passages.
96024
There are a few errors in the book that the editor should have picked up. In the Appendix 2A on pages 41-41 the text has the sine and cosine switched. Page 41, line 7 should read in parentheses: (that is AB/OB and OA/OB) referring to the Figure 2A.1. The error is repeated in the text under the figure. Segment AB is opposite the angle theta, segment OA is adjacent to the angle. The sine of the angle is the ratio AB/OB not OA/OB, and the cosine of the angle is OA/OB not AB/OB. This appendix begins with the authors desire to "complete the review of essentials for readers who may have forgotten some of their mathematical training, by recalling the simple definition of the trigonometric functions sine and cosine..." Doesn't inspire confidence in the rest of the book which is laborious to read with prolonged arguments that I found very difficult to follow. Wikipedia's discussion of Bell's theorem was more lucid and understandable. Another error is on page 432 (yes I read the entire tome, including all end notes). On line 12 the thickness of the myelin sheath of the human nerve cell is stated as "precisely of the order of 10 to the 5th power in cm" Of course since the range of thickness is .5 to 2.5 microns (or .00005 to .00025 cm) the text should have placed a minus sign before the fifth power. The author is obviously very brilliant, perhaps absent minded, but certainly not a very good writer in my opinion. Of the 20+ books I have read on Quantum Mechanics, this one is near the bottom.
2438253
book has a lot of good information and recipes, but also has some basic arithmetic errors so one has to be very careful when using the recipe measurements.  Check your work and make sure your calculations are the same as in the book. If not, recheck the calculations and measurements and use your numbers.
3696070
Enjoyed the creativity of this book as it gave me new ways to look at familiar territory. My one complaint is that some points were not clear. The author needs to be more precise in his explanations.
4460050
I actually wanted to give this book 3.5 stars, for reasons you'll see below, but the facts are simple.

1) This is a very short book.  The Appendix begins on page 117.

2) The book's one saving grace is the author's interesting analysis of the geometry of the circles.  It's quite satisfying to see a diagram starting from scratch, with the addition of a circle here, a pentagon there, a circle here, etc. ending up with a complete replication of the crop circle under discussion.

3) Aside from the geometrical analysis (which I found compelling), the remainder of the book is little more than a brief diary of a few visits of the Dutch author to a few well-known circles.

4) For padding, there's a nice six-page spread of color photographs, with absolutely no analysis.

I love that the author took the time to do some geometry to figure out how to recreate some of the more famous circles, and for that I give this book kudos.  The rest of the book is not very interesting, though, and I've read many other clearly superior books.  For one, it seems like the book was self-published and in need of a professional editor.  It almost seems like the author had some good ideas and diagrams, presented them and explained them, then completely ran out of time and/or steam toward the end.  The final 30 pages are mostly throwaway references to photographs of circles.

I recommend "The New Circlemakers" and "The Gift" instead.
3285057
This book a lot of good ideas. That is one of the problems with this book, it is filled with a lot of good ideas that are not really developed. The book is 50 miles wide and an inch deep.

It is no surprise, the author at one point talks about how important ideas are.  I have found that a lot of people have a lot of ideas, the value of a leader is the ability to turn those ideas into reality. Since before history man has had the idea of human flight, it took the WRight brothers to turn that idea into a reality.

It is also clear that the author is part of the religious right. I didn't expect that while reading a book on leadership that such a bias would bleed through.

There are better books out there.
1362594
This is one beautiful book. The whole book is one long thread about geometry and vectors. To make this review short, I'll say you absolutely *must* have this book if you want to set yourself on the proper track to Linear Algebra. In fact, this book could almost be considered an Analytic Geometry book 'done right.' But be careful: I said almost. By that I mean that some staple AG stuff is missing. For instance, no long discussions about a plane intersecting a sphere, no quadric surfaces. So it does lack the sort of drill exercises you need to succeed in an AG class - but such stuff is not its purported goal, anyway -  but then again, your 'vector 6th sense' will increase tremendously with this book. I wish I had discovered this book while I was having my Analytic Geometry. Now I'm taking a Linear Algebra class and I'm glad I found this book.
It also is full of other interesting insights and relations to other topics, including some applications to Calculus (motion) and some topology.
4925422
This book is a very good book as introduction to linear algebra and as a bonus you get to learn some neat little Mathematica programming hacks and techniques.  However, there are some weaknesses that should be noted.  While it would seem that the book is aimed both the practical and theoretical audience, it tilts more heavily towards the theoretical.  While engineers and engineering students will get a lot out of the book, mathematicians and math majors will be much happier.  If you are of a practical mindset, you are able to skip the sections that are of no interest with little loss of continuity.  The book would be more valuable if it contained more information on matrix manipulations and calculations.  There are some errors, but they are minimal and make themselves evident if you carefully follow the material.
649783
I ha to use this book this summer .  The geometry concepts are not clear an unorganized.  I had  instead to make my lessons from Big ideas.
My students also did not like the Spring Geometry student edition.
1539399
Wickham is an incredible writer.  I read this book the first time when I was in college.  I thought his ideas were quite interesting and his humor fabulous.  I was particularly take with the material on Einstein. He had one criticism of general relativity that I found quite persuasive.  I have persued it over the years with physicists, some of whom are well respected and in one case famous.  Non of them answered Wickham's objections.  This is not to say the theory is wrong.  The equations work fine in predicting outcomes, it's only Einstein's verbal characterization of gravitational force being replaced by curved space time.  Although it is not widely publicized it has been replaced by particle(gravitons) interchanges.

It was only in rereading this book and his The Misbehaviorists last month that I realized that he was more than a good writer, but a profound thinker, the equal of anyone I have read.
4669622
This book was quite hard to review. There are parts I found extremely interesting, and other parts I thought were full of sloppy thinking and misleading analogies. But overall, I think it is a worthwhile book to read. I think it is appropriate to divide the book into four separate sections, each of which deserves to be reviewed separately.

The first part is an attempt to show that some of the rules of algebra (particularly the rules for manipulating signs) are really counter-intuitive, and also an attempt to gain the perspective of an elementary algebra student who cannot understand why the rules are what they are. It is this part that I think is the worst part of the book, and in his attempts to show that the rules are counter-intuitive, all he manages to do is show that _his_ intuition works quite differently from _my_ intuition. This part is the section in which I found the sloppy thinking and resort to false analogy which I mentioned earlier. It seemed to me that there were things the author just didn't understand, but as I read further in the book, I found that he actually understood them even though he didn't seem to at first. This section would get three stars if I felt generous, or even two, if I were to review it alone.

The second part (actually intermixed with the first in its location in the book) describes the difficulties that mathematicians (even great ones) had in comprehending the concept of negative and imaginary numbers, and as such it provides some historical background for the rest of the book, which justifies its inclusion. If I were to review this part by itself, it would get three stars, meaning "it's OK," but it hardly justifies the book.

The best part of the book is the third. This is a very interesting attempt to come up with an algebra that differs from the usual, where he has to maintain consistency, and so he looks deeply into questions as to what further modifications to traditional algebra have to be made to go along with a postulated change. Much like the introduction of non-Euclidean geometry, the process leads to an odd-looking algebra, but one which fits together, and it is this part that I liked well enough to rate as five-star, bringing the overall rating for the book to four. This part made the book worthwhile for me.

Finally, the author ends with one very long chapter that probably summarizes what _he_ wants the book to be, though the previous section is what _I_ want of the book. He advocates a concept of a mathematics that would be suited to explaining problems of physics in a more natural manner, even if it might look different from traditional mathematics. I would have been happier if this part were shorter, though I think the author himself probably considered this part to be the major thesis of the book and this is why he devoted so much of the book to this part. This part is actually interesting enough that I'd rate it 4 stars, though as I said I'd prefer it more streamlined.

That is an overview of the book: very uneven, with both very good parts and bad, but if everything is all combined, the total package is a pretty good one.
4370931
If you are looking for abstraction with little in the way of intuition I suggest Conlan " differential manifolds"

If you are an applied mathematician or physicist this book is for you.

I have always beleived that to truly grasp mathematics one must be provided with a reason for WHY things are the way they are and WHAT IDEAS the expression must express. This is best done with examples and exercises.

I digress.

The book restricts is exposition to two and three dimensions. Some of the topics can readily be bootstrapped to higher dimensions.

The book starts with basic ideas of curve, directional derivative and tangent vector in Euclidean space with a sprinkling of differential forms to wet the appetite.

It then moves into the notion of frame fields along curves resulting in the Frenet formulas which express how the frame fields change along the curve. These are expressed in terms of the frame field themselves giving ideas of curvature and torsion.

The book then abstracts these concepts to show how we can talk about change of frame fields along arbritrary directions not just along the curve. The tools used to do this are the covariant derivative and connection forms which can then be used to develop connection equations ( abstracted analogue of frenet formulas ) and then the cartan structural equations.

The book talks about isometries and defines euclidean geometry as those properties preserved by isometries. It then abstracts once again to surfaces in R3 using patches and appropriate conditions on the overlap without introducing manifolds although these are briefly mentioned later.

We then see how calculus in euclidean space can be adapted to surfaces using these patches. The corresponding concepts of function, differentiability and tangent vectors on these objects is introduced. Forms on these surfaces are introduced and their application to integration theory on these surfaces is developed showing how forms on the surface are " pulled back" to euclidean space using the idea of differential of a map and integrated there. The integration gives the volume ( area ) of that surface. Stokes theorem is introduced.

We now move into the idea of shape operators on the surface and show how these describe how the normal vector on the surface move in various directions giving ideas of mean and gaussian curvature . We see a very nice interplay of algebraic analysis leading to a geometric analysis.

The book then deals with studying geometrical properties on surfaces using the Cartan methods described earlier.

We then see how to define intrinsic geometry of any surface. Namely those properties of the surface that are preserved by isometries. From the definition of isometry we see that these rely on on the concepts of tangent vector and inner products. Shape operators and mean curvature are not intrinsic.

We now study the geometry of surfaces specifically the intrinsic geometry without reference to an imbedding space ( R3). An abstract "surface" is endowed with an inner product. A different inner product gives a different geometry. We talk about gaussian curvature and covariant derivative which are intrinsic.

Geodesics are introduced as is the gauss bonnet theorem which relates a geometric property to a topological one.

The book concludes with a chapter on global properties ( 2 d surfaces ) especially how gaussian curvature influences geodesics and how the two completely determine the geometry of the surface.