1 comments about A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series).

1. Discrete maths underpins most of modern cryptography and information theory. Quite different from continuum maths like calculus that a student might already be familiar with. Here, Anderson provides us with a concise introduction to the subject, that assumes no prior coursework in this field.

   He manages in a short text to cover a wide range of reasonably advanced issues, like the finite projective planes and magic squares. In keeping with many of the Springer maths texts, the level of analysis is not trivial. (Not a Dummy's book!) Still, with careful attention, a competent student should be able to assimilate these ideas.

3 comments about Fragments of Infinity: A Kaleidoscope of Math and Art.

1. Mathematics and art have many things in common, something that practitioners of both often go to great lengths to refute. In this book, Ivars Peterson, one of the truly great practitioners of the art of popular mathematical writing, shows us how intertwined they really are. The sculptures that he describes and explains are truly astonishing. I looked at some of the photos for several minutes, seeing many different things, even though I was limited to the two dimensional projection. Without a doubt, the piece itself must be truly breathtaking.
   Many popular mathematics books have delved into the synergy of math and art, but never to this extent or with this effectiveness. This is by far the best book I have ever seen in this area and I recommend it to my artist friends as well as those who practice math.



2. "Fragments of Infinity: A Kaleidescope of Math and Art" is a compilation of beautiful examples of mathematical art. It will give the lay reader more than an inkling of the connection between advanced math and beauty -- a connection that is ordinarily very difficulat to convey. And it will give the mathematics professional something to savor as well.

   Unfortunately, the book has two major flaws:

   1) It entirely omits art from computer graphics, which is perhaps the largest source of extraordinarily beautiful mathematically-based art these days -- and it is art which translates to the printed page just as well as traditional sculpture or painting does, and

   2) This book displays a shaky grasp of mathematical concepts by the author and most likely an absence of fact-checking by the publisher. For example, although the book's main mathematical topic is geometry/topology, the author shows on page 141 that he does not even comprehend what a Moebius band is, where he claims that the triangular but assymetric recycling symbol is a Moebius band (correct), but that the symbol having full 3-way symmetry is not a Moebius band (incorrect). Unfortunately, gaffes like this are widespread in the author's previous books as well.




3. Fragments of Infinity is one of my favorite books. One reason is because the author Mr. Peterson gives an indept explanation as to how mathematics and art work together. I really loved the pictures and illustrations. I actually used them as a guideline for my own artistic creations. I've even made several model spaceships with the information given. This book also has an excellent source of information for students of mathematics to use on everyday homework assignments. I would suggest this book for an artistic person, whether it be a child or adult, who has a problem with math because "Fragments of Infinity" is an excellent resource to enhance one's understanding of math along with the creativity of art.

4 comments about The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes.

1. From over 300 references, David Darling has compiled what I, a non-mathematician, consider to be an excellent encyclopedia of mathematics. There are over 1800 entries. There are simple definitions, more in-depth explanations, graphs and many photos. He illustrates well the application and appearance of many abstract mathematical concepts in the real world of art, architecture, etc.
   
   In addition to the hundreds of 'pure' mathematical references, he also includes many entries that are fun for everyone. These entries include puzzles, games and tricks.
   
   I enjoyed the background and historical information included in the biographies of the many mathematicians covered. Historical information about concepts and values, e.g. pi, is also included, such as the time Indiana almost voted to round pi off to 3.2!
   
   This book would be an excellent library builder. It is hard to read straight through - I tried it and failed - but as reference and reading here and there it is great. It is good enough that I want to find his other references and check them out as well.



2. I enjoy reading mathematical dictionaries. Whether I read it from cover to cover or scattershot style, I always learn something new. In this dictionary, I learned about the "Seventeen or Bust" distributed computing project, where the goal of the project is to check the remaining seventeen possibilities to be the smallest Sierpinski number. I also was reminded of many other mathematical facts that I have encountered sometime in the past.
   The manuscripts that I receive as co-editor of Journal of Recreational Mathematics contain a wide variety of mathematical ideas. To handle them all, it is necessary to keep a mathematical dictionary handy. Since this book is well written and has over 1,800 entries, I have placed it on my essential reference shelf.
   
   Published in Journal of Recreational Mathematics, reprinted with permission.



3. I have had an interest in Recreational Mathematics ever since my High School days; at least 55 years ago. I can still remember constructing a 15 Puzzle using a block of wood and my mother's wooden yardstick,with numbers pasted on from a calendar.Then there was the cardboard set of Tangrams I made after reading about them in a book.The next thing I can recall was Magic Squares and learning how to solve any odd-number.I was then nearly driven to distraction trying to find the "secret" to solving even- numbered Magic Squares. In High School,after encountering Logrithms for the first time,I couldn't get enough of them.I was talking to my Math teacher one day after school,telling him how fascinating I found them. He reached into his desk drawer and pulled out a Slide Rule.He asked me if I knew what it was. I had never seen or heard of one. He showed me how it was based on Logrithims and could be used to multiply,divide ,etc. Then he handed me a little booklet and sent me packing with it and the slide rule. It was the most fascinating thing I'd ever seen and almost as much fun as girls and shooting pool.I guess my love for puzzles and such was what led me into pursuing college and eventually becoming an Engineer.
   All through the years,I've retained this interest in Puzzles and Recreational Mathematics. I started to acquire books on the subject,and once reading about Sam Loyd and the "Cyclopedia of Puzzles" ,I couldn't contain myself until I could at least see it and maybe even acquire a copy.It was published in 1914,and included over 5,000 puzzles,tricks,conundrums,riddles,etc.,of which about 1'000 are illustrated.Solutions are printed in the last pages.However,a number of puzzles were selected as "Prize Puzzles" and the solutions were withheld.A prize of $100 would be awarded to the person who sent in the best set of correct answers before January,1915.Because of errors,multiple solutions,impossible solutions,etc., it was impossible to determine a winner. It was quite a story!.After much effort,I finally got myself a copy and without doubt it is my prized puzzle book possession. I have never seen another copy,but it is sometimes shown in other puzzle books. I believe it has been reprinted ,and a condensed version was also published.
   Over the years,I have added many Math and Puzzle books to my library and now have about 600.
   I go through all this ,just to show you how much I think of this new book by David Darling.
   I don't know whether it should be called a Dictionary,an Encyclopedia, (it's not a "Cyclopedia" as Sam Loyd called his),a Compendium, or what. It is all those things and much more.But not to worry,Darling had to call it something and I guess his title is as good as any.
   It is a basic reference book dealing with all kinds of things,people ,definitions,theories,puzzles,terms, and Recreational mathematics. If you are reading about anything or anybody in these areas and want to know more;this will be the book to turn to to get started.
   The book is organized alphabetically,like an encyclopedia,but also has an Index by category. It has an extensive and excellent Reference as well.
   There is no doubt that I will turn to this book often in the future.It's only a shame I didn't have it ;or something similar to it many years ago.
   Please don't take a few things I'm going to say as nitpicking. That is not my intent,So,here goes;
   
   On page 278 it talks about the Rubik's Cube solution record being around 20 seconds. In 2003,the World Championship was held in Toronto.The winner was able to set a new record at around 16 seconds. This year,2007 a Canadian Championship was held. The winner did it with an average of 14.21 seconds.including one solving under 10 seconds.One solver managed to solve it in 4 minutes and 54 seconds...blindfolded.
   On page 117,the 15 Puzzle is said to have been invented by Sam Loyd who could not obtain a patent. In 2006,Jerry Slocum published a magnificient book on this puzzle.In it you will see who the real inventer was,and how Sam Loyd fooled everyone about it for 115 years. It was actually invented by Matthias J. Rice in 1879,and was originally called the Gem Puzzle.This book does a marvelous job of researching the history of this puzzle.(See my review,June 6,2006.) Mr Slocum has also recently published another excellent book on Tangrams which I also reviewed on Jan 6,2004.He has written several other books on Puzzles,has the world's largest puzzle collection,and heads up the Slocum Puzzle Foundation and Museum in Beverly Hills,California.
   The author has done a very good job of discussing Polyhedra,and has shown several in his book. I would like to point out the work done by Magnus Wenninger,who is the world's expert on constructing Polyhedron Models. He has written an excellent book on the subject as well. He has a web site showing many dozens of his models. Just search the net under Mangus Wenninger .If you enjoy these models,it will blow you away. You can even purchase them at extremely reasonable prices. I first became aware of him through someone who constructs similar models.He takes a different approach,and builds his using balls and sticks. They are simply delightful and remind me of the illustration of the molecule at the top of the cover of this book.
   Just to keep things interesting,there are many puzzles included throughout the book. If you have been interested in this sort of thing ,you'll have encountered many of them over the years. If Mathematical Recreations is new to you;this book is a wonderful introduction to it all.
   What more can I say? If you're into Mathemtical Recreations,Mathematics in general and Puzzles of all types ;you are going to love this book and want a copy.
   I have been searching for the name to describe someone who is interested in solving puzzles. The best I have been able to find so far are; METAGROBOLOGIST and OMNIHEURIST. if you know of any others ,I would be pleased to hear from you.
   
   Thank you David,it's a great book!



4. This encyclopedia of mathematics was quite worthwhile to read nevertheless.I expected an in-depth review of various famous math formulas and procedures for calculating numbers and short stories about the people who created them.Most of the items listed were interesting to read about.Yet,some were just trivial in nature.Based upon the glowing reviews,i felt compelled to investigate this book further.For the serious math student,this book is more crust than bread.For a book entitled,'Universal',it's fairly enclusive to the British and German mathematicians only. Now,puzzlers and ratzlers may be entertained by the charming entries within and even given the impetus to advance their research into weightier mathematic descriptions.However,this book only appears on the 'heavyside',not really enriching enough to nurture a sprouting engineer into fructation.A better title would simply be,"A Short History of Popular Mathematics and Puzzles".

1 comments about A Dictionary of Weights, Measures, and Units (Oxford Paperback Reference).

1. This gives a very authoritive discussion on many of the topics of regular and metric measures.

5 comments about Handbook of Mathematics.

1. Bronstein's "Taschenbuch der Mathematik" is a longtime favorite among german science and engineering students. English language readers should be aware however, that there are numerous different editions of this book. Not only were the german editions constantly enlarged and reworked, but there were also two publishers of the same book, one in East Germany (Teubner Verlag), one in West Germany (Harri Deutsch Verlag). Today both of these publishers sell a "Taschenbuch der Mathematik" based on the original Bronstein, yet they are completely different books. The english edition by Springer Verlag advertised above is based on the current Harri Deutsch edition. An english translation of the Teubner edition is now available as the "Oxford Users' Guide to Mathematics" from Oxford University Press. It is mostly considered to be the better 'Bronstein' (even though Teubner and OUP have dropped his name because the new edition was completely rewritten by E. Zeidler).



2. This book is exactly what the title says it is; a handbook of mathematical techniques and formulas for scientists and engineers. It is more a handbook than a book on mathematics and assumes a prior knowledge on the subjects covered. Readers of this english version of the Bronshtein should take note that it is a "raw" translation of the german version and so some discussion may not do justice to the theory. This in no way takes away from the fact it is an exceptional book and you'd be hard pressed to find any other book with more mathematical content.



3. This handbook contains more material than I find in any other single source that I happen to have. But I don't use it as frequently as I use the analogous CRC handbook, or MathWorld and Wikipedia on the Web, or the ancient NBS handbook. Why not? Because one uses a handbook, not as a textbook, but as a source for things one should know, but don't (or perhaps once knew but have forgotten). So one wants to find the thing one is looking for, refresh or extend one's memory, and then put the handbook aside and go back to the problem one is trying to solve. I have trouble locating what I'm looking for in Bronshtein and Semendayev, and when I find it, I often find that I have to look up things elsewhere in the volume to get all of whatever it is I was looking for. So I try my other sources first, and if they don't answer my question, I pick up this book, resignedly, and expect to spend hours rather than minutes getting whatever it is I want to know. There is nothing wrong with that; indeed, this book often supplies me with answers to questions I can't find answered elsewhere.
   
   In case the reader of this review attributes my difficulties with this book to a lack of mathematical background, I'll remark that my academic training, very many years ago, was in math, so I find that I can follow the discussion in this book of any particular thing I look up; it's just a slow process for me. I'm not surprised that it's a favorite in Germany (and in Europe more generally); Europeans in their mathematical training are expected to deal with tough subjects by dogged persistence, and probably feel more comfortable with this style than I do, given my US background. So, overall, it's a book I couldn't do without, but hate having to spend time in.



4. I highly recommend the Handbook of Mathematics. It is an excellent resource for every engineering student and professional engineer.



5. Product was "as expected". I am very satisfied with the quick response to my order.

5 comments about All the Math You'll Ever Need: A Self-Teaching Guide.

1. I am not even halfway through this book and have learned a lot. Math is and has always been my worst subject. I know more now than I have ever known about math. I'm sure by the time I am done with this book I will still be a satisfied customer.



2. Excellent book except that it doen't teach how to calculate loans and mortgages.



3. I was about to take a test for a state job when I took a practice test and realized I had forgotten the formula's for my Math..I got this book
   and within a few days I was up to speed..It is an excellent way to refresh your Math knowledge..I found the book easy to read and the solutions to the Math problems were fully explained in an easy to understand way..I had been out of school for quite a while and this book helped me to do very well on my test..Thank you Math made easy :)



4. Hard to follow at first. Helped me pass the nursing entrance exam, after being out of school for 20 years.



5. This Math book is one of the best ever !!! Simple examples , Simple explanations ! This book makes Math fun .

No comments about Mathematical Investigations.

No comments about MP Basic College Mathematics (softcover).

3 comments about Merriam-Webster's Guide to Everyday Math : A Home and Business Reference.

1. Many of us forget math concepts we were introduced to at school. For a quick brush up, this is a good reference book. Fractions, decimals, percents, arithmetic concepts, elementary algebra, trigonometry and other such items are all covered. Besides, in keeping with its title of "everyday math," the book also goes into such things are interest rates, IRA and 410(k) math, stocks, mortgages, basic book-keeping and even casino gambling! The occasional anecdote or story pertaining to math (one was on the titles of alcohol measures such as jeroboams and rehoboams, another on the Father of Algebra) give welcome breaks from the technical text.



2. This a very helpful book. I know a home-skooler wacko who distrusts government but trusts this volume enough it is the main textbook in maths for her 6 year old. I claim responsibility for introducing wacko and her treble wacko hubby to his book ... desperation, the kid is not going to be engineer material [but I can hope] but I am trying to save him from a life of flipping hamburgers.
   That written, much of this book covers what was called `practical math' ... really useful stuff not `rocket science' stuff culled from an MIT blackboard.
   This book not only well written and understandable it is totally without the sick `humor' which seems to be in style in maths books.



3. I can't imagine what's not to like about this book. You won't find derivative tables or anything but you will find explanations and formulas for almost any math you'll need in daily life. I especially like the book because it gives explanations and concepts that lie behind the numbers and formulas. For example, in the money section you'll find the standard formulas but you'll also find hints about investment strategies (mathematically based) and hints for reading stock tables. A great reference book.

3 comments about New Directions in the Philosophy of Mathematics.

1. Hi, I'm one of the contributors to Tymoczko's anthology, and I would like to suggest a related book on the quasi-empirical view of mathematics. That's my book "The Limits of Mathematics" just published by Springer Verlag. Together these two books make a nice set. Greg Chaitin, IBM Research



2. After almost a century in which the attempt was made to reduce philosophy of mathematics to set theory, philosophers have begun to reconsider the traditional approaches. The Tymoczko volume provides a solid intro to these new approaches, that is both readable and insightful. A background in formal logic, or traditional philosophy of mathematics, is not presupposed, as there are basic essays that should get the reader up to speed on the terminology. Nor does one have to be a mathematician to appreciate the thoughts presented. At the same time, I don't believe any mathematician would be offended or alarmed by the presentations of this book.

   Ultimately, there is no final consensus offered. Rather, the topic is reinvigorated with a collection of fresh approaches that do not falsify the experience of mathematics by trying to reduce it to something else.




3. To most people, "philosophy of mathematics" probably sounds like the driest subject in the world. I admit that a typical person in the street would probably never want to read this book, but many people who would be put off by the title would find it fascinating.

   The basic question is how we should think about mathematics. When we do mathematics, are we describing an independent reality, following arbitrary rules, building a social construct? One can ultimately say only so much about this particular question, but it leads off in many wonderful directions. To me, the highlight of this book is the article by Thurston, which provides a beautiful description of how mathematicians actually think about and do mathematics. It really rings true to me (I'm a mathematician too), and is much better than any other account I've ever seen.

   In general, whenever people seriously discuss the philosophy of mathematics, they are likely to make revealing comments about their approach to the field. People who are curious about this (e.g., students considering studying mathematics, or anyone who has heard about the results of mathematics and wonders about the mindset behind them) should read the book. As a bonus, once they start reading the essays they'll rapidly start caring about the philosophical issues as well, even if they've never thought about them before.