1 comments about Mathematics Activities for Elementary School Teachers: A Problem Solving Approach (6th Edition).

1. A fantastic book! The most effective way to teach is through ACTIVE PARTICIPATION. This book provides 300 pages of practical, hands-on, concrete math activities that children love. It allows children to truly understand the underpinnings of math--how math works! The activities can be used for grades K-8. Each activity explains the purpose, materials, student grouping (individual, group, or whole class), and how to get started. Here's what's really wonderful--the supplies are contained in the back of the book. The supplies are made of thick card-stock paper that can be lamined. Examples of the supplies are: base ten blocks, geometric patterns, various size matrices, difference puzzles, beansticks, place-value boards, multiplication and division frames, fraction strips, fraction arrays, fraction game board, fraction cards, etc..etc.. You will absolutely LOVE THIS BOOK.

1 comments about Developmental Mathematics (paperback edition) (Martin-Gay Developmental Math Series).

1. Turned out this is the book the teacher was using, it has all the answers in it.

1 comments about Mathematical Snippets: Exploring mathematical ideas in small bites.

1. This book collects an eclectic mix of short subjects and shows a math link to each. Most are extremely trite. many of the subjects have some math background, but the math is not discussed.
   
   This book might be suitable for a child, but not an adult. Buy something else.

5 comments about Ant Colony Optimization (Bradford Books).

1. This book is a fine compilation of what have been done with the Ant Colony paradigm so far. Highly readable, even for people without previous experience in the field of optimization.



2. Fifteen years after the elegant double-bridge experiments by Deneubourg et al. that formed the basis of the Ant Colony Optimization algorithm, Marco Dorigo, the inventor of ACO, and Thomas Stützle, an expert on stochastic local search methods, have pooled their knowledge to summarize the current state of the art.
   This book gives a well paced introduction to ACO, describes its use in various optimization problems and gives interesting examples of its applications in industry. Explanations are clear and concise and, with the exception of a few well defined technical terms, free of scientific jargon. It is a pleasure to read for everyone with an interest in optimization theory. However, if you are looking for a book that celebrates the beauty of nature's problem solving capabilities, you are better of with "Swarm Intelligence" or Flake's "Computational Beauty of Nature". The initial idea of ACO may be bio-inspired, but this book has a crystal clear focus of the computational considerations in optimization theory.



3. Being an ant isn't very complex, but it's a daily fight for life. The losers in that fight don't count, but the winners get to vote.
   
   That is the basis of ant colony optimization. There are many parts to the idea, all of them very simple. First, there are many routes to the goal (food, if you're an ant) - some are better, some worse, you don't know which are which in advance, and the answer may change over time. Second, it's a random search. If you find any answer at all, no matter how convoluted, you get to vote on your route. Third, there are many other ants, all voting. Any leg of a trip that is heavily followed must be part of a good route, and gets many votes. There are details, but that's about it.
   
   Chapters 1-3 are the most readable, and convey the basic spirit of the family of algorithms. Ch. 4-6 will drag a bit, for the general reader, but go into significant detail about the ant algorithm and specific applications.
   
   Ch. 7 ends the book with a warm, informal discussion of the algorithm's history and some delightful variations. Dorigo, the principal author and founder of the ant school, uses this chapter to express his pure joy at having found such a wonderful thing, and at the similar approaches that others have also found.
   
   The approach has some real limits. For example, it can solve only problems that look like finding the shortest route. The good news is that a wide range of unlikely problems can all be cast in these terms. The better news is that, given the many variations available, some form of the 'stigmergic' approach will probably solve any problem in that range. Best of all, though, is the sheer cleverness and the sincere appreciation expressed by the authors.
   
   Nature is economical, but a brilliant problem solver. This is written by someone who as able to listen in on one of the lessons.
   
   //wiredweird



4. The central idea in the book is to analyse what evolution has provided us. In the form of ants being able to find the shortest path over terrain. This ability has inspired the research described herein.
   
   The book can be read as a fascinating deconstructionist approach to observing and manipulating ant colonies. By trying to look under the observations to discern the fundamental algorithms at work. And then to apply these to such longstanding contexts as the Travelling Salesman Problem.



5. Ant Colony Optimization focuses on the fact that ants foraging for food will quickly form a trail that is the shortest possible ditance betwen the food and home. Rach ant follows the scent trail laid on a path by previous travelers and adds its own pheromone to the scent, both going and coming. With a choice, ants tend to follow the strongest scent. Of a pioneer pair, the one choosing the shortest path will make the round trip before the other. Each pheromone trace evaporates in time, but an ant's antenna can detetct the slightest trace. That is a simplification of the introductory chapters of the book. The "pheromone trail" scheme is used to devise "artificial ant" which then takes part in the comnstruction of powerful ant algorithms for solving intractable problems such as the classical "Traveling Salesman" and other routing problems. The book is a complete text for a college course, with a large bibliography and many internal references to sources on the Internet. It is well written, with pseudo code showing how each algorithm can form computer programs. I can't evaluate the difficulty, but for me the math in later chapters is above my reach, but gratifying, nevertheless.

5 comments about MATLAB Guide.

1. I am going to also write a review on "Mastering Matlab 6.0", I will be also comparing the two books in the reviews. It is the basis of my review here. I am assuming (seee below) that one has learned Matlab at the beginning level and is looking for a book to get you to the Journeyman level.

   If you are considering Matlab as a scientific computing language - look no more. It has licensened the "Maple Kernal" as part of its "Math Symbolic ToolBox", it uses LAPAK from FORTRAN for the algorithms for Matrix operations; it uses a high level language (very C++ like) and its own consise syntax for matrix manipulations as well as "Handle Graphics" to produce impressive looking plots and reports. In otherwords, it combines the best of various approaches. If you do not know C++, I advise that learn that first before attempting to learn Matlab.

   Comparing "Mastering Matlab 6" (MM6) to "Matlab Guide" (MG):

   *Both books are NOT for absolute Beginners, I think the assumption is that you will first study the book that comes with Matlab and the supurb "Help" Documentation that comes with the program. There are also good starting out tutorials on the net - search: "Matlab; Tutorial". The US Navy has a consise tutorial to get you started.

   *MM6 does a better job on teaching to the next level beyond the Mathworks supplied documentation and beggining Tutorials.

   Where Matlab Guide falls short compared to MM6: *MM6 WINS HANDSDOWN ON TEACHING version new to 6.0 specific features. You are short changing yourself by going for a 5.0 text. It is not as well cross referenced as MM6. "Where is the code to solve real world problems" is a grievance I have with MG.

   *MM6 is geared more towards a programmer/scientist/engineer really needs to know; whereas, MG is geared to a mathematician. If you want "A survey of Mathematics with Matlab as your Guide" (a more appropriate title in my opinion) then this (MG) is your book. This book really jumps around. Example: Fibonacci sequence on p9, Collatz iteration on p10, Systems of Linear Ordinary Differential Equations on p12, Sierpinski gasket (fractal geometry) on p.17....

   WHAT IS MISSING in MG: * Matlab 6.0 specific features. * Extending Matlab with Programming languages * Integrating it in with Windows./GUIs/ Dialog boxes.

   Don't get me wrong, I eventually will read all of this book and learn a lot of math in the process - but to get to the Journeyman level in Matlab as an engineer or scientist, I reccomend MM6 instead. If you want to get real math specific, MG is your choice - but you will not learn as much Matlab and problem solving with Matlab.




2. I bought this book because I saw the good reviews about it here. I just started to learn Matlab, so what I really need is a book that can describe things clearly, and STEP BY STEP. When I was reading the first chapter, which is a small Matlab tutorial (The authors stressed that the readers should walk through chapter one), I got so frustrated because there are so many functions and procedures I don't know and the authors don't explain (They defend this in their preface though). I moved on to the rest of the book and I found that it happens everywhere: this book keeps jumping on some fancy math subjects without explaining clearly the fundermentals. They didn't bother to explain the syntax for lots of programs.
   I gave up on this book. What I had to do is find a online tutorial to get me started. I did find one good tutorial from University of Dundee, you can search its website in google. I am going to keep Matlab Guide in case I need it some time. But for starters, look elsewhere.



3. This is a book that doesn't ignore that MATLAB is a tool for mathematicians, but at the same doesn't alienate the non-specialist.

   Starting with a basic tutorial and continuing with useful short cuts and introductions to script files, functions and graphics this book gives the reader an immediate working knowledge of the basic functions and data structures of MATLAB.

   Later chapters address linear algebra (with treatment of eigenvalue problems, linear systems and matrix decompositions) and numerical methods (for differential equations and other problems); both with enough mathematical background and each topic can be accessed independently.

   The book finishes with important topics such as optimizing functions, input and output, use of the Symbolic Toolbox and a final chapter with more tricks and tips.

   You are left convinced that the authors are extensive users and admirers of this software, and through this book the reader can become the same.




4. Matlab Guide is a clearly written, well structured and quite comprehensive account of the capabilities of Matlab. In each chapter, the material explained swiftly progresses from the simple to the more complex, making this book a concise source of information and an excellent reference for the intermediate to advanced Matlab user. The focus is on mathematical topics; the pieces of example code are a nice mixture of playful toys and serious applications. Also, the book contains important hints concerning efficient programming, it has a very agreeable layout, and the citations at the end of each chapter do their job in keeping the reader's mood at a high level. Clearly, absolute beginners may have a hard time working their way through it, and the coverage of isolated topics, like file input/output, is a little meager. However, this is only a minor point. All in all, so far having used matlab primarily for data analysis (electrophysiology) I very much enjoyed and benfited from a fresh look at it from a different perspective.



5. This is a good book on MATLAB but it is not designed for beginners. This book covers the basics, programming, graphics, linear algebra, and numerical methods. It also has a chapter on symbolic computing with MATLAB using the Symbolic Math Toolbox. However, if you are just beginning to learn MATLAB, check the book "MATLAB for Beginners: A Gentle Approach".

No comments about Learning Mathematics in Elementary and Middle School: A Learner-centered Approach (4th Edition).

5 comments about Mathematical Methods for Scientists and Engineers.

1. I looked at the table of contents for this book and determined that I already have every chapter in this book in my math books, and ones that can be found for less total than this book (using Dover). If you can handle looking in more than one book, you can get this entire book from one of each of the following: introductory analysis (Taylor & Mann, among others), any diffeq text and your choice of Dover books on complex analysis. There is no point to owning this book.



2. The book is essentially like calculus for people who are considered dummies by dummies. Its too easy and I don't think there are people out there who are as stupid and still take calculus as the author hopes to find. I had to buy it because my professor had put it as required. A much terser book is by Arfken and Weber.



3. I loved this book. It's got all the necessary topics, and occaisionally if you look in the right place a neat trick. I majored in math and took two math methods classes all of which used different books and I think this is your one stop shop for it all. My only complaint is that the material is basic. best probably for undergrads majoring in math/phys/chem/engin



4. This book is promising but ultimately falls short. First, the order of the book is rather strange, placing matrices in the middle of the book as if to divide the calculus and complex analysis in two. Once you get over the way the book is sorted, the book improves slightly.
   
   But then you start looking at all the typos and textual errors in the book and it is clear that the book is in dire need of a second edition. Typos are all over the place, from mislabelling figures to labels that make no sense. Division lines are often missing and reading the answer key is like flipping a coin to see whether the answer provided is reliable.
   
   The way the book is worded is often confusing, and the writing is something that Arfkin and Weber certainly excel far better in than McQuarrie.
   
   Over all, I would bet that a second edition makeover of the book would do wonders, but I wonder why this book is necessary when better books such as Arfkin and Weber are out there in the first place.



5. The book came very quickly - well before the latest estimated arrival date. It was in the described condition - very good. Overall a very good experience

5 comments about Martin Gardner's Mathematical Games.

1. Martin Gardner's 30 years of Mathematical Games columns in Scientific American magazine are some of the most fun and interesting reading I've enjoyed. I searched out back issues in the high school library, had my own subscription, and collected as many of the books as I could find. When I was looking for one of the books I didn't have and found this complete collection, I immediately ordered it. There are very few authors in any field who are as clear in their writing and as enthusiastic in their delivery as he is. The content is easily worth the full 5 stars.
   
   But the reason I dropped the rating to 4 for this particular edition is its sometimes haphazard quality of image scans. In the worst cases, the color or shading in the original figures is now black-and-white and of such high contrast that important distinctions are mostly or completely lost. For example, the reversi piece colors in figure 29 of "New Mathematical Diversions" are indistinguishable as are the four-color map areas (of all things!) in figure 43. Many figures show moire patterns from rescanning the original halftones. Yet other figures have been reproduced with much greater care, even in color. Some pages with landscape layout have been rotated for easier reading but others have not. In a few cases, the black-and-white photographs in my books have been replaced with much better color photos. Some books are missing a back cover scan.
   
   The oddest example though, and somehow in keeping with the topic, is figure 109 in "Fractal Music". In my copy of the book, this is a reproduction of Magritte's "The Two Mysteries" and the caption says so. In this edition, it is a redrawn version and the caption now says it is "a caricature" of the Magritte work. At least 4 of the books appear to be affected by poor images and at least 6 of them appear to be fine.
   
   Despite these problems, it's very handy to have the complete set of books in one place. But I'll be keeping the 4 books with the bad scans until a new edition fixes them.



2. Those of us old enough to remember Martin Gardner's columns in Scientific American should buy this CD at least for old times sake. All the favourite characters like Dr Matrix and his daughter are there and it brings back many happy memories of trying to work out some of the problems Martin posed



3. It's always a pleasure to read anything by Martin Gardner. By getting his works on disk, I can have them on my laptop - much easier than books. The only reason I give this collection 4 instead of 5 stars is that I would have liked the books to be in a more searchable format than PDFs - a minor complaint.



4. Millions of people around the world have had their interest in mathematics lit, kindled or fed by the writings of Martin Gardner. His regular column "Mathematical Recreations" appeared in "Scientific American" for over a quarter of a century and those articles were readable, entertaining and highly educational.
   This CD-ROM is a collection of all his articles organized according to the book in which they appeared. The books are:
   
   *) Hexaflexagons and Other Mathematical Diversions
   *) The Second Scientific American Book of Mathematical Puzzles and Diversions
   *) New Mathematical Diversions
   *) The Unexpected Hanging and Other Mathematical Diversions
   *) Martin Gardner's 6th Book of Mathematical Diversions from Scientific American
   *) Mathematical Carnival
   *) Mathematical Magic Show
   *) Mathematical Circus
   *) The Magic Numbers of Dr. Matrix
   *) Wheels, Life and Other Mathematical Amusements
   *) Knotted Doughnuts and Other Mathematical Bewilderments
   *) Penrose Tiles to Trapdoor Ciphers . . . And the Return of Dr. Matrix
   *) Fractal Music, Hypercards and More . . .
   *) The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications
   
   The opening page displays icons of all of the books and clicking on any icon switches the display to a split screen where the left section contains the table of contents and the right contains the text of the book. Clicking on any entry in the TOC takes you to that article. The collection is searchable, so if you have only a dim recollection of an article you read years ago, you will still be able to find it.
   Martin Gardner is a very humble man, arguing that his skill in mathematical exposition is due to the fact that he does not know very much mathematics. He claims that this forced him to research his subject thoroughly before he began writing the article. I find this the only questionable position that he has ever taken; in my opinion the man is a mathematical genius.



5. 
   Martin Gardner has written very entertaining and engaging books about an incredibly wide variety of mathematical worlds and puzzles, and in the process made complex mathematical ideas come to life. This CD features 15 of his books in pdf form. The pdf files consist of page scans, which makes the pdf scroll a little slowly, but that isn't much of a problem.
   
   I highly recommend this to anybody interested in recreational mathematics.

5 comments about The Universe and the Teacup: The Mathematics of Truth and Beauty.

1. Chapter two, second paragraph: "The Milky Way galaxy contains 200 billion stars..."
   Chapter two, a few pages later: "Fifteen billion is also more or less the number of stars in the galaxy." Obviously, the number of stars in the galaxy is not precisely known, but we do know that 15 billion and 200 billion are two different things. One of the author's "truths" is self-evidently not true. Purveyors of "truth and beauty", whether scientists, gurus, philosophers, spiritual leaders, or journalists, often regard their subject and their audience far too casually. Here we have a case in point. Perhaps most books contain 'typos' and the miscues inherent to humanity, but here it seems that both the author and the editor were asleep at the wheel, something that needs to be addressed if the book achieves a second printing (and I don't see why that would happen).
   The subject is truly fascinating; or at least it should be -- the relationship of aesthetics, mathematics, and logic. At the deepest levels of the human intellect's inquiries, the answers are all about a mysterious mathematical beauty. The reality of this escapes most people, which is why the "National Bestseller" heading on the cover of Cole's book intrigued me. Apparently the book has enjoyed a larger readership than most such popularizations. Unfortunately the superficial, disjoined 'newspaper style' of science serves the material poorly. The writing rambles almost aimlessly. The books of many mathematicians and physicists have examined the relationship of reality, reason, mathematics, and aesthetics. Devlin's 'The Language of Mathematics' is very good. Fairly recent works by Penrose, Davies, Rucker, Berlinski, Greene, and others come to mind. Some of these books are far better than others. This volume is one of the others.



2. Being disenchanted with religion, I picked up this and other books in search of some other kind of truth. I do feel as though after reading this book I have a much better understanding of what 'truth' is and what it's not. I think those who nit-pick about their claims of little discrepancies in the book are really missing out on the bigger picture. The book is full of interesting little facts and factoids but the interesting thing to me was to see how she's pulled together these common insights that are gained from so many fields of study. I think this was just about my favorite book ever.



3. That's a direct quote from Amazon, and boy, were they right. Only Cole would link the O.J. Simpson trial to the discovery of the top quark in order to explain various roads to truth. The best part is the relationship between beauty and truth, in which she explains the unexplainable--showing how Einstein's theories (and in fact, all modern physics) is based on the notion of symmetry. But there's also so much less etheral food for thought here: the geometry of fairness, for example!



4. Expounds some sort of "new age" mathematics where clarity,
   accuracy and consistency are evidently unwelcome. Perhaps
   this was intended to make the result non-threatening, but it
   is neither beautiful nor useful.
   
   It will go down in history -- with luck, leaving not a trace.



5. Three stars? For a book that was a best seller from LA to Taiwan, and is an absolute delight? Beloved of physicists and teachers across the country? Clearly, politics has tainted many of the comments. Yes, Cole is a liberal--but then, so are many scientists... and for a good reason! This is a five star book if there ever was one.

2 comments about Classical and Quantum Computation (Graduate Studies in Mathematics).

1. The book covers classical and quantum algorithms;-- of the 250 or so, pages of text, roughly the first 50 pages are "classical", the rest quantum;-- and indeed the aim of the book is to teach the wonders of the qubit-algorithms. While other books, such as Nielsen-Chuang, serve as (more or less)comprehensive references, the present book (by Kitaev et al) is focussed on complexity. The mathematical prerequisits are minimal, but a reader with some understanding of basic ideas from CS, and from quantum theory (at the level of ch 1 in Nielsen-Chuang), will get more out of Kitaev et al. The book is a translation of a Russian 1999 original, but it is really well done, and nicely updated;-- for example, a handy appendix was added, covering elementary math terms that are used.
   The book does a great job in explaining the fundamentals, both at the level of the *intuitive ideas*, as well as the mathematical proofs. The big question is why some qubit-algorithms (such as P Shor's factoring algorithm), are a lot better than classical counterparts(for example polynomial vs exponential), and a reader comes away with a good understanding of this in the end.



2. I started off learning Quantum Computation and Quantum Information by reading Nielsen and Chuang's book in order to do research in my junior year on quantum cyptography. Despite the completeness and popularity of that book, it did not exhibit enough explanation and insights for me to be truly satisfied that quantum computation will truly take flight one day to be implementable in place of classical computation.
   
   Recently, in my preparation for my qualifying exam in Quantum information at MIT, I commenced reading this book. The feeling was like drinking a long cool sip of water after a 10 mile run. In particular, I really like the mathematical rigor of the writers. I have known Kitaev as a clear and careful presentator while I was at CalTech as an undergrad, and this is clearly reflected in his book. I definitely would recommend this book to anyone interested in Quantum computing and quantum information, professionally or amateurishly to buy this book (and no, I was not bribed to give this review in order to pass my quals!).