5 comments about Statistics for People Who (Think They) Hate Statistics.

1. The book was brand new and arrived very promptly! The only thing I would caution you when buying this book, is that is does NOT include the CD with it...so research a little further before purchasing. Overall, great experience and a great book!



2. This text is easy to read, easy to understand and therefore not intimidating as far as Stats Texbooks go.



3. the order matched the product description perfectly and i got my book in 2 days as promised. i was left extremely satisfied with my purchase.



4. This book is a good but it truly does not cover biostatistics as well as Clinical Epidemiology by Fletcher or Designing Clinical Research by Stephen Hulley. I think that the other two books are a better buy for your buck. This book is well written but very specific in whom it will appeal to--namely those users who need assistance in the use of the computerized statistical packages.



5. It seemed the author in an attempt to make statistics easier, made it more difficult. Also, my professor does not like the book, and is forced by the universoty to put it on the syllabus and recommended. Also, very few exrcises to work from and practice.
   
   Do not buy this book, not worth the money or time.

5 comments about Journey through Genius: The Great Theorems of Mathematics.

1. This is a great book whether you are a fan of, or a practicing mathematician. Good reading and a great library reference addition.



2. First things first: You have to really like maths to appreciate this book. If you have ever wondered how to prove Pythagoras' theorem geometrically, or would like to find out how Archimedes estimated pi, this is the book for you. If not, buy another.
   
   The book has a good mix of stories, explanations and mathematical proofs. It actually answered questions I have been wondering about for a long time (proving Pythagoras' theorem and finding the formula for solving second order equations), but even if you are not the nerd I am, there is a big chance you will find this book fascinating.



3. This is a required text for a class of mine. Easy to read and follow along even if you're not a mathematically inclined person. Enjoy.



4. Not being a mathematician I can only reply as a lay person. I hope William Dunham sticks to his task of transmitting the thread of how certain mathematical ideas evolved from previously unrelated sources.I will be re-reading this particularly in terms subjects such as the connection between the binomial theorem and the developmentof calculus and other explanations you do not find or cannot follow in textbooks. Long live William Dunham.



5. A very enjoyable reading for those interested in basic math mixed with just enough relevant history to make it interesting.
   
   My only quibble is that even though we read about Gauss, the prince of math, in two large sections in different chapters, his work is not showcased as main topic.

5 comments about The Humongous Book of Calculus Problems: For People Who Don't Speak Math.

1. This is the best calculus book I have ever seen. The author really does understand that quite a lot of people (like myself) struggle with calculus even if they have been strong math students prior to calc. His "refresher" section is very thorough, and I learned things that I never learned the first time around (synthetic division, the formula for factoring a "non-simple," let's call it, quadratic, and a couple of other things). This is in spite of the fact that I (barely survived) Calc III.
   
   When it comes to the calculus portions themselves, somehow Kelley makes sense! I don't know how he has managed it, but he has created maybe the first understandable calculus text.
   
   High schools that teach AP Calculus AB and/or BC, and colleges and universities, need to scrap their "mathematically heavy" textbooks and replace them with this. Ok, colleges and universities will never do this, thinking that they are training mathematicians and such, but if you struggle with even the "pencil-pushing" parts of calc (like I did), how are you going to be able to understand proofs, etc. anyway?
   
   All high schools should use this. Students' AP scores would thank them for it. I was an A or A+ student in math my entire life until I got to calculus...and then this subject made no sense to me at all and I really could not, for the life of me, understand or solve the problems. It really is a different kind of math, no matter what anyone says. I aced algebra, trig, and pre-calc, so that wasn't the problem.
   
   This book really deserves all the praise it receives. Go through this, then get a supplemental text such as Schaum's to work more problems.



2. This book is truly written for people who really do not speak math...like myself! I understand what he writes about...and my calculus text is ridiculous to try to understand. This seems to be the perfect compliment to a class. Highly recommended. One thing I do wish is that there was some space between the problem and the solution so that we could try to work the problem out...but then the book would be even bigger and that's not practical. I guess just keep on with sliding the paper down the page...



3. This book is good in showing many if not all types of problems for Pre cal review and calculus but its name deceives. I was hoping that it would have practice problems. All does is that it shows you how to solve a type of problem, just once. Its a good aid for those taking calc classes, but its not as good for self study. For that The Calculus Lifesaver is much better to learn calculus, and standard textbooks or workbooks are better for providing practice.



4. Excellent book,I always had serious problems with calculus because I don't had a good preparation on high school,and now that I'm studying University this book was really helpful.



5. I'm going back to school after a long time away. I'd never taken calculus in my first time through undergrad and graduate school so I was nervous about taking it the first time.
   
   This book is handy in that it explains, in pretty simply language, what's going on in a certain step, especially in those steps were people most often say, "Huh? Where did *that* come from?"
   
   If you're looking for a book that gives you the same basic problem asked for in many different ways, this isn't the book. Go for Schaum's or Problem Solver by REA. But this book might help you figure out exactly what you're missing if you're working your way through a million Schaum's questions and find yourself stuck.

5 comments about Statistical Inference.

1. This is the second edition of an excellent book. Casella and Berger put together a text that many faculty began choosing for the first graduate course in mathematical statistics. This second edition is improved over the first and puts more emphasis on the algorithms than the asymptotics. It covers modern topics like resampling and is verywell presented.
   
   When I was a graduate student we used Ferguson and Cox and Hinkley and we also used Lehmann's book for hypothesis testing. This book starts with basic probability and goes on to cover all the bases. It has everything one needs in a modern text on mathematical statistics. I have seen it referenced very often in statistics articles and I decided that I had to get a copy for myself in spite of the high price. i think this should be one of the preferred texts for the first year PhD course in mathematical statistics. It certainly requires a full year of calculus as would any good math stat book but the level is even higher than that and that also should be expected by the students.
   
   Typically first year PhD students in statistics would take this course concurrently with a course in advanced probability that includes measure theory. So the measure theory knowledge gained by the student in the probability course will and should be needed for the latter chapters of this math stat course.



2. This book is absolute misery! I would like to echo another review that basically stated if you have to take a class with this book, just drop it now and save yourself the grief. Truer words were never spoken! The Preface states that the prerequisite is 1 year of calculus. That is an outrageous lie! Maybe if you took calculus at Princeton or MIT, you will have a fighting chance. Otherwise you better have the sophistication of writing and understanding proofs that are on par with a real analysis background, and you will definitely need a firm grasp of all the major combinatorial identities and proof techniques before you even attempt to read it, let alone destroy your GPA with it! There is a solution manual floating around the internet, and that too is worthless. Most of the proof techniques used in that rotten book end up as handwaving, and if you have a well trained professor, you will get crushed trying to use some of those techniques. Many of the answers in the solutions manual are just wrong as my professor has PROVEN to us on a number of occasions. The bottom line is dont believe anyone who tells you that 1 year of calculus is enough to read and understand this book. It simply does not apply to most of us, and Casella and Berger should be ashamed of themselves for trying to pass this off as a first year graduate textbook for anyone other than a pure mathematician.
   
   To further highlight the absurdity of this book, here is a quote from p 237: "Furthermore, with the current availability of cheap, plentiful computing power, the importance of approximations like the Central Limit Theorem is somewhat lessened." Que idiotas!!!!!



3. This is a fantastic book. It is very well written and is a pleasure to read. The problems at the end of each chapter are extensive and help get a very good understanding of the material. This was the required text for a quarter based graduate level course on Statistical Inference. We had an excellent teacher who picked problems very well and that perhaps kept us from getting bogged down. Many of the problems are by no means trivial and require time to solve, which is where a great instructor helps. If you are planning to use this book for self-study, then I would recommend perusing the problem sets from classes, based on this book, that are being offered at some institutions, in order to whittle down the problems to an illustrative subset, before delving into others. Hope this helps.



4. This text is quite good, with numerous examples, but beware of the many errors or cases of sloppy reasoning. A sampler:
   
   p. 319. The maximum likelihood estimator for the binomial distribution, unknown number of trials, is unique. Not true: n=2, p = .4, sample = (1,6) is a counterexample.
   
   p. 265. If S is the sum of k idd uniform (0,1) random variables, then Prob(S <= t) is t^k over k!. Not true: this would give prob(S <=k) > 1.
   
   p. 62, 82, 84: Moments are unique (or non-unique). Nonsense, it is the pdf's that are unique or non-unique.
   
   p. 444. Method to find a shortest pivotal interval. This is a non-proof. Apparently the authors haven't heard of Lagrange multipliers.
   
   Note also that apparently there's no source for problem answers. This may or may not be considered a drawback.



5. the book was delivered in a few days and the condition of the book was good.

5 comments about Data Analysis Using Regression and Multilevel/Hierarchical Models.

1. Like all of Gelman's stuff, damn fine work. Nowhere near as advanced as his Bayesian pubs - and, hopefully, the next book will address HLM Bayesian models in a rigorous manner - it's where the world is moving.



2. Andrew Gelman has written an excellent book about regression models, with examples solved in the R language. He provides enlightning views of even complex subjects, such as mixed-effects models. A reader not familiar with R, should probably acquire some knowledge of R before he/she can fully benefit from the book, but this in itself is a worthwhile investment. (R is freely available; see [...]). Although it is an introductory book, the author manages to convey valuable new insights to more advanced readers. This is a book that after you read it once you will pick up time and again to enjoy the presentation of the topics and to benefit your own work. Highly recommended, in particular to those getting started with R (or Splus for that matter).



3. A great book for addressing how to work with data on multiple levels. It is both accessible and useful!



4. This book is full of examples and very well written, contains everything one needs for deep insight into multi level analysis



5. Andrew Gelman is a top researcher in Bayesian statistics as well as an excellent writer. He has written an excellent text on Bayesian data analysis that uses the Markov Chain Monte Carlo methods for dealing with hierarchical linear models. This book starts out on an introductory level covering a wide variety of statistical modeling problems including logistic regression and multilevel logistic regression, generalized linear models and causal inference. The MCMC methods are taught using BUGS and R. This book is not exclusively Bayesian as both likelihood and Bayesian procedures are presented. The topics are general but the emphasis is on social science applications. It is very comprehensive and has received enthusiastic reviews from well known statisticians including Dick Deveaux, Brad Carlin and Jeff Gill. Jeff's review is here on amazon. Jeff is a colleague of mine and he has written one of the finest introductory texts on Bayesian methods including the hierarchical models. His text is now out in its second edition. Jeff also wrote his book with the social scientists in mind.
   
   Jeff's review has been the most looked at and voted the most helpful on this site. As this topic is a specialty area for him more than it is for me, I recommend that if you are interested in the material in this book that his review is very much worth reading.

5 comments about Complexity: The Emerging Science at the Edge of Order and Chaos.

1. I found the book disappointing. This is definitely NOT in the league of Chaos.
   
   In particular, the coverage of the material of the subject, complexity, was very thin. Waldrop would bring up a subject, address it with some metaphor, and then move on without providing any details. The vast majority of the book is a series of stories about scientists at the Santa Fe Institute who had their inner-child hurt on their journey to discovering complexity. A better title for the book would have been "The Road to Santa Fe: A Tail of Grief."
   
   The book had two redeeming features, the breadth of the material covered and the bibliography; both provide direction for more fruitful reading. Really, getting the feel for most of the subjects covered in this book could be found by putting 'complexity' into wikipedia and reading for a day, though.
   
   Since it was not a complete waist of my time, I gave it 2 stars.



2. If you want to focus on complexity...then go to this book's index and start reading at the first page which mentions Kurt Godel.
   
   As you proceed forward you will then find that this book spends progressively more time actually discussing the mathematical concepts underlying complexity or edge of chaos analysis and less time giving war stories about the founders of the Sante Fe Institute...which studied complexity.
   
   Using this method you will learn about complexity theory which posits that simple algorithms can give rise to complicated outcomes.
   
   Like a program to simulate a flock of birds in flight:
   
   This book says that their flight can be similuated by the application of three simple coeffecients relating to maximum distance between birds, their common rate and distance of movement and finally a coeffecient directed to all birds to encourage them forward to being the center bird and leading the pack.
   
   It doesn't take much creative thought to realize that the rules governing birds in flight must be similar to those governing genetic diversity and ultimately molecular diversity and creation itself.
   
   In this way, ideas "merely" having to do with economics become VERY BIG indeed.
   
   It's not surprising that this book was recommended by Richard Hofstadter (author of Godel Escher Bach) and likened to the (much better) Choas by James Glieck. The point is that the characters that this book introduces are very relevant to the discussions started by Hofstadter and so ably advanced by Glieck.
   
   Read the book...or at least those pages following the first mention of Kurt Godel...and you'll see why.



3. Very disappointed in it. More form than substance. Author was too intent on patting CA schools on the back.



4. If you liked Gleick's Chaos, you'll love this book! Though it isn't a book directly concerning Complexity Theory, it definitely gives the reader a great understanding concerning the developments of Complexity Theory and its differences from Chaos Theory. It will definitely make you rethink even what you have just read.



5. This is a brilliant and riveting account of the birth of the science of Complexity at the Santa Fe Institute told in the form of detailed and human biographical profiles of some the leading scientific voices in the movement. Some reviewers here have complained that this isn't a book of science, per se, but more of history. While you will not find the math, code, detailed analysis of various models, or even illustrations of some of the compelling graphics; you will find well wrought descriptions of the basic theories and the evolution of thinking that delivered them. Getting the social and broader scientific context for the founders is a great introduction. Then you can read their books to get the nitty gritty, and you'll appreciate it better for having gained the long range perspective from Waldrop.
   
   Complexity and emergence are some of the most compelling ideas to come out of the science of chaos - and are real paradigm changing ideas that promise to transform science in the 21st century and beyond. Complexity is the study of how agglomerations of agents behaving individually come to manifest dramatically complex group behaviors (called "emergent phenomena") with a richness you could never derive from the study of the simple components. Commonly studied emergent behaviors include the stock market, economies, flocks of birds and fish, the rise of life from pre-biotic molecular soup, the properties of complex molecules compared to the properties of their component atoms, etc... Methods of study are frequently computer simulations that model emergent complexity using simple rules in a recursive way reminiscent of chaos theory research. Indeed, Langton shows that emergent complexity is along the same continuum as chaos, but pitched at the edge between chaos and static order - literally the "edge of chaos". Some of the same scientists feature in both theories too - particularly Doyne Farmer of UCAL Santa Cruz.
   
   The fact that informational order appears spontaneously seems to violate the 2nd law of thermodynamics - but does not because only information is being created, not energy. Kauffman calls it "order for free". This emergent order is deeply significant in a number of ways. First of all it provides a way of studying the structures of reality that are too messy and dynamic to fit classical reductionist science. But, more importantly, the reality of emergent complexity says something deeper about a creative generative force in the universe which resonates deeply with human spiritual feelings. Seeing order emerge spontaneously feels like witnessing "creation". In the latter chapters we see that evolution moves complex systems closer towards the edge of chaos (lambda around 1/4). Not only does this give a mathematical model for "evolutionary fitness" (which previously had been only definable as a tautology: evolutionary fitness = higher rates of survival (i.e. fitness)) but this also suggests a deeper concordance between a particular degree of chaos and some powerful natural property of phase transition that somehow engenders all the amazing dynamical systems we marvel at - particularly life itself on all its levels, from the swirling metabolic action of cells to the cellular group behavior of complex organisms such as ourselves, and our higher level social behavior. It's not an accident of evolution - it's an important, universal and inevitable law of nature, like gravity or electromagnetism.
   
   Waldrop gets this and he takes you into Langton's computer lab the night he has his epiphany while playing the game of "Life" and other critical moments of inspiration. While this book doesn't spur you to take out your calculator and do the math like Gleik's "Chaos" it makes you feel the magic and gives you a heck of reading list to pursue further.

5 comments about Everything and More: A Compact History of Infinity (Great Discoveries).

1. this book offers no recommendation for what mathematical principles a reader should be familiar with before starting it but any claim of it being accessable to an average reader would be misleading.
   if seems not only like no attempt was made to relate most of what is being described to any commonsense foundation, but that it was academically overwritten into a code that even someone who already knew all the information contained in the book would have trouble following. in my ironic experience the "emergency glossary" definitions themselves contain more undefined or ambiguous terms than any other part of the text.



2. I suppose this might just be his style of writing but I just can't stand it. Having read 9 other math related books over the past month, this was a huge disappointment. He uses all sorts of acronyms and idiosyncrasies that just go too far. I got half way through it and then decided to skim seeing if I could find anything that caught my eye. Thinking maybe his discussion of the Continuum Hypothesis should be good, I read that. Of course, he misstated it, confusing which equality was known and which was hypothesized. This doesn't seem huge, but its just silly that in a book about infinity, DFW states one of the most important undecidable hypotheses in all of math incorrectly and actually presents something that is easily provable (c=2^N0). Why not just one star? He did get me to read 100 pages...



3. I (and many of my professional scientist colleagues) thought Gleick's "Chaos" was one of the worst books ever written on math - so confusing and uninstructive it called the whole subject into question. So it is not surprising Gleick praises this book: it is worse than "Chaos". The grammar, punctuation, and style are so tangled I found myself rereading passage after passage to sort out Wallace's meaning. He uses dozens of obscure, undefined, unusual, and unobvious abbreviations, with the index to them lost in the text, and no index at all to the book as a whole, which is very negligent for a technical work. There is no organization into chapters, just numbered sections which do not coincide with any natural divisions in the material. "Stream-of-consciousness" writing may do for Joyce (though he was not known for lucidity), but it is hopeless for presenting technical material. Many of Wallace's explanations explain nothing: "Fourier Series is vital to understanding transfinite math", he writes, and then blows the subject off with a jest (p 115). And there are plain errors: "when n<0, (p+q)^n becomes the Binomial Theorem" (p 117). Finally, the subject-matter itself is questionable: modern mathematicians still regard infinity as an intractable concept that leads to preposterous contradictions, as Archimedes and Galileo found and as Wallace's own examples demonstrate. "Is the area of an infinitely-long and wide sheet of paper infinity squared?" "Are some infinities bigger than others?" If questions like these have cogent answers at all, it is going to take someone more coherent than Wallace to explain them.



4. I was expecting an exciting book.
   I was disappointed.
   This book has no chapters, lots of text message abbreviations, and many phrases ending in a period.
   
   Three-quarters of this book is background information.
   
   When the payoff comes, actually talking about infinities,
   the reationship among alelf null, cardinality c, and alef 1
   is left as a "problem for the reader" for 20 pages!



5. Since DFW has committed suicide, we will not see an edition revised by him. In re-reading the reviews, it appears that style means a lot. I personally found the book witty. It was a little slow sometimes because of the convolutions he introduced in style, but mostly I kept plowing (and chuckling) through. The librarian who sent back the book did a disservice to some readers. Not everyone likes to learn in the same way. With that kind of attitude, many years ago I would have had Rudin's books removed as too concise to be useful. Of course, there are many mathematicians who love those books for just that reason, and I would have done them a disservice.
   
   I am a physicist with a math minor. To me, the best part of this book was his explanation of why mathematicians insist on the epsilon-deltas of mathematical rigor. No one ever did that before. If I could have read this in high school, I probably would have finished my math major as well as my physics major. Instead, the whole epsilon-delta thing seemed ad-hoc and inexplicable in purpose. I could never accept the need for rigor demanded in advanced analysis.(a drunken prof and Rudin's book didn't help either) DFW showed how a crisis in dealing with the infinite and with infinitesmals led to the development of the what we call the foundations of analysis. Just excellent.
   
   I envied him his high school math teacher, who seems responsible for much of the really good parts of this book. No, DFW wasn't a mathematician and he (in spite of what some reviewers seem to think) knew it. He made clear that he wouldn't be able to do justice to Godel. But incompleteness is moderate difficult. DFW didn't know much about Fourier series, but did know they were important enough to mention.
   For some students, that's the way to get them interested, just mention something and let them go dig (so much easier now with the internet).
   
   Remember the subtitle -- a compact history of infinity. So it is more history oriented than a mathematical tome. I had recently read Lillian R. Lieber's Infinity (which I see has been reprinted) and it has her sparse, but excellent development of the concepts. It doesn't have much historical detail though. So everything and more was a pleasure.

5 comments about Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition.

1. "div, grad, curl and all that" is the quintessential book of vector calculus. No other description I can think of would do it justice.



2. The book provides a very good and concise review of vector calculus. Also helpful is the context of electricity and magnetism making it a good companion book the advanced E&M class at my school [as it is recommended for]. Also good for learning Vector Calculus on its own.



3. I picked this book up, based on the reviews that said it would explain vector calculus to "engineers". I probably read the book 3 times, but I never felt I really _undestood_ the material. A few years later, I think I do understand the material; looking at the book, many of the things I read seem obvious now. I feel this is where most of the reviewers were coming from...
   
   The book is great if you already know the material, and just need a nice, unifying refresher. It is not that great for learning it the first time, since there is very little application of the material, and for me that is what motivates me to understand something. Morse & Feshbach is much more rigorous and dense, but that is where it first "clicked" for me. Also, I think this book is supposed to be in tandem with a more standard Calculus reference. Between two books one might have a better time at figuring things out.
   
   There are a few very good figures in the book that have helped me understand some key concepts (the flowchart relating the different operators and their associated assumptions), but the lack of rigor and general long-windedness of the book could actually be considered a fault, rather than a benefit "for engineers".
   
   Also, buy the cheapest edition of this book you can find. They are all basically the same (only the problems and very minor wording change between editions). Don't think you need to get the latest edition, get a cheaper earlier edition.



4. even if i tried, i couldn't find anything to complain about. The book looks great and it arrived in a timely fashion.



5. This little gem of a book is simply amazing. It managed to explain in a clear and concise manner how line and surface integrals are derived along with how div and curl are tied into those. Something Anton and Larson (with the latter making a considerably better effort) could not achieve. Everything started to make sense after reading/referencing this book.

4 comments about Statistical Techniques in Business and Economics with Student CD.

1. I was pleased from start to finish. It was the correct book, in great condition, it had the CD as stated and it came in a timely fashion.



2. Its a text book, examples are good and the link to excel has been benificial. Good luck on your course.



3. the book was new and was shipped on time! I love it. My books are time sensative and I was able to get them on time. Thanks!



4. The book is a textbook and purchased for class, so of course it fulfills its purpose. I do want to say that Amazon.com's service has been exceptional.

5 comments about The Road to Reality: A Complete Guide to the Laws of the Universe.

1. A book with this breath and sublty comes along a couple of times in a generation. There have been Feynman's Lectures on Physics, Misner Thorne Wheeler Gravitation and others. Penrose is a world class mathematician and physicist (but you already know that). I cannot begin to adequately review this book even handedly because his audience is really other stellar mathematical physicists which I certainly am not.
   
   I had the requisite math background so I understood most of it from cover to cover. But I am under no illusion that I have mastered the material. I can say the content is superficial and tricks the lay reader into thinking he has mastered something when he has not.
   
   We are talking about maths that are even beyond the Ph.D. level of mathematical physics here folks! How can even Penrose condense tens of thousands of pages of textbooks that one routinely must grasp to get where he is with so much facility? The publisher must have thought (and Penrose rationalized) that they could sell more books if they touted that even a mathematically challenged reader could get something from it. This is not the case.
   
   True, I was thrilled at Penrose's intuitive grasp of difficult abstractions that had me puzzled from studying more pedestrian texts on these subjects. Simply breathtaking. I was a page turner from the get-go. However I was under no illusions that I was learning something other than vaporware.
   
   The most interesting idea that caught my eye was his critique of symmetry. Animals have evolved to be pattern recognition machines. Survival goes to the brain that can see the "tiger burning bright in the forests of the night. Who has framed thy fearful symmetry?"
   
   Physicists and certainly mathematicians have been guided by a mystical belief that Nature must follow some beautiful elegant mathematical plan. What is the platonic world of ideas but the symmetry of our own evolved brain functions? -- Good for this time and place but not generalizable. It has worked so far but what if looking for symmetry is wrong. What if framing our equations in terms of groups is wrong. What if Nature is chaotic, asymmetric, fractal?
   
   Penrose entertains that the last 30 years has produced nothing which makes sense or is even observable. Yet physicists blindly 'theory-on' capivated by their presumptions. The point is they have lost sight of the physics, the data, the observations.
   
   As Firesign Theatre once said "The People! Give them a light and they will follow it anywhere!" Well, we know from history where this goes. Penrose suffers from his own criticisms and wants to create something like Einstein's elegant relativity applied to quantum gravity. Who can blame him? What is learning but man's vain search for God?
   
   But what if QFT's incredible accuracy is only an accident like the resonance particles. Feynman and others fudged enough to get the answers they were looking for even though QFT is not in principle normalizable. It is not even beautiful!
   
   What if Einstein and unitary quantum mechanics was the last hurrah of this sort of elegance in our species? Strings are beautiful but we will never know if the theory is observable. I'm afraid the measurement paradox is confusing what side of the experiment the measurement is taken.
   
   It is consciousness and evolved brain structure that is the problem. Penrose in other books has the (admittedly crack pot notion) that quantum gravity collapses the wavefunction and thereby creates consciousness. But maybe he was looking in the right direction?
   
   It is time to examine ourselves and our inherited prejudices as Nature is not only stranger (non-symmetric, anti commutative) than we suppose; it is stranger than we can suppose (Arthur Eddington). The future of physics and maths lies in understanding the limits of our own brains. Maybe the largest symmetry group that exists (the "Monster" of 196K dimensions) is the symmetry group of the thinkers which discovered it. And there are no groups bigger than this!



2. This book is perfect for where I'm at right now, which is at an advanced undergraduate level of studying physics. It covers pretty close to all of the ideas in physics that are out there right now, and most of the major areas of mathematics that are involved in explaining these physical theories. As such, it makes a great review of what I've encountered so far, and gives the clearest exposition I've yet encountered for many of the advanced ideas that I've only thus far encountered tangentially. Even for "basic" ideas, Penrose often chooses a way of explaining an idea that is significantly different from how most texts will explain them. His explanantions of complex numbers and the uses of the complex plane, differential forms, and 4-velocity and 4-momentum pop out in my memory as particularly good, and are concepts that I don't feel I entirely "got" until here. Also, he builds the concepts upon each other slowly and systematically, giving the entire book a "story arc" that's rare among physics and mathematics texts. Most of the second half of the book is devoted to what could be considered "cutting edge" physics, and he does an excellent job of evaluating the strengths and weaknesses of the various approachs.
   
   That being said, if this is your first exposure to these topics, you will be lost. The math is generally more clearly built up from what would be a non-mathematically minded person's starting point, but even that has points at which an extremely subtle mind is needed to fill in the intervening steps. The physics is even more difficult if you've had no exposure, but I personally found this to be one of the books virtues. For instance, you will probably come away with no understanding of electromagnetism and how electricity and magnetism came to be seen as unified if this is your first exposure, but for those who already have encountered it at an undergraduate level, you will come to a much deeper appreciation of its symmetries.
   
   All in all an excellent book, but the publishers should reconsider the way they are marketing it as a book for the layman.



3. It is not possible to express the ideas of modern physics without using mathematics very different from what one studies in high school. But a popular physics book can hardly assume more than a high school level of math. Therefore popular physics books are impossible.
   
   Penrose's 'The Road to Reality' is a demonstration of this proposition. Penrose must be congratulated for facing the problem head on, not shying away from the formulae and trying to teach his readers all the mathematics needed. Penrose is more capable than most for such an undertaking, and often he comes up with clever, intuitive ways of explaining difficult concepts. But ultimately the beautifully-crafted intuition collapses due to the lack of a supporting structure of necessary technical details and hard proofs and the reader is left holding fuzzy ideas which he cannot independently apply.
   
   The book would be a great way for a graduate student in physics or mathematics to see the big picture. Others would do well to stick either with less ambitious popularizations or to go straight to the textbooks. For the former, my recommendation would be Penrose's own The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science) while for the latter there is no better place to begin than Singer and Thorpe's Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics) and Needham's Visual Complex Analysis.



4. I highly recommend the reading of this impressive book. It is able to embrace almost all of the mathematical background a serious theoretical physicist should have...and it does so in a both deeply and understandable fashion. It is suitable for anyone interested in knowing why something arising from tbe human mind is capable to describe the Universe. This book may be suplemmented by Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics), by Mikio Nakahara, a reading recommended for those who may want to go even deeper into the mathematics-physics relationship.



5. This book took some time to read! In my opinion, if you want to understand current work in physics, you need to have the basics under your belt. Roger Penrose starts with the basics and works all the way through at a very challenging pace. He introduces the necessary math in a very straight forward, easy to understand way in the first few chapters and they were fascinating! After that, it gets even better building on the very basics where he began. This is not one of those books that you can read in a weekend or on a long plane trip, so plan to take some time and enjoy this one. It will be well worth the effort.