5 comments about Stochastic Differential Equations: An Introduction with Applications (Universitext).

1. This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.
   
   First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.
   
   Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.
   
   I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).



2. A well written book in Mathematics
   Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
   To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.



3. I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
   The book quickly moves to interesting applications of the theory, which is motivated very well.
   It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.
   
   With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!



4. Oksendal is not as formal as KS, Karatzas and Shreve (Brownian Motion and Stochastic Calculus), but it is easier to follow. The exercises in the first five chapters are very informative. Exercises in last chapters are more difficult (as they should be). After studying by this book, you may want to go deeper by using KS.



5. If you aren't a bit of a Math wonk, this book can be a bit daunting. But it is worth wading through the Math if you want to understand the "WHY" behind all those formulas and results. If you are looking for a gentler introduction and the "real formulas" Quants use, check out Paul Wilmott's books.
   
   The text generally starts with an intuitive example for the chapter and then starts methodically working through the underlying mathematics to get to the meaty results. The exercises are worth the effort as they reinforce the chapter work and offer additional insights.

5 comments about Star Maps for Beginners: 50th Anniversary Edition.

1. It's true, it doesn't show where the planets are but for identifying constellations and stars, any time from about 6 pm to about 5 am, you can't beat this book. I write a What's Up In the Sky weekly column and I'd be lost without this book. It gives basic information, delineates the differences in the seasons, skywise, and throws in some mythology also. The chart, telling which sky map corresponds to the time of night is invalueable. I can't imagine looking at the sky without this book.



2. I'll echo the comments of the reviewers below. I've looked at many books of star maps and I've written articles on the night sky for local newspapers. This book is by far the best - it's easy to use and the constellations are depicted just as they appear in the sky - without a lot of confusing, unnecessary additions. The accompanying essays are informative, entertaining and easy to understand.

   It's a huge shame that this book evidently has not been updated in 10 years. So, yes, the planet information is out-of-date. (But before you learn to find planets you first need to learn to identify constellations and bright stars - that's where Star Maps for Beginners outshines all the others.)

   I, too, have given away countless copies of this book. It's great for almost all ages. (Well, let's say for a bright 10-year-old and up.) I'm buying it again as a gift for someone who sells telescopes for a living. He never heard of it and he doesn't know what he's missing.




3. My tattered copy sitting on the shelf as I write this attests to it's value. I'm no major astronomer in any sense of the word, but a major part of what I DO know about the night sky was gleaned from its pages. It is what the title suggests: "For Beginners". It refrains from being too technical, the charts for the months of the year are easy to understand and use, and it's ar less expensive than other books of its kind. If your wish is to begin a hobby in astronomy, or better yet, if you simply are curious as to how to find your way around the night sky, this is a wonderful place to start. You will amaze yourself with what you'll know after only a few nights with this book. However, please note how up-to-date your copy is when buying it here or elsewhere. Hopefully, it will be as much a joy to you as it has been for me these past six years.



4. My son loved this book of constellations. They were easy to read and had good information.



5. The Zodiac On The Ceiling Of The Denderah Temple In Abydos, EgIpt(Egypt).
   You can borrow, but you must give proper respect to the rightful heirs.

5 comments about Quantum Field Theory.

1. This book provides clear, explicit calculations and well presented examples. It uses a modern description and weaves the various aspects of this subject together in a coherent whole. Mark Srednicki has done a great job with this book.



2. I was at Caltech 1984-86 in Phd. theoretical physics program and they were still using Bjorken & Drell and then Ramond for the final quarter - I fell behind when we hit chapter 8 renormalization never caught up and to my regret dropped out and became a professional high limit poker player. Every few years I would buy another QFT text - I tried them all (Peskin & Schroeder, Ryder, kaku, Weinberg, Itzykson & Zuber, Hatfield, Zee)- learn a little but still never felt confortable with the subject. Then I discovered Prof. Srednicki's book on the internet and realized this is the book I have been waiting for. The subject is presented logically and coherently from a theorist point of view.
   
   Renormalization, path integrals etc. are all treated from the beginning with a toy phi-cubed theory. What other field theory book actually shows you the double taylor expansion as in 9.11 page 60 and then clearly explains all the symmetry factors and numerical factors that lead to the final feynman diagrams.
   
   The best part of the book is the problems - they are neither trivial nor research projects - so far I have worked almost every problem in part 1 (scalar fields)- and they are all instructive and doable. I particularly liked problem 10.5 on field redefinition - when you solve this one you know you understand the material on feynman diagrams and scattering amplitudes.
   
   The treatment of scalar fields followed by spinor fields and then gauge fields enables one to learn the subject and gain confidence without overwhelming you with all the technical details and indices at once.
   
   The only other book that compares with this one are Weinberg's which I would recommend tackling after Srednicki. I would also recommend Zee's nutshell book for those like myself who read QFT books for fun.



3. This is a useful book. For the first section he is mostly doing phi^3
   theory in 6 dimensions, which is unrealistic but good because he can
   touch on all the crucial concepts like renormalization, and asymptotic
   freedom in this simple context, making them as understandable as possible.
   He never sweeps subtleties under the rug, so you really learn how they
   arise. And he is careful with factors of i and 2 etc, so you have
   confidence that there is really a coherent story to follow, and it is
   worth your time to work things out for yourself. (Lots of misprints,
   but a well-maintained web page lists them.)
   
   Things I found less convenient:
   
   1) There is only one level of structure: short chapters. There are no
   sub-sections in chapters to make the logic clearer. And he refuses to
   ever cite any equation from another chapter, so either he repeats
   equations unnecessarily, or just cites a whole chapter, leaving you to
   search it for the relevant equation. And so there is no single place
   where all the crucial results are collected. Each time you need a
   basic formula you have to search through the book for it.
   
   2) Charged scalar fields are important as a precursor to fermions
   but are only studied in the problems. In phi^3 the field is neutral.
   
   3) Symmetry factors are never properly explained. There is a detailed
   discussion on real-space Feynman diagrams, but then suddenly he
   switches to momentum space, and we never learn how to do symmetry
   factors for an arbitrary momentum-space diagram.



4. Quantum Field Theory by Mark Srednicki is a true gem. He posts a (beta)pdf of the text on his website so you can see for yourself. However, In the words of John Baez: "nothing beats sitting in a cafe with a friend, notebooks open, and working together on a regular basis." So get the book, work through the problems, and (as much as possible) discuss them with a buddy over coffee. Cheers to good physics.



5. Background: I used this book in an introductory graduate course in QFT at Brown University, but I had read through a couple of other QFT texts before taking this course.
   
   The book is split into three main sections: 1) scalar fields 2) spinor fields and 3)vector fields. By developing QFT exclusively for scalar fields in the first section, Srednicki is able to separate the difficult parts of field theory from the complications and technicalities of spinor algebra, which was very helpful for me.
   Also, this approach allows the author to discuss some subtle aspects of quantum field theory much earlier on than usual (for example: effective field theories, Wilsonian renormalization, the renormalization group, spontaneous symmetry breaking, etc...). In particular, the book contains the best introduction to renormalization that I have seen. It takes a very modern standpoint, and was able to clear up many of my conceptual issues with the topic.
   There are a couple of other features/issues that the potential reader should probably be aware of:
   1) While the book introduces canonical quantization, it develops most of the material through the path integral formulation
   2) Srednicki develops spinor algebra using two-component Weyl spinors, which in my opinion is more elegant and useful for studying SUSY (but which may bother those who are used to the 4-component Dirac notation)
   3) The material is presentated through a large number of short (usually 3-4 page) chapters, which allows the author to cover a lot, but not always in great detail. Therefore (as with any QFT text), I would recommend supplementing the sections of this book with other texts (personally, I found Srednicki's informal approach complemented Weinberg's texts well)

5 comments about Principles of Quantum Mechanics.

1. Great quantum book, covers material fully and in a logical order. Much better than Gasiorowicz, which skips around a bit too much.



2. I discovered Principles of Quantum Mechanics (2nd ed.) recently and I am writing to praise it! This is a QM text you can study on your own. It introduces Dirac notation and the mathematical underpinnings of QM before getting into the theory and applications.
   
   The mathematical approach makes the material both more enjoyable and more easily approachable. I am in media res studying the book, but I have a suggestion. It would be valuable to have a companion workbook running parallel to the text replete with worked problems. I like to instantly find our whether I am correct when I work problems (which allows me to move forward at a more rapid rate) and such a workbook would fill that need.
   
   Only one other physics text (Classical Mechanics by Taylor) that I have encountered recently has the flow of writing and can hold one's interest like a novel. Well done, Professor Shankar!



3. Having been scouring my old college text and many other books on Quantum Mechanics I found them lacking in their ability to explain the mathematics behind the theory. This text approaches the subject by way of Linear Algebra and Vector Spaces.
   Shankar's Text lays everything out brilliantly buy hitting the mathmatics FIRST then going into the theory. I am working my way through the first chapter on the mathematics which is very clear so I have no doubts that the text on the theory will be just as lucid.
   Once you can turn the crank of the mathematics then the theory will be open to study for you. That's the trick.
   Excellent text for someone who has had either a good grounding in linear algebra or undergraduate QM.



4. 
   I bought this book when I tried to learn QM by myself. I am not stupid
   and I know how to differentiate and to integrate but boy is this book
   hard to understand. This is a book for people who already understand
   the subject not for those who have major problems understanding it.
   
   If you have an IQ of 170 then this book is for you. If you are around
   the 120-130 mark and have trouble with advanced math I recommend starting
   with Linus Paulings - Introduction To Quantum Mechanics.
   
   You have been warned :)
   
   John



5. I am a lecturer who teach QM mostly. I've read various QM books so far. Apart from being reader-friendly, Shankar's book touches my mind in several points. Dirac equation (chapter20) is superbly written. The book explains very well how the matrices Alpha's and Beta are chosen to form the Dirac Hamiltonian. The fact that they are traceless and they have eigenvalues +1 or -1 is awesome. Furthermore, it gives a clear and beautiful picture that Dirac equation can reduce to Schroedinger one with E&M interaction plus H-fine structure whereas most other QM books treat this in more-unfriendly ways. The first 7 chapters may be read by advanced undergrad students. Stern-Gerlach experiment is well explained compared with averaged QM book. Another touching point is the Chapter of spin. Most QM books seem not to mention the linear independence of 4 Pauli matrices clearly whereas it is nicely proved in Shankar's book. The seeming drawback in my viewpoint is that path integrals should not be treated too much in a QM book(2 Chapters). It should be contained in the books of special fields. Something like 2nd quantization or field operator should be instead. However, in overall, this QM book is quite valuable to our academic world, and deserves 5 stars.

1 comments about Group Theory in the Bedroom, and Other Mathematical Diversions.

1. If you liked the book "Freakonomics: a rogue economist explores the hidden side of everything" (which I loved), there is a good chance you will like this one too. The author may have screwed-up giving it the title he did and by adding "and Other Mathematical Diversions", as it may put off or scare off a lot of people who would find it enjoyable. One would be hard pressed to find a mathematical equation anywhere in the book.
   
   Take for instance the first chapter, "Clock of Ages", on the astronomical clock located in the Strasbourg Cathedral, in the city of Strasbourg, Alsace. Though the current version of the clock dates from 1843, not only was it designed to be Y2K compliant, it is also Y10K functional, designed to directly display the current year up to 9999 and the only revision needed to make it correct for subsequent years would be to paint the number "1" to the left of the display. It will continue to display such events as the correct date for Easter even in the year 19999 (Easter falls on April 3rd in 11842). Though solely a mechanical device, the gears of the clock were designed to be accurate to an error of less than one second per century. There is a gear in the clock that turns only once every 2,500 years and the celestial sphere out in front of the clock will complete one full precessional cycle after the passage of 25,806 years.
   
   After his discussion of the beauty of the design of this clock, the author then takes up a philosophical discussion of time, asking if anyone will still care what date Easter will be in 11842, or even if we will still be counting in years of the Common Era.
   
   The second chapter, "Follow the Money", demonstrates how through even an entirely random process, wealth tends to become concentrated in the hands of a few people, even in a fair system.
   
   The remaining chapters are similarly varied and all are interesting.
   
   A great book with a wide variety of interesting subjects and an engaging, erudite writing style.

5 comments about The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century.

1. This is a very intriguing read about the history and the developments in the study of statistics throughout the twentieth century.



2. Salsburg writes a selective account of the history of statistics in the 20th century. In so doing, he tackles the philosophical issue of a scientific revolution from deterministic to stochastic thinking (he writes that this is a revolution in the Kuhnian sense). I haven't personally found another book which displays the big picture of what happened so clearly, and from that standpoint consider this book a must read on the topic. It is well written and appears to me to successfully communicate to a broad audience.



3. I have given several copies of this book away to my statistician colleagues, as it is an outstanding overview of the development of statistics in the twentieth century.
   
   It is not particularly technical but it probably would appeal only to statisticians, students of statistics, and others interested in the impact of statistics on the advancement of science.



4. The Lady Tasting Tea is a new book by David Salsburg (a Ph.D. mathematical statistician, who recently retired from Pfizer Pharmaceuticals in Connecticut). The title of the book is taken from the famous example that R. A. Fisher used in his book "The Design of Experiments" to express the ideas and principles of statistical design to answer research questions. The subtitle "How Statistics Revolutionized Science in the Twentieth Century" really tells what the book is about. The author relates the statistical developments of the 20th Century through descriptions of the famous statisticians and the problems they studied.
   
   The author conveys this from the perspective of a statistician with good theoretical training and much experience in academia and industry. He is a fellow of the American Statistical Association and a retired Senior Research Fellow from Pfizer has published three technical books and over 50 journal articles and has taught statistics at various universities including the Harvard School of Public Health, the University of Connecticut and the University of Pennsylvania.
   
   This book is written in layman's terms and is intended for scientists and medical researchers as well as for statistician who are interested in the history of statistics. It just was published in early 2001. On the back-cover there are glowing words of praise from the epidemiologist Alvan Feinstein and from statisticians Barbara Bailar and Brad Efron. After reading their comments I decided to buy it and I found it difficult to put down.
   
   Salsburg has met and interacted with many of the statisticians in the book and provides an interesting perspective and discussion of most of the important topics including those that head the agenda of the computer age and the 21st century. He discusses the life and work of many famous statisticians including Francis Galton, Karl Pearson, Egon Pearson, Jerzy Neyman, Abraham Wald, John Tukey, E. J. G. Pitman, Ed Deming, R. A. Fisher, George Box, David Cox, Gertrude Cox, Emil Gumbel, L. H. C. Tippett, Stella Cunliffe, Florence Nightingale David, William Sealy Gosset, Frank Wilcoxon, I. J. Good, Harold Hotelling, Morris Hansen, William Cochran, Persi Diaconis, Brad Efron, Paul Levy, Jerry Cornfield, Samuel Wilks, Andrei Kolmogorov, Guido Castelnuovo, Francesco Cantelli and Chester Bliss. Many other probabilists and statisticians are also mentioned including David Blackwell, Joseph Berkson, Herman Chernoff, Stephen Fienberg, William Madow, Nathan Mantel, Odd Aalen, Fred Mosteller, Jimmie Savage, Evelyn Fix, William Feller, Bruno deFinetti, Richard Savage, Erich Lehmann (first name mispelled), Corrado Gini, G. U. Yule, Manny Parzen, Walter Shewhart, Stephen Stigler, Nancy Mann, S. N. Roy, C. R. Rao, P. C. Mahalanobis, N. V. Smirnov, Jaroslav Hajek and Don Rubin among others.
   
   The final chapter "The Idol with Feet of Clay" is philosophical in nature but deals with the important fact that in spite of the widespread and valuable use of the statistical methodology that was primarily created in the past century, the foundations of statistical inference and probability are still on shaky ground.
   
   I think there is a lot of important information in this book that relates to pharmaceutical trials, including the important discussion of intention to treat, the role of epidemiology (especially retrospective case-control studies and observational studies), use of martingale methods in survival analysis, exploratory data analysis, p-values, Bayesian models, non-parametric methods, bootstrap, hypothesis tests and confidence intervals. This relates very much to my current work but the topics discussed touch all areas of science including, engineering in aerospace and manufacturing, agricultural studies, general medical research, astronomy, physics, chemistry, government (Department of Labor, Department of Commerce, Department of Energy etc.), educational testing, marketing and economics.
   
   I think this is a great book for MDs, medical researchers and clinicians too! It will be a good book to read for anyone involved in scientific endeavors. As a statistician I find a great deal of value in reviewing the key ideas and philosophy of the great statisticians of the 20th Century.
   
   I also have gained new insight from Salsburg. He has given these topics a great deal of thought and has written eloquently about them. I have learned about some people that I knew nothing about like Stella Cunliffe and Guido Castelnuovo. It is also touching for me to hear about the work of my Stanford teachers, Persi Diaconis and Brad Efron and other statisticians that I have met or found influential. These personalities and many other lesser-known statisticians have influenced the field of statistics.
   
   The book includes a timeline that provides a list in chronological order of important events and the associated personalities in the history of statistics. It starts with the birth of Karl Pearson in 1857 and ends with the death of John Tukey in 2000.
   
   Salsburg also provides a nice bibliography that starts with an annotated section on books and papers accessible to readers who may not have strong mathematical training. The rest of the bibliography is subdivided as follows: (1) Collected works of prominent statisticians, (2)obituaries, reminiscences, and published conversations and (3) other books and article that were mentioned in this book.
   
   The book provides interesting reading for both statisticians and non-statisticians.
   
   Dennis Littrell comments in his review that he missed the fact that the formulas common in mathematical statistics were missing. For statisticians and mathematicians such things help put extra meat bewteen the bread in the sandwich. But personally I do not see where that would contribute much conceptually to the book and it could have the effect of turning off the non-mathematically inclined medical researchers and other medical professionals who could learn to appreciate the role of statistics in the scientific advances in the twentieth century. Also note that I have the hardcover version of the book. The only difference between the hardcover and the paperback edition is the reduced price. Publishers often do that with popular books to increase sales.



5. I really enjoyed this book.
   It makes you understand that science is not perfect, that not everybody agrees or thinks the same about the issues, and that there is always much to be done.
   It was interesting to know a little of the lives of the people behind the ideas, and also how often the desire to resolve practical matters pulls science.

5 comments about Calculus of Variations.

1. Ok, not everyone needs to (or wants to) know calculus of variations. But if you are among the ones who, this is a great book to get started with (assuming you are in grad school and have a decent handle on calculus and some basis in dealing with differential equations). The text is clear and concise, and the financial investment is minimal. A good buy!



2. This is a classic text and I would recommend it to graduate students and mathematicians who need a review of the subject. Great for us physicists as well.



3. As a physicist I want to find a book to refresh my memory on theoretical mechanics. I came across this one, and after reading its first 4 chapters in continuation, I kow I don't need any other book. What a treat! Written by a past master, the book costs you next to nothing; yet as it's written by sure hand, it hasn't slightest pretention, just plain and insightful, natural and smoth flow, leads you almost effortlessly fowward. Even though I learned the subject before, I don't know of or even imagine a better exposition. Wow, I started to love Russian mathematicians.



4. This book is a "must have" for those wanting to study topics in functional analysis.



5. I like this book, certainly what I have read of it. I'm now digging around near page 75, and it struck me that for the first time I really "get it" - In particular, this was about the use of the Legendre transform. The authors start with a very gentle introduction of it, and then, while things become more abstract, the text never jumps too far and never leaves the reader too much in puzzling. It's ought to be studied though, and it's not "easy".

No comments about The Complete Idiot's Guide to String Theory (Complete Idiot's Guide to).

4 comments about A Student's Guide to Maxwell's Equations.

1. Maxwell's equations represent a comprehensive and descriptive condensation of (once believed to be disparate) electromagnetic phenomena, into a gloriously concise set of self-consistent (albeit arcane) mathematical statements. Daniel Fleisch has lucidly crafted explanations both of Maxwell's equations that describe EM phenomena, while simultaneously employing the latter to motivate, justify, and describe the vector calculus of the former with great clarity--the perfect synthesis. The author addresses chapters to each of the four equations in turn: (1) Gauss's law for electric fields, (2) Gauss's law for magnetic fields, (3) Faraday's law, and (4) the Ampere-Maxwell law; describing each first in its integral then differential forms, with brief expansion of the utilities for each form. The final chapter concludes elaborating the true nature of light as part of the greater EM spectrum, culminating in motivation of the wave equation and determination of c, the speed of light. I wish I had a shelf full of similar pithy, fun-reading, and revelatory books on other like topics!



2. This is the best overview of Maxwell's equations I have ever come across. I cannot praise it enough for it's brilliant clarity.
   
   If you have taken or are taking an electromagnetism or vector calculus course, you may have run into the classic problem of not being able to see the forest through the trees. These courses can be very dense, and anything that can help give a sense of perspective can be very helpful. Daniel Fleisch's book is just such a tool. It provides a thorough overview of Maxwell's equations with stunning clarity. Each equation is broken down into it's component parts, and the physical significance of each part is thoroughly explained. In this way, not only are the core concepts of Maxwell's equations made clear, but many concepts from vector calculus are also brought out in crystal clarity, (I got much more out of this book than I did the often recommended "Div, Grad, Curl"). It will help you see the "forest through the trees".
   
   Also of note are the problem sets at the end of each chapter. The problems work very well to reinforce the concepts from each chapter. They are not overly difficult or too simplistic. They are geared specifically at reinforcing concepts. The author has also posted on his web site a set of solutions for every problem, and each of the problems is thoroughly worked out with clear explanations. This is a HUGE plus for anyone picking up this book for self-study.
   
   In my mind this book is a perfect compliment to an electromagnetism or a vector calculus class (or as a review after having taken such a class). Although the writing is clear enough that one could probably get a lot even without having had a vector calculus class, ideally one would have had at least some minimal exposure to vector calculus. It's not that you need to be an expert in vector calculus; all the concepts are explained very well in the book and the actual calculus you need for solving the problems is minimal, but in my mind the book will work best for those with some exposure to vector calculus.
   
   My only suggestion to the author would be to include a table summarizing Maxwell's equations, (and perhaps a table of some basic constants). Other than that, this is a perfect book. It is THE standard by which other self-study books ought to be compared.
   
   Update: When I wrote the above review I was half way through chapter 4 (of five chapters). Having completed the book, I do want to point out that the beginning of chapter 5 ('From Maxwell's Equations to the Wave Equation) does include a summary of Maxwell's equations. It would have been nice to have such a table at the front or back of the book for quick reference, but the summary is there, contrary to what I had originally thought. Chapter five also has a nice summary of the del operator and its use in finding the gradient, divergence, and curl. And finally, chapter five provides a very good physical description of the Divergence Theorem and Stokes' Theorem. So all in all, there is really little one can fault in this book. It's the book to get if you want to see the forest through the trees.
   
   
   [Side note to author (written before the above update, and answered by the author in the comments): I believe the solution to problem 2.3 for surfaces 'A' and 'B' should include a factor of 1/2 since the area is a triangle; I did not see a feedback form on the website, or I would have posted there.]



3. The best book clearly I have read in the last year; it combines simple calculus and EM physics into a readable book. Because I already knew Stokes theory, the divergence theorem and all the other math, I was able to read this book in about a week. You get the solutions to the problems on the website and great podcasts also. I would like to see more from this author on other subjects like quantum physics in this format; the technology is out there to provide podcasts, and maybe even do videos of some experiments to clarify the results.



4. Like most practicing engineers, my understanding of EM is based more on experience rather than rigorous mathematical theory.
   I'm sure many of us can remember being exposed to vector calculus as applied to EM as undergraduates, but regarding it as an academic hurdle to be overcome, rather than something that might actually be useful later in a professional career.
   The situation is worsened latterly by the evolution of EM modeling tools, which do all the donkey work for you - further reducing the requirement for a sound understanding of Maxwell.
   But one day, you run into a problem that needs a bit more than the stock solutions - what now ? You rush to your text books, and you than discover that you have forgotten everything from your college days, and without your friendly old professor on hand, everything looks like gobbledegook !
   I always been amazed that such an important subject is always presented so poorly, even in well regarded text books. In my opinion, a book should convey understanding - not just regurgitate facts.
   Fleisch does an excellent job of conveying the concepts of div,grad and curl. The influence of the late Prof Kraus is clearly evident in his style (ref Electomagnetics, Kraus). Fleisch uses analogy to help the reader get an intuitive feel for the problem before diving into the maths. Personally, I fully endorse this approach - Fleisch is also diligent enough to highlight the limits of the analogous approach, which should keep the purists happy.
   My only minor criticism of this book has already been stated by another reviewer, a tabular summary of equations covered in each chapter would be helpful. Also having the word 'student' in the title means I have to keep it stowed in my draw when not in use to avoid embarrassment ;)
   So just own up - you're just like me - you never really understood Maxwell, and have been afraid to ask ! Get this book and sort your EM life out.

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

1. I love Mathematics and Physics The writter obviously loves them too judging by his 'Teacher' approach in presenting both subjects. The carefully crafted presentation in this book is a welcome approach for subjects such as these. I'm not finished reading the book but I already love it. Thanks for taking the effort.



2. I love this densely packed, entirely informative book. It gives a new level of understanding for those who enjoy reading about mathematics but who (like myself) have received no formal training in the field. There is a handy "notations" section, which was great, but I could have used a glossary as well. Otherwise, a great book and one I'm very glad I bought.



3. excellent general primer for Quantum Mechanics and modern physics. Penrose is writing at a level for the reader who is willing to do some work to understand a very complicated subject. A much more educational experience than the usual books on quantum mechanics for the general reader



4. This is definitely the most comprehensive book ever published on theoretical physics, written by one of the most influential theoretical physicists alive! But the reader should be forewarned : it is not easy reading, even if one skips the maths, as Penrose suggests in the Introduction...
   Now, if one wants to understand everything, then it becomes really challenging, and I don't think many readers would be up to it. By understanding everything, I mean understanding enough to be able to do the exercises, and , believe me, this is no easy task!Especially that the author forgets most of the time that this is supposed to be a book for the "general public",so he writes as if he were giving a lecture to his graduate students.That is, he assumes that the reader knows already a lot about the subject at hand. Take, for instance, his explanation about the "clock paradox" of Special Relativity : not only is this explanation very special to Penrose, but he does not even explain what the "paradox" is all about! And so the reader who encounters it for the first time would tend to think that the paradox is only the fact that the voyager ages slower than the observer who stays behind, which is not altogether true...
   The other aspect of the book that struck me is that Penrose distances himself from mainstream physics on two very important paradigms: spontaneous symmetry breaking in the early Universe, and inflationary cosmology. For him, there is no sufficient observational evidence for these two "speculative theories", as he calls them. Many cosmologists and physicists would surely disagree with him, but he has the honesty to express his beliefs, even when they are "out of phase" with those of other "pundits".And he has some very solid arguments, stemming from a deep insight into the Second Principle of Thermodynamics. It would be very interesting to see what the "inflationists" have to say about Penrose's arguments!
   But be that as it may, I would not hesitate to recommend this book to all those readers who, like myself, are passionately looking for an explanation to the laws that govern "Reality", i.e the Universe we live in.
   
   Finally, I would like to add here that "Publishers Weekly" makes a comparison between this book and Hawking's "A Brief History of Time". But this comparison is untenable: Hawking's small book is but child's play compared to this treatise!



5. 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!