5 comments about The Joy of Mathematics: Discovering Mathematics All Around You.

1. This book could have been good if the author had done a careful job of writing the text, and perhaps if the illustrations were original, and above all if the author had understood the material she was writing about. Sadly these are often not the case with this book.

   Rather, this book gives every sign of being essentially copied from bits of many dozens of other books. All the illustrations appear to be low-quality xerographic copies from other books (clearly used without any permissions).

   But worst of all, the book is chock full of misstatements, misconceptions, and sentences that don't convey any meaning.

   This book gives the non-expert reader the impression that he or she is learning something, but a great deal of the time this is just the illusion of learning.

   I will list a few of the errors and illusory learning that I can readily find:
   ________
   p. 6: The illustration of the cycloid curve should show it to be in a vertical direction where one arch meets another; instead it is at 45 degrees to the vertical.
   ________
   p. 7: It is stated that when marbles are released in a cycloid-shaped container, they will reach the bottom at the same time. This phenomenon occurs for a bowl whose cross-section is an *inverted* cycloid, but that is omitted.
   ________
   p. 13: Both the "impossible tribar" and "Hyzer's optical illusion" are NOT mathematically impossible, contrary to what is written. (They can be constructed in 3 dimensions.) Twistors are mentioned but not defined, even in a rough, metaphoric way -- just not at all.
   ________
   p. 18: It is mentioned that pi cannot be the solution of an algebraic equation with integral coefficients, but there is no discussion in the book of what such an equation is.
   __________
   p. 19: Also, it is stated that the probability of two randomly chosen integers' being relatively prime is 6/pi. Not only should the correct number be 6/(pi * pi), but the idea of randomly choosing an integer is left completely undiscussed, although there is no known way to do this.
   ________
   p. 38: The Platonic solids (aka regular polyhedra) are discussed here, but although they are defined twice, neither definition is correct. (The author neglects to mention that the faces of such a solid must be *regular* polygons.)
   ________
   p. 45: The Klein bottle is discussed and illustrated here, but there is no mention that a genuine Klein bottle cannot be constructed in ordinary 3-dimensional space. (The familiar model of a Klein bottle depicted here is a self-intersecting version of the real Klein bottle, which does not intersect itself. This is much like the fact that a picture of a knot drawn in the plane must appear as if the knot intersects itself, though it does not do so in space.)
   ________
   p. 46: The illustration at bottom purports to show what the model of the Klein bottle would look like if it were sliced in half. The halves are erroneously shown as identical, but they should be mirror images of each other.
   ________
   p. 78: The title of this page is "Fractals -- real or imaginary?"
   This is an entirely misguided question that will only confuse the reader. All mathematical concepts are real within mathematics, and do not exist (except as approximations) in the real world.

   It's a worthwhile topic in the philosophy of mathematics, and could well have been introduced in this book, but it has nothing whatsoever to do with fractals per se.
   ________
   p. 91: Here the author attempts to describe a model of hyperbolic geometry (in a circular disk) devised by Henri Poincaré. However, she gets it exactly backwards, saying that objects get smaller as they approach the boundary of the disk.
   (She may have been well-aware of how this model works, but her prose is at best completely ambiguous.)
   ________
   p. 96: Here it is stated that it has been proved that knots cannot exist in more than 3 dimensions. Apparently the author is unfamiliar with an extensive and thriving field of higher-dimensional knots. (For example, a sphere can be knotted in 4-dimensional space.)
   ________
   There are many, many more such gaffes, but I fear I have gone on too long. I just wanted to make it crystal-clear that this book is riddled with erroneous and vacuous statements.




2. Sorry to say but this book is a dud. While the concept of presenting interesting mathematical facts is great the presentation is so brief, so wrought with errors, and so incomplete that the work is not worth perusing.
   
   Some of the "chapters" have answers at the back of the book and some do not. It appears that the author could not make up her mind wether this was to be a "math tricks" book or a "popular mathematics" presentation substantiated by theory.
   
   There are many other excellent books that are more fulfilling. Journey Through Genius comes to mind.
   
   All in all a disappointing work.



3. The widely divergent reviews reflect a lack of understanding of the purpose of this book. It is meant to touch on many mathematical ideas, not to go into depth on any one idea. My son read this at age 8, then at 10, and again at 12 - getting something more out of it every time. Many of the ideas intrigued and inspired him to seek out more information on his own, to research and understand more deeply. For that purpose, it deserves the highest rating.
   
   I did not give 5 stars because there are some instances where I did find errors, these do not detract from the purpose of the book, but they are annoying to those of us who try to delve deeper. What I consistently found myself doing is researching from the internet and other print resources. But the idea originated from the overview in the book.
   
   Many recreational mathematics books are inaccessible to beginners or math phobes. This book allows you to sample many, many ideas without feeling overwhelmed by details you may not understand. If you want details, you go explore the world opened up by the book.



4. if the discoverable arithmetic of the everyday natural world interests you, try this; and then you may want to explore her other work along this line.



5. My appreciation for Theoni Pappas is enormous as for an observer and admirer of the world around her and mathematician. These factors cannot be separated, as at first you have to do more than just look around, but you have to have a beautiful mind of a child and be an intellectualist at the same time, not just to take things for granted, but as a child be curious and ask questions and finally as an intellectualist and mathematician find answers to them.
   Yet, there is more to it. It is so, as the author popularizes mathematics. She answers the basic questions about role of mathematics in our lives. Most people associate mathematics as calculating especially money, yet in mathematics the theory models or formula are created, and it occurs that they find application in our material world sometimes even centuries afterwards. Let us look at some examples in the book "The joy of mathematics": - earthquakes and logarithms- connection lies in the method to calculate earthquakes' magnitudes by means of Richter scale, which is logarithmic, - the catenary & the parabolic curves- who takes as an obvious phenomena- the Golden Gate Bridge in San Francisco- it looks gorgeous, but what it looks like is connected with construction equations, which contribute to the fundamental thing, that it really is invulnerable and cannot be destroyed by the mass itself, as well as additional natural forces. Even Galileo noticed the curve to be parabola, - Thales & the Great Pyramid- Egiptians' calculations of the height of a pyramid were based on shadows and similar triangles, -the Dome of Milan -Gothic plans incorporating the application of geometry and symmetry in architecture, and lots of stuff like that. If you like to notice more around you, astound your friends, you should read such books, as there is more beauty around you than what you just see.

3 comments about Dynamic Programming and Optimal Control (2 Vol Set).

1. really nice book on dynamic programming... easy to understand and contains all requisite details.



2. It's a good book for dynamic programming, though it requires substantial knowledge of mathematics.



3. *This is easily the best book on dynamic programming. It certainly is the most up-to-date book on this topic. The first volume covers numerous topics such as deterministic control, HJB equation for the deterministic case, Pontryagin principle, finite horizon MDPs, partially observable MDPs, and rollout heuristics. The second volume treats the infinite horizon case for the regular MDP --- average reward, discounted reward, semi-Markov control, and even some reinforcement learning.
   *I love the notation. The proofs in this book are much easier than those you will find elsewhere. (This opinion is based on my study of proofs in other texts.) The treatment is very sophisticated and yet very accessible! Furthermore, what is really a bonus here --- something you won't find in the other books --- is a discussion on the stochastic shortest path (SSP). The SSP makes it so easy to analyze the average reward problem and the finite horizon problem with a stationary transition probability structure.
   *I strongly recommend this book to all readers interested in understanding the basics of DP and the convergence proofs underlying the DP machinery. It is a must on your book shelf if you are working on research in DP or topics related to DP such as reinforcement learning or adaptive (approximate) DP.

5 comments about Chaos and Fractals: New Frontiers of Science.

1. Chaos as a physical theory began essentially in the 1970's, but as a mathematical field it has existed since the early 1900's. This book covers only the mathematical study of chaos, and is addressed to those readers who have a fairly strong background in undergraduate mathematics. A knowledge of dynamical systems and measure theory would help in the appreciation of the book, but are not absolutely necessary. The application of fractals and chaos to finance is now legendary, but other applications, such as to packet networks and surface physics are not so well-known. Current research in chaos is done predominantly in the context of information theory, wherein the goal is to understand the difference between chaos and noise, and develop mathematical tools to quantify this difference. The BASIC code in the book gives away its age, but can be easily translated to one of the symbolic computing languages available now, such as Maple or Mathematica.

   This is a sizable book, and space prohibits a detailed review, but some of the more interesting discussions in it include: 1. The video feedback experiment, which can be done with only a video camera and a TV set. This is always a crowd pleaser, at whatever level of the audience it is presented to. 2. The comparison between doing iteration of a chaotic map on two different calculating machines: a CASIO and an HP. The difference is very dramatic, illustrating the effect of finite accuracy arithmetic. 3. The pictures illustrating the Chinese arithmetic triangle and Pascal's triangle as it appeared in Japan in 1781. 4. The space-filling curve and its relation to the problem of defining dimension from a topological standpoint. This discussion motivates the idea of covering dimension, which the authors overview with great clarity. They also give a rigorous definition of the Hausdorff dimension and discuss its differences with the box counting dimension. 5. The many excellent color plates in the book, especially the one illustrating a cast of the venous and arterial system of a child's kidney. 6. The difficulty in measuring power laws in practice. 7. Image encoding using iterated function systems, which has become very important recently in satellite image analysis. This leads into a discussion of the Hausdorff distance, which is of enormous importance not only in the study of fractals but also in general topology: the famous hyperspaces of closed sets in a metric space. 8. The relation between chaos and randomness, discussed by the authors in the context of the "chaos game." 9. L-systems, which are motivated with a model of cell division. 10. the number theory behind Pascal's triangle. 11. The simulation of Brownian motion. 12. The Lyapunov exponent for smooth transformations. 13. The property of ergodicity and mixing for transformations, the authors pointing out that true ergodic behavior cannot be obtained in a computer where only a a finite collection of numbers is representable. 13. The concept of topological conjugacy. 14. The existence of homoclinic points in a dynamical system. These are very important in physical applications of chaos. 15. The Rossler attractor and its pictorial representation. 16. How to calculate the dimensions of strange attractors. 17. How to calculate Lyapunov exponents from time series, which is of great interest in many different applications, especially finance. 18. The Julia set, which the authors relate eventually to potential theory.




2. At least 50% of this book can be well understood by any 1st year, exact science student. There are a couple of mathematical issues that are more senior-like, but never mind. With the appropriate teaching or guidance, a lot of practical, advanced tasks can be tackled down. I could use this book all along for giving examples for college (university), undergraduate students of almost every mathematical subject: numerical analysis, calculus, linear algebra, group theory, algorithm theory, visualization in 2 and 3 dimensions, topology...you name it, after reading this book. No fuzzy theory or wavelets or any other advanced statistical method for dynamical systems is formally mentioned, though. However the concept of measure is very well introduced and described with examples. For physics is not bad for dynamical systems theory. Although no Hamiltonian or Lagrangian formalism is mentioned, the description on how to obtain Lyapunov exponents out of a set of differential equations is very good. Engineers get their share too: useful examples are given about, e.g., feedback and control theory (mind you, it is not a book specialized in, say, robotic control using chaos theory, but it is a good start). For philosophers and the layman there are quite a few pages as well. The foreword from Mitchel Feigenbaum, just to give an example, tells us a kind of summary which "warms up" the reader and "exorcises away" the possible fantasies an unprepared reader could have regarding (or against or in favor of) the word "chaos". Nice color plates for those with artistic inclinations and the graphics are just so very well printed, you can practically "follow" their computation. Not a bad book at all for your personal (or institutional) library, I may say.



3. I found the 1992 edition of this book at my local public library, and was (like all the other reviewers here) very impressed at the quality. The book deals with a highly technical subject, but does it in a way that you can follow even if you don't have advanced math training. The numerous color plates were also very beautiful. And to top it all off, there were "do it yourself" exercises at the end of the chapters, showing you how to program your computer to run these figures! OK, they use the old BASIC language, but still the code is clear enough that you can follow it and see what's really going on with these equations.
   
   So I was so pleased to see a copy of the updated edition at a bookstore. In particular, I was eager to see if they'd updated those "do it yourself" exercises for use with EXCEL. However, as I read through it I was disappointed to notice two changes from the previous edition: first, all of the programming examples had been eliminated; second, the print quality of the color plates was noticeably poorer. And I didn't see much new material added - in fact one of the reviews above observes that the text itself is virtually unchanged. Considering the steep price of this tome, these were significant points to consider. Used copies of the old edition cost under 20 bucks, and IMHO are a better deal (I ended up buying one). So if you're ready to buy, just do yourself (and your wallet) a favor and compare the two editions first.



4. Thanks to S.J. Will for the tip: Get the FIRST edition (used), as I did and save more than half the price, even of a used copy of this newer edition. Can't compare the two (having not seen the new one) but I can say the color images are very sharp in the older book. As far as content, I too have looked at and bought several books trying to understand fractals. (I am not math-literate, beyond high school algebra.) I found this book most helpful, but NOT easy for the general reader, beyond the first few, introductory pages. As other reviewers have noted, most of it is WAYYYY over the head of anyone who's not a college math major, but skipping through the examples and exercises (some of which are very rewarding if you can stay with it), I found the general explanations, the excitement of the authors, the broader significance of fractals all to be well-worth the price. -- And hey: at over 900 pages ( ! ) and with FORTY color plates, this book is an astounding bargain. Strongly recommended, even for novices.
   
   "The Colors of Infinity," based on the video documentary by Arthur C. Clarke is a good introduction to fractals. An enjoyable DVD is included of the original TV program, especially if you learn better by watching and listening. The accompanying animated fractals are fascinating, but frustratingly poor resolution. For a more philosophical approach to fractals, I highly recommend "Heaven's Fractal Net" by William Jackson.



5. This book is a dream come true.
   No other publication comes close to such complete coverage of the subject.
   It is highly readable even for a novice like myself.
   It has been a great joy to me.
   Many thanks to the authors for doing such a great job.

5 comments about The Roman Triumph.

1. This book more than fulfills expectations. It is a much needed correction to earlier studies of the triumph. B. calls into question much that has been considered factual knowledge about the triumph by showing the inconsistencies and scarcity of the ancient evidence. A must read for everyone interested in the topic. B. has also gone to great lengths to make the text accessible to a non-scholarly audience, while maintaining high expectations of that audience's willingness to think critically about problems of historical research.



2. Not all history books are written to be read by those of us who are not academics. When Mary Beard takes on a subject matter, all that changes and history not only comes alive, it becomes clear and enjoyable. Thank you, Ms. Beard. This book has, of course, led to me looking for related subjects of the Roman Empire, as well the as the Republic.



3. This book did not keep my interest. It nit-picked the roman Triumph to death. A continous flow of information would have been helpful. But we stop at each street corner, and nit pick the corner and then proceed a little further, and nit pick some more...I still don't know the how, why or wherefor's of the triumph.



4. Lots of interesting info on the Roman triumph, but unfortunately the author gets in the way of her own topic. Statements like "The book will show..." and "I will prove..." belong in the Introduction. Instead, they're all over the place. Phrases such as "Now I'll turn my attention to" and "as we'll see in chapter 9" are littered throughout the book, leaving the reader to feel as though the actual book will, in fact, begin any minute now, we just have a few more previews to get through. I can't stand it when authors continually call attention to themselves like this. Just GET ON WITH IT. Also, whole paragraphs full of rhetorical questions (which historians should we believe? why should we believe them? how do our beliefs color who we end up believing? blah blah blah) put a frequent, and deadly, stop to the narrative. Maybe academicians like this sort of thing, but I don't think the average reader appreciates it. I know I don't. I'm halfway through the book; I'll finish it because of my interest in the subject, and in spite of the author's well-meant but exasperating prose.



5. When a Roman general won a great victory the Senate would frequently vote for him to be given a triumph. The Roman triumph was Rome at its most glorious, according to many. It was mostly "about display and success" (p 31). The entire city seemed to shut down to watch the gaudy parade; work was suspended, songs were sung, and everyone came to cheer on the victors.
   
   Imagine seeing Pompey's booty carried through the streets, the beaks of wrecked pirate ships, the gold and plunder, and the beaten captives, now in chains. Floats were popular. Tacitus mentions "replicas of mountains, of rivers, and of battles" (p 109). In case anyone in the crowd wasn't aware of what happened, actors were hired to perform the roles of the soldiers.
   
   It appears that nearly every general and politician and Rome longed to have a triumph.
   
   The defeated were so horrified at the thought of the display and ignominy that we know of quite a number who preferred suicide to participating in a triumph. Famously, of course, Cleopatra, but also Mithradates and Virrius. "When defeat appeared inevitable, Virrius persuaded some twenty seven of the Capuan senate to join him in drinking poison" (p 116).
   
   Those captives who were made to walk through the streets in a Roman triumph to the jeers of the mob had little future happiness in store later. Many were slain. Some, like the defeated Jews driven to Rome after the end of the war in 70 AD, ended up as slaves who helped to build Vespasian's coliseum.
   
   For anyone with an interest in Roman history, this is a book to savor.

5 comments about Introduction to Mathematical Statistics.

1. Excellent Introduction to Mathematical Statistics
   
   Introduction to Mathematical Statistics
   
   by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
   by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)
   
   Publication History:
   
   First Edition
   * (Year 1959)
   * (245 pages)
   
   Second Edition
   * (Year 1965)
   * (383 pages)
   
   Third Edition
   * (Year 1970)
   * (415 pages)
   
   Fourth Edition
   * (Year 1978)
   * (448 pages)
   * (ISBN-10: 0029789907)
   * (ISBN-13: 978-0029789902)
   * (ISBN-10: 0023557109)
   * (ISBN-13: 978-0023557101)
   
   Fifth Edition
   * (Year 1994)
   * (576 pages)
   * (ISBN-10: 0023557222)
   * (ISBN-13: 978-0023557224)
   
   Sixth Edition
   * (Year 2004)
   * (692 pages)
   * (ISBN-10: 0130085073)
   * (ISBN-13: 978-0130085078)
   
   
   I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.
   
   The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.
   
   The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.
   
   Another of my favorites is the last chapter on "Non-Parametric Statistics."
   
   The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."
   
   
   Other references on mathematical Statistics:
   * (Mathematical Methods of Statistics. (PMS-9))
   * (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
   * (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))
   
   
   Probability Theory
   * (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
   * (An Introduction to Probability Theory and Its Applications, Volume 2)
   
   
   The Linear Model
   * (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
   * (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))
   
   
   Non-Parametric Models
   * (All of Nonparametric Statistics (Springer Texts in Statistics))
   * (Nonparametric Statistical Methods, 2nd Edition)
   * ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])
   
   
   I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as were the older editions. I recommend it to others with no reservations.



2. Excellent Introduction to Mathematical Statistics
   
   Introduction to Mathematical Statistics
   
   by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
   by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)
   
   Publication History:
   
   First Edition
   * (Year 1959)
   * (245 pages)
   
   Second Edition
   * (Year 1965)
   * (383 pages)
   
   Third Edition
   * (Year 1970)
   * (415 pages)
   
   Fourth Edition
   * (Year 1978)
   * (448 pages)
   * (ISBN-10: 0029789907)
   * (ISBN-13: 978-0029789902)
   * (ISBN-10: 0023557109)
   * (ISBN-13: 978-0023557101)
   
   Fifth Edition
   * (Year 1994)
   * (576 pages)
   * (ISBN-10: 0023557222)
   * (ISBN-13: 978-0023557224)
   
   Sixth Edition
   * (Year 2004)
   * (692 pages)
   * (ISBN-10: 0130085073)
   * (ISBN-13: 978-0130085078)
   
   
   I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.
   
   The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.
   
   The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.
   
   Another of my favorites is the last chapter on "Non-Parametric Statistics."
   
   The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."
   
   
   Other references on mathematical Statistics:
   * (Mathematical Methods of Statistics. (PMS-9))
   * (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
   * (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))
   
   
   Probability Theory
   * (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
   * (An Introduction to Probability Theory and Its Applications, Volume 2)
   
   
   The Linear Model
   * (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
   * (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))
   
   
   Non-Parametric Models
   * (All of Nonparametric Statistics (Springer Texts in Statistics))
   * (Nonparametric Statistical Methods, 2nd Edition)
   * ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])
   
   
   I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.



3. Excellent Introduction to Mathematical Statistics
   
   Introduction to Mathematical Statistics
   
   by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
   by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)
   
   Publication History:
   
   First Edition
   * (Year 1959)
   * (245 pages)
   
   Second Edition
   * (Year 1965)
   * (383 pages)
   
   Third Edition
   * (Year 1970)
   * (415 pages)
   
   Fourth Edition
   * (Year 1978)
   * (448 pages)
   * (ISBN-10: 0029789907)
   * (ISBN-13: 978-0029789902)
   * (ISBN-10: 0023557109)
   * (ISBN-13: 978-0023557101)
   
   Fifth Edition
   * (Year 1994)
   * (576 pages)
   * (ISBN-10: 0023557222)
   * (ISBN-13: 978-0023557224)
   
   Sixth Edition
   * (Year 2004)
   * (692 pages)
   * (ISBN-10: 0130085073)
   * (ISBN-13: 978-0130085078)
   
   
   I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.
   
   The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.
   
   The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.
   
   Another of my favorites is the last chapter on "Non-Parametric Statistics."
   
   The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."
   
   
   Other references on mathematical Statistics:
   * (Mathematical Methods of Statistics. (PMS-9))
   * (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
   * (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))
   
   
   Probability Theory
   * (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
   * (An Introduction to Probability Theory and Its Applications, Volume 2)
   
   
   The Linear Model
   * (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
   * (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))
   
   
   Non-Parametric Models
   * (All of Nonparametric Statistics (Springer Texts in Statistics))
   * (Nonparametric Statistical Methods, 2nd Edition)
   * ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])
   
   
   I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.



4. Excellent Introduction to Mathematical Statistics
   
   Introduction to Mathematical Statistics
   
   by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
   by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)
   
   Publication History:
   
   First Edition
   * (Year 1959)
   * (245 pages)
   
   Second Edition
   * (Year 1965)
   * (383 pages)
   
   Third Edition
   * (Year 1970)
   * (415 pages)
   
   Fourth Edition
   * (Year 1978)
   * (448 pages)
   * (ISBN-10: 0029789907)
   * (ISBN-13: 978-0029789902)
   * (ISBN-10: 0023557109)
   * (ISBN-13: 978-0023557101)
   
   Fifth Edition
   * (Year 1994)
   * (576 pages)
   * (ISBN-10: 0023557222)
   * (ISBN-13: 978-0023557224)
   
   Sixth Edition
   * (Year 2004)
   * (692 pages)
   * (ISBN-10: 0130085073)
   * (ISBN-13: 978-0130085078)
   
   
   I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.
   
   The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.
   
   The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.
   
   Another of my favorites is the last chapter on "Non-Parametric Statistics."
   
   The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."
   
   
   Other references on mathematical Statistics:
   * (Mathematical Methods of Statistics. (PMS-9))
   * (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
   * (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))
   
   
   Probability Theory
   * (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
   * (An Introduction to Probability Theory and Its Applications, Volume 2)
   
   
   The Linear Model
   * (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
   * (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))
   
   
   Non-Parametric Models
   * (All of Nonparametric Statistics (Springer Texts in Statistics))
   * (Nonparametric Statistical Methods, 2nd Edition)
   * ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])
   
   
   I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.



5. This was the main text in an undergraduate mathematical statistics class I took at University of Maryland. I didn't find it all that helpful--too much important material is shunted to examples, which are not completely explained, or exercises. I would recommend the Mood, Graybill, Boes book as an alternative, unless you have a class where this is required.

5 comments about Statistics, 4th Edition.

1. Many introductory statistics texts suffer from one of two ailments. Either they incorporate too much mathematics for non-statisticians or they provide oversimplified and sometimes incorrect explanations. This text is excellent and is favored by many statisticians who teach the introductory service course for non-statistics majors. The book provides excellent and insightful explanations. It is written by well-known Berkeley statisticians with great theoretical and applied experience, so it is not oversimplified or inaccurate. On the other hand Friedman and his co-authors took pains to minimize the necessary mathematics. It covers all the topics one would want to include in a first course. Real examples are used throughout to illustrate the value of the methods. These include clinical trials and observational studies, telephone surveys and opinion polls and some models in genetics.
   Discussion of the data snooping issue is important, particularly as we move into an age where data mining is now feasible with current computing power.



2. A famous edition of an old standard for stats and I gave this to someone as a gift but knew of it and was told by him that it is still one of the best books on the subject matter.



3. After having progressed through the first 11 chapters of this text, I feel that this text has easily become one of my favorites.
   
   The text uses various real-life case studies (some examples that come to mind are height and weight, IQ, and drug studies) that it will revisit throughout the text. They are, more often than not, interesting and help underscore the practicality of statistics. You cannot go more than several paragraphs without getting involved in a case study.
   
   Although this text is not math-intensive, it does foster something much more useful than an understanding of mathematical equations; it teaches you to think critically about the information that is presented and the questions that are asked of you. To be able to think critically and understand statistics is of the utmost importance, as everyday statistics is, in some way or another, used to justify something. Statistics can be a dangerous tool, and if you don't have a good knowledge of statistics, you may become of a victim of it; the book clearly highlights this fact with examples such as the NFIP vaccination studies, the use of ecological correlations commonly used in political science and sociology, and various observational studies.
   
   If you want math and nothing but math, do not buy this book.
   
   If you want an engaging text with practical examples that will help you to think critically about not only statistics, but also about information in general, I would strongly suggest purchasing this text.
   
   I would also suggest purchasing this item if you want a text that will help you understand the "why" of statistics, not just the "how".



4. No clear examples.
   Unfocused style.
   Celebration of ignorance.
   Overpriced at 0.01+shipping.



5. An excellent intuitive approach to presenting statistics, a subject that can be baffling to the beginner.

5 comments about Optimal Control and Estimation (Dover Books on Advanced Mathematics).

1. Very good treatment of Kalman filter



2. This book has been less influential on me than some others but nontheless I use it to find information on material that is almost impossible to find elsewhere in any kind of reasonable time. A broad range of topics is covered, not just optimal control. This has been particularly useful in understanding some the actual designs I have been asked to analyze.



3. "Fundamentals of Kalman Filtering" by Zarchan is a good book on the subject, but with a cost that exceeds one hundred dollars, this is a real stretch on the budget of college students who are just looking for some help. This book is a great one for people interested in nonlinear controls and the Kalman filter at a budget cost. The book introduces stochastic optimal control concepts for application to actual problems with sufficient theoretical background to justify their use, but not enough to get bogged down in the math. The book gives the reader with little background in control theory the tools to design practical control systems and the confidence to tackle more advanced literature - something that both the professional who is a little rusty and the student can appreciate. The reader should have mathematical maturity on the level of second year calculus.
   
   The first chapter introduces the reader to the concept of optimal control. Chapter two provides a review of the mathematics of control and estimation. For the seasoned reader, you can proceed directly to chapter three with no real loss. Chapter 3 address optimal control of systems that may be nonlinear and time-varying but whose inputs and parameters are known. It illustrates how open-loop control policies generalize to closed-loop control laws when system dynamics are linear and the cost function is quadratic. Chapter 4 presents methods for estimating the dynamics states of a system that is driven by uncertain forces and is observed with random measurement error. Here is where the excellent discussion of the Kalman filter is located. Chapter 5 discusses the general problem of stochastic optimal control where optimal control depends on optimal estimation of feedback information. Chapter six focuses on linear time-invarient systems for which multivariable controllers can be based on linear-quadratic control laws with linear-Gaussian estimators.
   
   The book's examples and problems are directed at confidence building, and thus most of them are rather simple and have the purpose of illustrating concepts, not getting bogged down in mathematics. There are also numerous worked out numerical examples, which is a welcome pleasure in such books that are often very theoretical. Highly recommended.



4. A great Mathematical Derivation of Least Squares to Weighted Least Squares and then the derivation of the Kalman Filter. Great for Undergraduate mathematicians and electrical engineers.



5. This is an excellent and very comprehensive book. I used it primarily to learn about state estimation. I had already taken courses on estimation, but this book was superior to the texts we used in class. It addresses many practical issues that are left out in the other textbooks that I've seen. Issues like how to determine the discrete-time process noise covariance given continuous dynamics and continuous time process noise covariance are covered by Stengel.

3 comments about MATLAB Demystified.

1. Overall this book is a reasonable introduction to Matlab 7.x but it tends to drag in places and seem rushed in others. Also, there are enough typographical errors in the examples to make it difficult to arrive at the expected results especially if one is a beginner. For example, the solution to one of the quiz questions in chapter 5 requires the use of the "eval" function which was never introduced in the book.
   
   Oddly one of the most powerful features of Matlab, programming, is pasted onto the end of the statistics chapter as a brief introduction whereas it should have it's own chapter and covered in a lot more detail. Also, there are chapters on transforms and curve fitting but strangely no mention of time series.
   
   Lastly, quizzes at the end of each chapter often leave out key material introduced in that chapter. Also, the final exam at the end of the book leaves out half of the later chapters.
   
   This is an OK book if you want to master the basics of Matlab quickly but on it's own it's not enough. I would recommend the much better Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers instead.



2. First three chapters, The MATLAB Environment, Vectors and Matrices and Plotting and Graphics, provide a good introduction to Matlab. However, author does not mention that the Symbolic Toolbox is required to work the examples in Chapter 5, Solving Algebraic Equations and other Symbolic Tools, Chapter 6. Basic Symbolic Calculus and Differential Equations, Chapter 8 Integration, and Chapter 9 Transforms. It appears the author assumed the only persons who would buy the book were college students who bought the Student edition of Matlab. Persons who only have access to the commercial version of Matlab will not be able to work the examples in Chapters 5, 6, 8, and 9.



3. If we could classify books intended to teach software in two categories- those focused on the tricks of the latest version and those ones centered in the contextualized applications - MATLAB Demystified would belong to the first class of books. A nice "direct to the point" approach on how to model, code and simulate real life situations. Accessible for all people interested in programming computers easily.

5 comments about Touch and Feel: Shapes.

1. My son is only 5 months old, and he seems like picking up all the book-like objects, so I don't know if he is especially interested in this book or not.

   As a parent's opinion, I like the different texture it offers to my kid to touch in the book, that's why I have bought quite some "touch and feel" style books for my baby. But I find this less perfect.

   I find this book not too creative and imaginative. They always use "buttons" as one of the examples of many shapes. For example, when they introduce circle, there are buttons; when they introduce square, there are buttons; and even heart shape, there are buttons. They could have chosen a greater variety of objects.

   "Cushion" is another object that appears a lot. In both the square and in the star shape sections, there are cushions. I think they could have at least use star fish instead of cushion in the star shape section. That will help the kids to learn more about different things besides different shapes.




2. This Dk touch and feel book is not their best. It feels like they just slapped a few ideas together and didn't really try to come up with real-life, meaningful texture examples. I agree with the other reviewer who said it was repetitive; it is! Enough with the buttons already! Plus, the textures seem forced, like the best idea they had for "fluffy" is a pencil case? and "shiny" is a star that feels bumpy? The examples don't seem relevant to a baby's world.

   (...)




3. This is our second touch & feel book and my son really enjoys the new textures introduced in this book. Not neccesarily the best touch & feel book out there, but still decent.



4. Toddlers really seem to be drawn to the Touch and Feel books. It's a unique way for them to learn and they enjoy it!



5. A fun way to teach shapes to your little one. I thought the images in this book were not as good as they could have been, but all in all another good book by DK.

5 comments about Just Enough Carrots (MathStart 1).

1. A young rabbit and his mother go to the store to pick-up a few things: carrots, peanuts and worms (!). As the mother rabbit picks up different quantities, the young rabbit whines and complains (in a cute way) about the amounts. The mother rabbit compares the amounts to other shoppers in the store using the terms more, fewer and same. Graphics summarize the terms for each item.

   The rhymes strike me as clumsy, but the book is fun to read with various voices for the mother and young rabbit. The young rabbit's facial expressions and gestures lend nicely to telling the story.

   One part that might be of special interest is the young rabbits enthusiasm for carrots. He *likes* to eat them and begs his mother to buy more. For children who don't like carrots, this might just encourage them to "munch, munch and crunch" along with their rabbit friend.

   Both my boys enjoy the book, but my 18 month old seems particularly enamored with it. It's a bit too basic for my three year old, but he still has fun with it.




2. A wonderful way to introduce the math concepts of comparing amounts.



3. I think this book is a great way to introduce beginning math concepts. There is also a section at the back of the book with suggested questions and some activities to further extend the concepts presented. As for comments on the rhyming, I thought it was well done. Any of the "awkward rhymes" were so "barely there" that I hardly noticed them (only because I was looking for them). I felt that it contained enough rhymes to maintain interest but not so many that you are focusing on the rhymes and not the concepts presented.



4. This book helped me introduce more than and less than relation symbols. Also it is easy enough for some of my students to read on their own.



5. This book introduces the counting concepts of the same, fewer, and more.
   
   As I read, I found myself wondering why the author would choose peanuts and worms (in addition to carrots) as items for Rabbit to shop for. I expected cabbage or green beans to be more appropriate and easy for children to relate to. I have not purchased many peanuts or worms when shopping with my kids. Of course my misunderstanding was solved by the end of the book when the guests arrived for lunch! What a fun surprise~
   
   The book is very age appropriate as young children are amazed by both the products in a store and what others are choosing to buy. Even adults will see an item in a strangers cart and think, "Maybe I should buy that too!"
   
   I particularly liked the way the graphics were drawn to explain the difference between the same, fewer, and more. I can see parents easily taking this a step further when children begin to count by having their children count the items in each boxed picture. The adorable drawings and a fun surprise make this a unique counting book.