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Customer Reviews (8)

vol 2 world of mathematics
I'm happy with the book, yet, when I ordered it I thought i had the deal of a life time on a used 4 vol. set. I double checked the page and each time i looked it seemed it indeed was the 4 vol. set. When, only one book, volume 2, arrived i went to the web site and looked to make sure i hadn't missed anything. it didn't seem I had but on closer inspection, further down the page it plainly said: volume 2. Unfortunately, Vol 2 was the one I could have done without. It would have been helpful,if,the information about what i was getting was the first thing i saw. then, i would have shopped some more and would have purchased the 4 volume set. I called and talked to one of your representatives and was told I could return it. I was thinking that would really be the best thing to do when i became ill and was hospitalized. Only now, am I well enough to sit at my pc and write this review. The book is in great shape. I will purchase from you again. good service and customer service.

Great Boxed Set on a Great Subject
I acquired this boxed set from a library sale for only $5, and I didn't read any of it for almost a year, what a mistake that has been. The articles included are unabridged and begin with an amazing commentary by James Newman, which adds to the experience of reading the article, which a commentary should do. The articles range from simple to fairly complex, but they are all fairly easy to grasp with a marginal grasp of mathematics.

All in all, this set is worth every penny that I paid for it, and much, much more.

Great Authors, Great Articles, Great Fun
I pencil in the date that I finish reading each article in James R. Newman's four volume, "The World of Mathematics"After a good many years, I now find that I am more than halfway through Newman's remarkable collection that spans 2500 pages.

Newman described his work as "a small library of the literature of mathematics form A'hmose the Scribe to Albert Einstein, presented with commentaries and notes".The topics have been chosen with care.Newman preceded each article with a thoughtful commentary.

The individual articles are not abridgements, but are reprinted in their entirety.Some articles are short, some quite long, some are easy reading, some are difficult, but few are overwhelming.

I have not systematically read section by section.I find that I skip around.Often, after Newman introduces me to some mathematical topic, I find myself sidetracked, exploring other books and authors.But eventually I return to Newman, select another article, and begin the cycle again.

The Newman collection was published in 1956 as a boxed set that occasionally shows up in used bookstores. More recently, the four volumes have become available in soft cover (a Dover reprint) and can be purchased individually.

What makes Newman collection so remarkable?The answer is great original papers, great authors, and wide ranging topics.

Imagine reading Descartes on Cartesian coordinates, Whitehead on mathematical logic, Weyl on symmetry, Dedekind on irrational numbers, Russell on number theory, Heisenberg on the uncertainty principle, Turing on computer intelligence, Boole on set theory, and Eddington on group theory.

I enjoy the biographical and historical articles scattered throughout the four volumes.I especially liked Bell's article "Invariant Twins, Cayley and Sylvester", The Great Mathematicians" by Turnball, and G. H. Hardy's "A Mathematician's Apology".

Mathematicians try to define just what is mathematical thought and how a mathematician creates mathematics. Clifford writes about "The Exactness of Mathematical Laws", Von Neumann on "The Mathematician", Weyl on "Mathematical Way of Thinking", Poincare on "Mathematical Creation", Newman on "Godel's Proof", and Russell and Whitehead separately offer their thoughts.

This is the "World" of mathematics. Newman's assemblage also includes a fascinating, eclectic mix of articles that I have not encountered elsewhere like "How to Hunt a Submarine", "Durer as a Mathematician", "A Mathematical Approach to Ethics", "Geometry in the South Pacific", and "The Vice of Gambling and the Virtue of Insurance".

I have had great fun wandering through this four volume set from section to section, article to article. I assume that someday I will finally read the last article.I expect that I will simply begin again. It would be hard to say good-bye to Newman's collection.

Superb reference text for the general reader..
This four volume set is a gem.I bought this treasure back in 1973 but Istill go back to it at least twice a week.The writing is uneven becauseof the different authors who have contributed articles.However, thesubstance of the book is top notch.Starting with the number system allthe way to the differential calculus and parts of game theory, the book isa treasury of mathematical delights.Just pick a chapter, and you are sureto be sucked in.Another point I wish to make is the design and layout ofthe books.There are no slick, extra large, shiny page designs here.Justplain 6 by 8 size pages with appropriate black and white diagrams.This iswhen books used to be more like friends, often in one's company, and muchperused.It is truly a shame that this series is out of print.If youhappen to find it somewhere introduce yourself!!

Es una obra Exelente para entender las matematicas
Al leer esta enciclopedia, aprendí que las matemáticas pueden ser fascinantes, y no muy difíciles de entender. Es muy agradable entender los razonamientos que impulsaron grandes descubrimientos, en estos Libros elautor nos explica claramente todos los pasos para ello. Nos muestra eltrabajo de los mejores Matemáticos y las consecuencias de sus trabajos. Noscontagia el gusto por esta ciencia. En México se puede conseguir en lalibrería La aventura de Leer .

Jorge Gallegos ... Read more

Product Description

Building on its reputation for accurate content and a unified system of instruction, the Seventh Edition of Bittinger/Beecher’s Developmental Mathematics paperback integrates success-building study tools, innovative pedagogy, and a comprehensive instructional support package with time-tested teaching techniques.

Customer Reviews (1)

Helpful Assistance
I purchased this book after looking through it at a student bookstore and deciding it would be very helpful in my college math course by providing a more realistic and detailed view of the problems. I am very satisfied with the assistance it has provided, but am disappointed in one area of linear equations that it does not address. Overall, it is a very well organized and helpful book. I am glad I purchased it, even though it falls a bit short in one difficult area !! ... Read more

Product Description
BETA Mathematics Handbook is a comprehensive, accessible reference compilation of all basic facts and information for pure and applied mathematics, probability and statistics, and numerical analysis and basic applications. It offers a unique blend of classical areas of mathematics such as algebra, geometry, and analysis with new, modern topics. As a result, the book is up to date with all the latest math information used frequently in science and engineering. Modern topics covered include:

Customer Reviews (2)

Comprehensive.
If you're involved in any aspect of applied mathematics, this book is worth its weight in gold. It is probably considered somewhat obscure in the US, since it's a Swedish book that isn't really marketed outside of Sweden,but I haven't seen anything as comprehensive anywhere.

The book containsall the formulae, theorems and tables that any student or professionalinvolved with mathematics or engineering could hope for. It assumes thatthe reader has a level of understanding equal to "I've taken thecourse, but forgotten the details".

It is comparable to the morewell-known"Mathematical Handbook" by Spiegel, but in my opinionmuch better. The coverage of the areas that Spiegel cover is equal orbetter. "Beta" also covers probability theory, random processes,numerical methods, simulation, and other areas that are used extensively inpractice but not even mentioned by Spiegel.

In my opinion, if you areonly going to buy one mathematical reference book, "Beta" is anexcellent choice.

A great 'dictionary' of Mathematics
I have found Beta Mathematics Handbook to be the most organized, informative, concise and well-written reference for mathematics of all levels, esp. for probabilities and statistics. I highly recommend it. Amust in every mathematician's bookshelf. ... Read more

Product Description
Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dramatically different approach allows students to attempt to discover concepts in a "Socratic" dialog with the computer. The discussion avoids the formal "definition-theorem" approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction. ... Read more

Customer Reviews (7)

WTF did he just say?!
Well I did't like math in the first place, but this just make my life a living hell.The Author is my teacher and he is very vauge.My Adventure Through Hell, or M.A.T.H. for short is the most amount of mental torture I have ever been through.I give this book 5 stars as a fire starter.I am sure that if I had a Ph.D like the author then I would be able to understand it.It seems as though he has made this book and forgoten that for the most part the students who read this don't have a Ph.D in math.In Conclusion, this book severly
S U C K S.

AMAZING BOOK
For once a book exists on the market that will make you think.I loved every minute of the book and I loved being able to learn things on my own.The concept of the book is to get you to think about the answers for yourself not for the answers to be given to you.I must say that the authors have outdone themselves with this book.If you are the type that loves to learn on your own then go for this book.Even so it is a great book to challenge your mind to.

WOW!
I too took a discrete math class that was based on this book.It's amazing how little can be explained in this little wonder. The text is riddled with questions for which there are no answers and then theexercises are merely a repositing of the questions found in the chapter. The result is that there are a lot of questions that no one can answer,except with the help of another text or exceptional teaching.Avoid thisbook at all costs. Personal note:When the class was finished, thestudents promptly burned the book....guess it was good for somethingafterall.

Terrible
This book was a terrible source of information on discrete mathematics, and the programming language of ISETL.It contained many, many questions, and absolutely no answers.It would introduce ideas and concepts withvirtually no coherent explanations and follow through with confusingexamples at best.This book should not be confused with a good jumping-offpoint because, if one had other resources to use, they would almostcertainly also contain more information.The exercises in the book are notbad, but they have relatively no basis in the book.As a work book with aREAL supporting text, this book might be of help to someone trying to learnthese concepts, otherwise...forget it.

It would be simpler to develop the theorems yourself.
This book is amazingly poor.As pointed out in another review, there are chapters in which Dubinsky doesn't even state the main theorem that he's discussing!This book jumps around every main topic in discretemathematics, never once making any concrete statements about the propertiesor laws governing anything.If a book that sits around and tells you tofigure it out yourself sounds appealing, pick this one up.Otherwise, grabsomething that might actually teach you something. ... Read more

Product Description

This edition of Mathematics with Applications continues to be an excellent learning tool for applied mathematics students. As always, the text includes the popular margin exercises as well as comprehensive review of algebraic topics, but with this revision comes the fresh insight of a new co-author. Also, at our customers' request, this textbook has additional calculus content, allowing the book to be all that you need and more.

Customer Reviews (15)

good buy
this product was speedy and a great buy in general. i highly recommend this seller

business math
This book is alright. It is outdated though, the book still uses examples from the 90's. Like Profit functions dealing with the sales of VCR's!

Math-21
It was in very good conditions. I payed half the price compared to the school's bookstore.

Mathematics Text
book recieved in a very good condition, quick response to email. thanks a lot for the speedy mail.

Cheating
The seller delivered the product promptly but cheated by not including the CD, I paid a lot of money only for the CD, he had clearly said that the CD was included in his sale details but later on cheated me, I will never buy from him again ... Read more

Product Description
Entertaining, easy-to-follow suggestions for developing greater speed and accuracy in doing mathematical calculations. Surefire methods for multiplying without carrying, dividing with half the pencil work of long division, plus advice on how to add and subtract rapidly; how to check for accuracy, master fractions, work quickly with decimals, handle percentages and much more. A valuable how-to book for anyone working with numbers on a variety of levels.
... Read more

Customer Reviews (7)

ALTERNATIVE ANGLE
Not bad.There are elements to committing speed math to memory.It has these.

Why Didn't They Teach Us This In School!
I'm a little angry (yes angry) writing this because I feel for the people out there that struggle with math you never stop to think there is another way.This book convinced me that math can be enjoyable if you give yourself time to practice the different techniques within this book.I never heard of complement addition or subtraction before and when I finally understood it...wow, what a help it was to me.I urge any parent, teacher, or anyone still foggy on the fundamentals of math to pick this book up.

Consistent, structured approach
Instead of providing a series of disjointed "speed techniques," Stoddard teaches a method of speed arithmetic that integrates the same principles throughout. In other words, the speed techniques you learn in addition will also be employed in subtraction, multiplication, and division. Stoddard's "no carry, no borrow" method is based upon the structure of the Japanese abacus called the Soroban along with making efficient use of the inherent ease of computing with 10. The methods Stoddard uses are historical and were first seen in print in the 12th century in a book about arithmetic written by the Indian mathematician and astronomer Bhaskara (1144-1185) entitled "Lilavati." The wonder and beauty of this method is its consistency (which is what mathematics is all about). Every arithmetic operation is approached the same way, a revolutionary (to some, that is) "left to right" procedure. One by-product of this consistency is that it lends itself to immediate estimates. Compare this ingenuity with the "hodge-podge" traditional way of teaching arithmetic and you will see marked productivity difference. I, as a math teacher, wish more students were taught this way. The simplicity of the methods, once mastered, generates an ease and accuracy of computation that is simply amazing to behold.

the best speed math book i've yet found
This book should be used to teach children mathematics in our schools.The concepts are simple and clearly described.
Unlike math i learned in grade school you only need to know addition up to 10 and the multiplication table to 9 times.
It is the first unified speed math concept book that teaches a fast way to do mental calculations without memorizing a multitude of various rules for specific mathematical situations.
After reading this, i have stopped searching for any further speed math books because i doubt any could compare.

VERY INTERESTING HISTORICALLY
but somewhat out of date. Stoddard attempts to apply abacus methods to mental calcualation. I found this book fun reading but a more practical book covering the same ground is Handley's SPEED MATHEMATICS. ... Read more

Product Description
Beautifully illustrated, and with complete patterns and the mathematics behind each project, this book successfully connects the worlds of mathematics and the fiber arts. Each chapter covers a different mathematical paper and corresponding needlework project and includes mathematical explanations, needlework instructions, educational material, and specific projects to demonstrate the principles discussed. ... Read more

Customer Reviews (2)

I love this book!Beautiful and educational
Ok, I'm a bit of a math geek -- I have my masters in math.And I'm addicted to knitting books and yarn (as a quick perusal of my review history will demonstrate).So I ordered this book.Each chapter presents a new concept and a new project.The projects are not your typical fiber arts projects but they are all beautiful.They also should give even the most math-phobic individuals a new appreciation of the math.

I have taught math online to adult college students and this would be perfect "supplemental reading" to show people that math doesn't have to be scary.

A very special attraction for math students and fiber art enthusiasts alike.
Knowledgeably compiled and deftly co-edited by Sarah-Marie Belcastro (Co-Director, Hamshire College Summer Studies in mathematics and Visiting Assistant Professor of Mathematics at Smith College) and Carolyn Yackel (Mathematics Instructor, Mercer University), "Making Mathematics With Needlework: Ten Papers And Ten Projects" is unique in that it combines mathematics papers with fiber arts project instructions. Each chapter showcases a particular project and that project features sections on mathematics and mathematics education along with detailed instructions for completing the needlecraft project. The featured projects include a Quilted Mobius Band (making a mobius quilt); Diphantine Equations (making a bi-directional hat); Sierpinski Variatins (making a Sierpinski shawl); a Two Knit Stiches Tours; Symmetry Patterns in Cross-Stitch; Algebraic Structure (making algebraic socks); Fortunatus's Purse; (K)Not Cables and Braids (making a pillow of Braid Equivalence); The Graph Theory of Blackwork Embroidery (embroidering a Holbeinian Graph); and making Hyperbolic Pants. Profusely illustrated, the text is fully accessible to non-specialist general readers with an interest in needlecraft, in the mathematics underlying needlecraft, as well as having a very special attraction for math students and fiber art enthusiasts alike. ... Read more

Product Description

Compared to other popular math books, there is more algebraic manipulation, and more applications of algebra in number theory and geometry

Presents an exciting variety of topics to motivate beginning students

May be used as an introductory course or as background reading

Product Description

Customer Reviews (2)

Good reference
Students and professionals who must use mathematics are often tripped up by three items: the vocabulary of math, the symbols of math and keeping up with "old what's his names" theorem or postulate. This book can help with all three of those traps.

Where Collins Dictionary shines is when you have to learn something new. Say you needed to learn Green's functions. A good start in learning anything about mathematics is to define exactly what you are trying to do. By looking up the definition of Green's functions, you discover that Green' functions are a set of integrating kernels used to solve non-homogeneous differential equations with boundary conditions.

Knowing what Green's functions are and what they are for, you now know *where to start* which is half the battle.

Another place where the Collins dictionary shines is that there are so many disciplines of mathematics that no one can know them all. It can give you an overview of an unfamiliar discipline and point you toward key topics. Unfamiliar with Linear algebra? You can get the nickel tour in a few minutes rather than a semester.

The best mathematics dictionary on the market
NOTE: I own the 1989 edition of this disctionary.I have no experience with the web-linked features.

This is an outstanding mathematics dictionary.Unlike other mathematics dictionaries that I have seen, this one is aimed at mathematicians.I used it repeatedly through my undergraduate and graduate careers, and still refer to it frequently now that I am a professor.I have mainly used the dictionary when discussing or reading about something outside of my own areas of expertise (such as when I forget the difference between a normal space and a regular space).

The dictionary is very strong on logic, but good in almost all areas of pure mathematics.The definitions are generally short andsuccinct, making it a good supplement to something like mathworld.

The writing style is easy to read, and occasionally humorous.The entry on "Null graph" reads "n. the graph a representation of which is shown in Fig. 257".Fig. 257 is a blank space.

I found this book so useful that I bought two copies: one for my office and one for home. ... Read more

Product Description
In 1977, the Mathematics Department at the University of California, Berkeley, instituted a written examination as one of the first major requirements toward the Ph.D. degree in Mathematics. Its purpose was to determine whether first-year students in the Ph.D. program had successfully mastered basic mathematics in order to continue in the program with the likelihood of success. Since its inception, the exam has become a major hurdle to overcome in the pursuit of the degree.

The purpose of this book is to publicize the material and aid in the preparation for the examination during the undergraduate years since a) students are already deeply involved with the material and b) they will be prepared to take the exam within the first month of the graduate program rather than in the middle or end of the first year. The book is a compilation of approximately nine hundred problems which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. Tags with the exact exam year provide the opportunity to rehearse complete examinations. The appendix includes instructions on accessing electronic versions of the exams as well as a syllabus, statistics of passing scores, and a Bibliography used throughout the solutions. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies. ... Read more

Customer Reviews (5)

Excellent Problem Book
The problems in this book are excellent, they are both entertaining and instructive.I thought I knew calculus, linear algebra, and all of the other typical undergraduate subjects very well, until I purchased this book.After working several problems, mostly without success, I realized that there is a big difference between knowing theorems and knowing how to use them.Since then I have worked these problems daily to improve my "working knowledge," and it has made me a much better mathematician.Learning the definitions and theorems is just the first stage of mathematical knowledge.In this form your knowledge is simply something stored in memory.In the second stage, you must turn it into something more like "software," something that is an active part of your thinking.The only way to do this is by solving problems, and for undergraduate mathematics, this is probably the best book of problems you will find.Highly recommended.

Excellent Problems!
These are great problems for those who would like to review undergraduate mathematics or those who would like to try some challenging problems. They are not as difficult as the problems on the Putnam competitions or those in the Math Monthly , but many require a bit of thought and some ingenuity. Some of the problems are routine, and if you don't want to review the basics, you can skip those and just try the more difficult ones. Even experienced problem solvers will have fun with some of these! Anyone who teaches undergraduate mathematics should have this collection. Highly recommended.

A real pearl!
This book is a rare peak inside one of the best Ph.D. programs in Mathematics in the world. It allows you to try out and test yourself on the same problems that the best young and aspiring mathematicians are testing themselves.

The problems are neatly arranged by subject and in increasing level of difficulty, and the solutions, are not only beautifully
written, but somewhat surprising and unexpected for a seasoned student. I pull mine out of the shelf on the rainy days and try a few more, and when I get one, I really savour it!

Challenging problems, or just standard textbook stuff.
The problem with the contents of this book is that they are mostly standard, or require a simple trick. Many problems also require quite a bit of knowledge in higher mathematics, which may be good if you want to test that.

However, this book is not for problem solving enthusiasts.

TESTYOURPREPAREDNESS!
A GOOD COLLECTION OF PROBLEMS THAT HAVE BEEN THE BENCH MARK OF SELECTION TO THE PhD PROGRAMME AT UNIVERSITY OF CALIFORNIA AT BERKLEY IN MATHEMATICS. THERE IS A WIDE RANGE OF PROBLEMS THAT COMPRISE SOME SIMPLE AND SOME HARDERNUTS TO CRACK.THE PROBLEMS HAVE BEEN PUT IN THE ORDER IN WHICH THEY HAVEAPPEARED IN THE EXAMS. NOT ALL QUESTIONS FIND SOLUTIONS IN THE BOOK HENCETHIS KEEPS UP THE SPIRIT OF THE EXAMINATION BUT THE SOLVED ONES SHALL HELPTO VENT FRUSTARTION OR OVER COME FALIURE AT TIMES. THIS BOOK IS A MUST READFOR STUDENTS WHO ARE PLANNING TO TAKE UP A PhD IN MATHEMATICS TO GUAGETHEIR AREAS OF STRENGTH AND WEAKNESS.A VERY WELL COMPILED SET THAT COMESYET AGAIN WITH THE GUIDENCE OF P.R.HALMOS. ... Read more

Product Description
As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks).

Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics. ... Read more

Product Description
Covering all branches of pure and applied mathematics, including algebra, geometry, mechanics, and statistics, The Penguin Dictionary of Mathematics is invaluable for students at the high school or university level. It is also a useful and versatile source book for economists, business people, engineers, technicians, scientists of all kinds, and anyone else who uses mathematics in the course of daily work. ... Read more

Customer Reviews (8)

reference book for Mathematics
Wonderful having this on kindle. I had the paperback as well. Very useful for school math teachers, and students of Mathematics.

Kindle version almost impossible to use
The content of this book seems to be good, but my problem is that the kindle version has no table of contents, no index and no search function. It is therefore impossible to quickly find the section that you want or the topic you want - you have to page through the entire book until something useful appears. This is a fatal flaw for a reference book.

Very nicely designed, but ...
This is a concise (sometimes too concise) dictionary of mathematics, probably most useful to a student who needs a quick reference when a text or other source misses a step.

The book is somewhat erratic, at times over explaining or oversimplifying and at other times leaving out too much. There are also some notable omissions. For example, I was a little surprised that Dirac Delta Function is not in the book at all. The book covers some areas but leaves out obviously related ones. So some important figures in the history of mathematics are included, others aren't (though arguably just as important).

Perhaps this is to be expected. As I said it is a very concise reference.

One last note: I have found Wikipedia to be an excellent reference on subjects like those covered in this dictionary. I prefer holding the book in my hand and especially being able to browse through the book. But if you don't approach things with that browsing frame of mind, Wikipedia or something comparable will serve you just as well.

Best High School/Basic College Math Dictionary available
Simply put this is the best math dictionary out there for the high school level and for most college students. Maybe there are some more appropriate ones for upper level college math/science students. I have found the descriptions and links in the text very clear and appropriate for most students. I greatly prefer this one over the Oxford math dictionary.

I highly recommend it for high school math students (and make sure you keep it until you are done with college). When more detail is needed beyond this text there's always google.

Highly recommendedfor college mathematics students
As a student studying mathematics, I find it very useul! Packed with 3200 terms and 200 illustrations, It's a great quick reference guide. I found things in this guide that I couldn't find in any other book or guide. Another thing about this reference guide is the lack of poor illustrations and examples. Some things this guide helped me with is PARABOLAS, ELLIPSES, HYPERBOLAS, GAMMA FUNTION, ZETA FUNCTION, FEIGENBAUM NUMBER, THE GREEK ALPHABET, and much more. I thank David Nelson and Penguin Books for such excellent work. ... Read more

Product Description
These books provide extra cumulative practice on basic facts, computation, word problems, mental math, and estimation skills. ... Read more

Customer Reviews (1)

Great product, great service
Good summer math exercises for my child, fits with our school district's curriculum. Wonderful service from Lily Street, arrived very fast. ... Read more

Product Description
Mathematics is a wonderfully austere science, but it also has a very human side. It is embedded in a colorful history filled with extraordinary personalities, deep philosophical debates, and breath-taking advances in knowledge. This book offers a brief but penetrating synopsis of that history.

This book includes many detailed explanations of important mathematical procedures actually used by famous mathematicians. This gives the reader an opportunity to learn the history and philosophy of mathematics by way of problem solving. For example, there is a careful treatment of topics such as unit fractions, perfect numbers, linear Diophantine equations, Euclidean construction, Euclidean proofs, the circle area formula, the Pell equation, cubic equations, log table construction, the four-square theorem, quaternions, and Cantor's set theory. Several important philosophical topics such as infinity and Platonism, are pursued throughout the text.

This book is written as an undergraduate textbook, but it is intended for anyone who wants to understand how mathematics grows out of, and nourishes, the total human experience. ... Read more

Customer Reviews (6)

Worthless
This book is utterly worthless in every conceivable way. It is a mystery to me why Springer have brought disgrace upon themselves by publishing this inept drivel. A complete account of Anglin's incompetence would require a review as thick as the book itself, but hopefully a few deterring examples will suffice.

First, there are many blatant factual errors, e.g.:

"There were five planets (or so Kepler thought) and five regular polyhedra. This could not be an accident!" (p. 158)

Since Kepler's work on Mars, Jupiter and Saturn are mentioned on the same page, one wonders whether it is Mercury, Venus or the Earth that Anglin imagines Kepler to have been ignorant of.

Other statements cannot even be called false since they are such ludicrous nonsense, e.g.:

"Just as many people before Lobachevsky thought that Euclid's parallel postulate was a kind of sacred truth, so many people before Hamilton thought that the law of commutativity for multiplication was ineluctable. For us it is a commonplace that this law need not hold, since we have a ready example of noncommutativity in matrix multiplication." (p. 195)

The notion that there is some sort of "law" out there about commutativity of multiplication that may or may not hold is a very childish misconception. Whether we call certain operations with matrices and quaternions "multiplication" or not is purely a matter of convention. Thus the alleged "law" that "many people" allegedly held for "ineluctable" has no meaning whatsoever other than as a thoroughly inconsequential claim about naming conventions. Anglin's stupidity is particularly disturbing in light of his immodest description of his own book as offering "a deep penetration into the key mathematical and philosophical aspects of the history of mathematics", "giving the student an opportunity to come to a full and consistent knowledge" (p. viii).

Let us give another example of what Anglin considers to be "a deep penetration" into philosophical issues. We read that "there are various objections to formalism," e.g. that "formalism offers no guarantee that the games of mathematics are consistent." Now, presumably in order to "give the student an opportunity to come to a full and consistent knowledge," Anglin professes to offer the other side of the coin: "the formalist can reply [that] although some of the games of mathematics are indeed inconsistent, and hence trivial, others are not" (pp. 218-219). It is not clear in what sense Anglin fancies the assertion that mathematics is consistent to be a "reply" the the challenge to prove as much.

Finally, the book is full of unsubstantiated revisionist history motivated by unabashed Christian propaganda ("God" is the entry in the index with the most references by far; more, in fact, than Euclid, Archimedes, Newton and Riemann combined), e.g.:

"Most of the mathematicians at the Academy and the Museum rejected the new truths [sic] of Christ's revelation. This is unfortunate because ... if the mathematicians had joined the Christians, the Dark Ages would have been brightened by a dialogue between reason and faith. As it was, this dialogue was postponed to the later Middle Ages, when thinkers like Thomas Aquinas (1225-1275) advanced philosophies that were influenced as much by the Elements as by the Bible." (p. 111)

What a loss for mathematics that we had to wait so many centuries for the great geometer Aquinas!

Trite; filled with unnecessary religious hot air
This is a simplistic and shallow book. Proof if any is needed that relgious dogma (and the authors desire to spread it ... even in a maths book!) poisons the mind. The authors frequent attempts to bring god into the picture are unsubtle, (mostly) irrelevant and unbelievably crass. I am disappointed in Springer; how on earth did they allow this to be published?

Nice Read overall
Not a perfect book by any stretch, but I am not the type of reader who has to agree with a book to enjoy it.Many histories of mathematics books are rife with anti-god, anti-religion references, this is a balance to that.Admittedly a little pushy the other way, but not a bad read.

Nice antidote to E. T. Bell
On the math side of things, this book provides a concise overview of the history of mathematics.Actually, I found it to be a bit "too concise" - I think that a college professor would be hard-pressed to stretch the book out over a one-semester "History of Mathematics" course.The content of the book is clearly designed for liberal arts students interested in the "History of Mathematics", rather than for mathematics students interested in the "Mathematics of History".In an appendix at the end of the book the author includes a number of sample assignments, tests and exams which I personally found rather useful.

Yes, I agree with previous reviewers that the author pushes his Christian views on the reader, but I must say that I found it a refreshing change to the tiresome and offensive anti-Christian propaganda found in E. T. Bell's book "Men of Mathematics", in which Blaise Pascal is made out to be a mentally ill religious lunatic, while Augustin-Louis Cauchy is made out to be a harsh and bigoted religious fanatic!

Terrible
The whole book is infested with very annoying and irrelevant
personal thoughts on religion. Mathematicians seem to fall in two
categories: Christian and atheist. The latter are generally evil
and of little relevance, while the former are moral persons that
have produced excellent mathematics. The following quotes from
the book illustrate its general attitude:

Exercise:
Even if the solar system is gravitatinally stable, it still needs
God to keep it in existence. Comment.

Some historians feel that to be 'scientific' they must do their
work on the assumption that there is no God.

Laplace's greatest contribution to mathematics was his phrase
'it is easy to see'.
... Read more

Product Description
Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle. Some of the topics may be familiar to the reader while the others will seem surprising or be new. By treating episodes, Aaboe is able to give the reader the details of representative pieces of ancient mathematics, bringing clarity and dispelling such myths as the assertion that the greeks allowed only ruler and compass in constructions. ... Read more

Customer Reviews (2)

A Fascinating Look at the Early History of Mathematics
It is very rare for any intellectual discipline today to be built on the foundation that is thousands of years old. The discipline for which this observation holds most unequivocally is mathematics: the discoveries and tools that have been created well over two thousand years ago are still as valid and relevant today as they were when they first appeared.

This book begins with the Babylonian mathematics and explores their use of the number system which had number sixty as its base. The author uses images of the original cuneiform clay tablet and through a series of intuitive steps shows how we can deduce what their number system looked like and how arithmetic operations were carried out. It is interesting to see how to do arithmetic in the base sixty in its own right, since it is not a number system that is used often. Nonetheless, the Babylonian number system is the source of our own way of dividing time and measuring angles in terms of minutes and seconds, and the book makes a persuasive case that this is actually a very compact way of writing down very small numbers and working with them efficiently. Unfortunately, after some interesting early developments Babylonian mathematics did not progress too far and remained on a relatively rudimentary level.

The bulk of the book deals with Greek mathematics. This is really where the story of mathematics as we understand it today begins, and Greeks already showed a remarkable level of mathematical sophistication. The author presents a few of the most important discoveries of Greek mathematics, primarily in geometry, although Greeks did make many other important contributions. Several important theorems are worked out following the original presentation as much as possible. Nonetheless many concessions were necessary in order to make the text legible for the modern reader.

One of the beast features of this book is that it's not just a description of ancient mathematics - there are numerous exercises throughout the text that aim to engage the reader and draw him or her in into the actual mathematical practice. It is quite remarkable in a way to be having the same thought processes that Euclid or Pythagoras might have been having all those centuries ago. In this limited sense we are able to achieve a sort of union of minds that is hard to imagine in any other sphere of human endeavor.

Early and timeless beauty in mathematics
While mathematics has a long history, in many ways it was not until the publication of Euclid's Elements that it became an abstract science. Babylonian mathematics, the topic of the first chapter, largely dealt with counting and the focus in this book is on the notations the Babylonians used to represent numbers, both integers and fractions. Although their notation had its' limits, we still use it today for time and angle measure.
And then there was Euclid, and all was ordered. There is no reason to believe one way or another that Euclid was the first to prove the theorems in his classic work, but there is no doubt as to his organizational genius. His "rigorous" setting down of the principles of geometric thought was truly a turning point in abstract mathematics, If you are not impressed when reading the material of the second chapter, taken from Euclid, then you have no aesthetic appreciation for what mathematics is. While the mathematics has been cleaned, the beauty has never been topped.
The next chapter is about the greatest genius before Newton, Archimedes. In fact, had he been blessed with better notation, it is possible that he would have invented, or at least pre-invented calculus. If even half of the legends about his mechanical skill are true, they are still amazing. Apparently, entire armies and navies were terrified at the rumor that one of his mechanical devices was about to be used. The crispness of his theorems and the logical progression will be just as instructive thousands of years from now.
The final chapter describes how Ptolemy was able to construct trigonometric tables. Using the chords of circles, he was able to construct tables that can still be used today. Civilization improves and mathematicians continue to expand the mathematical field and refine earlier work. However, the elegance of earlier work still shines through, and in this book you can experience some of the earliest mathematical diamonds, hewn from thought and destined to survive as long as humans do. ... Read more

Product Description
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology.
For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work. ... Read more

Customer Reviews (1)

There are some gems but you'll need to dig to find them
The authors of this compilation of articles are quite varied and include both artists and mathematicians who each have an article in this little book. Each of them has a lot to say on the subject of visualizing mathematics and the place of mathematics in art, unfortunately each of them seems to be talking to a different audience. This is the typical trouble you frequently encounter with a book that is a series of articles by a number of authors versus one consolidated textbook. Several of the articles that are centered on math completely avoid formulas while others carefully define all terms and go very deep into theoretical mathematics. To make matters somewhat more confusing, the articles are not in order of topic. Finally, several articles contain large amounts of philosophical or historical reflections on projects that are obviously important to the author, yet the author never bothers to introduce said project to the uninitiated reader. It is as though these particular articles were written by insiders for insiders.

However, there are some little gems in this book. There is a very good article by George Hart that includes an algorithmic description of how to build polyhedral sculptures in both computer and physical terms. This article should be read by anyone interested in platonic solids, and it includes much practical advice. I also really liked three of the articles on the relationship between math and music. Neuwirth has an article that describes the mathematical history of instrument tuning in which he includes Mathematica code that enables the reader to experiment with the procedure and hear the results. Simoes' article describes the algebra behind Schoenberg's 12-tone construction. Hellegouarch's article is a good follow-on to Simoes' offering in that he offers the algebra of how singers can break the algebraic rules behind our usual mathematical scale and get away with it. There are two very good articles linking dynamical systems to the aesthetics of pleasing visual design. Finally, there are a couple of articles on how to integrate mathematics and art into a course. One of the authorsdescribes a course he taught on knots that led to an exhibition. Another explains how he used his own computer program as the centerpiece of an interdisciplinary course for art students.

In conclusion, this book is very uneven as are many books that consist of articles by different authors, but it does have some unique and worthwhile entries that do fall under the banner of connecting math to art. You'll just need to wade through several overly theoretical papers that don't seem to go anywhere as far as the math/art connection go. ... Read more

Product Description
Setting the standard in middle school mathematics

Mathematics: Applications and Concepts is a three-course middle school series intended to bridge the gap from elementary mathematics to Algebra 1. The program is designed to motivate your students, enable them to see the usefulness of mathematics in the world around them, enhance their fluency in the language of mathematics, and prepare them for success in algebra and geometry. ... Read more

Product Description
Mathematics for Elementary School Teachers, 3/e, offers pre-service teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect the text to the hands-on activities in the corresponding Explorations Manual. ... Read more

Customer Reviews (4)

Text book as well as a career tool
I needed this book for a college math class designed for aspiring teachers. What I didn't expect to find was its clear and presise explanaitions and step by step procedures that help you not only solve, but understand the math problems. In addition, there are many helpful tools and ideas on projects and assignments that teachers can use in the classroom, no matter what grade they teach. I am not nor have I ever been a math lover, I have historically been the opposite. But believe it or not, I am now excited to get in the classroom and try my hand at teaching math to my students.

I'd also like to add that I purchased this book used and I was pleased that it shipped very quickly, and the book's condition upon arrival was exactly as described.

I don't know
Let me tell you something.I feel concern about it because I didn't receive the book that I ordered I receive a different one, so I have to run to the library and try to find the book to be able to do my class. I think is not fair because I really needed the book

Mathematics For Elementary School Teachers Text book
This was shipped fast and in perfect condition.Exactly what I wanted.

Excellent text for mathematics for el-ed classes
I teach a course in the fundamentals of arithmetic and logic for elementary education majors so I examined this book as a possible textbook for the spring semester of 2006. I found it very suitable, the coverage is exactly what needs to be covered and the presentation is targeted at the appropriate audience. My students would have no trouble reading and understanding the text. I was going to use it this spring when my schedule was suddenly changed and I was no longer teaching the class. However, it is likely that I will use this book if and when I teach the fundamentals class again. ... Read more

Product Description
BRAND NEW Student Edition **COPYRIGHT 2004** Beautiful looking book. Order now free tracking!!! ... Read more