Product Description
This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. ... Read more

Customer Reviews (9)

not the standard course book, but nevertheless a truly GREAT book!
Starting with the bottom line, THIS IS NOT a first-year undergraduate course in Mathematical Analysis and should never be used as such (you wouldn't use Hardy's A Course in Pure Mathematics, either, for all its venerable merits).

If you ARE doing first-course Analysis, you'll have to stick to whatever textbook your professor chooses (hopefully NOT Rudin's masterpiece). If you get stuck with that, you will do well to search for a more user friendly alternative or supplement in the line of BINMORE or BRANNAN's book (there are others, for the market is flooded in this area), some good text that emphasizes the fundamentals taking his time, that emphasizes the practical connection between Analysis and (high-school) Calculus, and that uses a lot of visual illustration for good. If you remain stuck still, then you will have 1) to rethink the wiseness in choosing a career that requires advanced mathematics, and/or 2) as a last resource there is the "Yet Another Introduction to Analysis", which isn't the standard textbook either, but it can get you unstuck and on safer ground.

Then, what on Earth do we need HAIRER and WANNER's Analysis by it's history for?
For starters, it's a VERY BEAUTIFUL book (in the line of Proofs by the Book, if you know what I mean, but a step lower). The explanations are right and straighrforward, at an accessible level that reminds me of that other gem of a book, DUNHAM's Euler: The Master of Us All. It has a lot of examples and graphic elements and takes you into a wonderful journey into what is rather more Calculus than Analysis, alohg the path taken by the great classics (without being a book on the History of Calculus -try EDWARDS for that, and forget Boyer's-). In addition, if you just don't read casually the book for the sheer pleasure of it, but you DO WORK through it and do the exercises, you will end with a sure grasp of the fundamentals of Calculus (and thet is what Analysis is supposed to be), a surer grasp than you would have memorizing the whole of Rudin's consecrated and masterful text, Another reviewer takes issue with the many short quotations that decorate the book, as epigraphs to every little section, that are intended to maintain a historic flavor. Some of them make good sense, and a few others are rather quizzical or downright cryptic: all in all, it's a rather idiosyncratic and funny feature of the book, but it's not a matter to take issue with.

IN SUMMARY: it's NOT supposed to be a standard textbook nor should it be used as one. But if you think that Calculus (and Analysis) is the greatest endeavor mankind has engaged in -take that "com grano salis"- and you remember still your high-school Calculus although you're not a working mathematician, but something more on the amateur side of it... if you appreciate mathematical books looking the beautiful way they should all look like (and remember -or get outright- Proofs from the Book)...
if you'd love getting a refresher on Calculus cum Analysis, THEN PLEASE DON'T MISS that book, so very clearly and beautifully conceived and written. One book like this occurs only a few times in a century, unfortunately you and I haven't written this one, at the very least let's share the joy of reading it, at whatever depth level we feel like!

contains very goodhistorical perspectives on analysis
This very interesting book contains very goodhistorical perspectives on analysis. If you want to know how things like trigonometric functions, logarithms, infinite series, differential and integral calculus and differential equations come about (but written from a modern viewpoint), then this is the book for you. It is not a book for casual reading like E T Bell's Men of Mathematics, but the reader will learn a lot of college and undergraduate mathematics along the way.

A quite magnificent book
I return to this book again and again just out of sheer pleasure. The depth of scholarship of the authors shines through on every page and the choice of historical material is fascinating.Topics like compactness and uniform convergencecan here be seen to have arisen out of genuine necessity-they are not (as would seem from other books)mere names in a standard syllabus. If you have any mathematica interest at all, take this book on holiday and sleep with it under the pillow to extract more from it by osmotic pressure overnight.

A Good Mix of Calculus and its History
This books gives a unique approach to Calculus using its historical development.The most notable feature of the book is that the order of topics is reversed from what has become standard in current textbooks.It begins with the analysis of areas and volumes.This is followed by derivatives, continuity, and the notion of function.This is the order in which analysis developed, but not the order one would follow if building understanding of the subject from a foundation upward.Historically, the foundations were laid last.

The book is not intended as a history of analysis.It is rather intended as a textbook or reference in which the topics are presented in historical order.The historical background is intended to give insight into a modern view of the subject.It accomplishes this admirably.

The book is filled with examples, quotes, vignettes, historical background, computer graphics, and copies of original documents.Special topics are interspersed throughout.The book gives us a fresh and envigorating view of Calculus.It is an invaluable resource.

A somewhat useful scrapbook with a poor second half
Chapters 1 and 2 treat classical differential and integral calculus. This is a disorganised mess of historical and mathematical tidbits. It's not a great place to learn calculus, but it's good side reading since there are many interesting topics, some of which are often neglected in today's books: continued fractions (!), complex functions already on page 56, an interesting section on differential geometry, Euler-Maclaurin summation, etc. The authors also have the very commendable habit of including charming facsimiles of figures from original works.

Chapter 3 "Foundations of Classical Analysis" and chapter 4 "Calculus in Several Variables" are almost completely ahistorical. The "by its history" part of the exposition is restricted to some scattered superficial remarks, including silly nonsense such as that if Leibniz had know of the intricate progression of theorems needed for a modern proof of the "fundamental theorem" then "he might not have had the courage to state and use this theorem" (p. 239). And in another parodic misuse of the historical perspective, the authors introduce Descartes's folium merely for the purpose of practising the determination of stationary points (p. 322)---of course, Descartes introduced the folium for a much more interesting purpose, but to learn that story we must look for an "Analysis by Its History" book worthy of its name. ... Read more

Customer Reviews (1)

Great fun!Great thoughts!Great math!
I recommend this book to anyone who thinks.

This book is one of my favorites to keep on the shelf by my computer.I find myself flipping through it often for an idea to spark a piece of writing or a quote withwhich to begin a math lesson.I find myself being surprised by theruminations of some famous mathematicians and famous non-mathematicians. Some quotes are from something they said, others from what they wrote, andsome are even from poems composed.They inspire laughter, contemplation, agrin (as we hear quotes from people confused about math), and even a desireto go out and examine the world with wonder... as mathematicians do.

Ialso need to add that they did a fantastic job of designing the book. There are illustrations and cartoons that compliment the different quotesor make interesting points all on their own.This is no small book ofquotes either -- not "a quote a page" -- but more of a slenderpocket volume with easy-to-read type and up to four quotes on a page.

Irecommend this book for anyone -- it's not just a math thing!

But anymath teachers out there?BUY THIS! You can use some of these to startsome wonderful lessons, mathematical conversations, and even some writingin your classroom. ... Read more

Product Description
Traces the story of mathematics from the ancient world to modern times, describing the great discoveries and providing accessible introduction to such topics as number-systems, geometry and algebra, the calculas, the theory of the infinite, statistical reasoning and chaos theory. ... Read more

Customer Reviews (9)

Comic book introduction to math
This book offers an outstanding summary of the changing mathematics over many centuries in a few illustrated pages.It is engaging, and presents the main concepts in simple terms that everyone can understand.I have read much on mathematics and its history, but found this book fresh and thought-provoking since you can go through the whole thing fairly quickly.I like its treatment of the social and policy issues related to mathematics, as well as the general neglect of non-European mathematical contributions in math education.Highly recommended.

Underwritten and overdrawn
This Introducing title is definitely a 'story' about mathematics and was a disappointment due to its lack of a general logical structure and its overuse of odd graphics.Sardar and Ravetz took an ethno-centric, historical approach in their presentation of the development of mathematics as a pan-cultural phenomena but lost depth and rigor in the process.Anecdotes about mathematicians were strung together as a means of exposition and development.Van Loon's graphics live up to his billing as a surrealist and collagist.The equations and definitions, strewn throughout the text and graphics, seem more like adornments than the book's nominal topic.Topology is barely mentioned which may indicate the authors' actual depth and breadth in mathematics.On pages 166-170 the authors reveal their agendas regarding ethnicity, gender, and elitism, and a "Euro-centric, Platonic image" of mathematics is identified as the barrier to global progress in this field - an astonishing assertion.Unsurprisingly, they provided no alternatives or solutions to this terrible problem.At best, the topic of mathematics appears to have overwhelmed the authors' abilities to employ the Introducing format.[FYI - I use the Quantum Theory and Fractal Geometry titles in this series as reference points.]

Not one of the stars of the Introducing series.
The Introducing series, employing as it does different illustrators and authors for each of its titles, is definitely hit-and-miss. Although I personally enjoyed this book a good deal, I have to say it counts as one of the misses.

The book focuses a good deal (too much in my opinion) on the personalities of figures from the history of mathematics, and when it finally gets down to the business of explaining difficult concepts from calculus and number theory, it skips around and uses terminology that was never defined in the book, tossing about opaque formulas that aren't explained, and so forth. As it happens, it was exactly that sort of thing that turned me off of math to begin with. It all starts out very interesting and clear enough, until somewhere along the line I feel like the bus is still barreling on down the road, but I've been left along the wayside.

Naturally some of this has to do with my own undeniable ineptitude when it comes to mathematics (part of the reason I picked up this book to begin with). But my main complaint with the book was with the illustrations. For the most part, they're distracting and unhelpful. Relying mostly on puns and including speech bubbles that explain and belabor the pun but don't have any thing to do with the math (the page on cyclic functions is obscured by drawings of people on bicycles, for example). Not only that, but for the most part the drawings themselves aren't original. In reading this book I had the distinct feeling that I'd seen many of the pictures before, and sure enough a quick google search determined that the illustrator has just pasted various royalty-free illustrations and shoddy clipart onto every page.

That said, I did find the book itself worth the read. But I doubt I'll be returning to it again, and it's short enough that I could have just read it in the bookstore and saved myself the money. I wish I had.

One of my favorites
I'm a big fan of the Introducing... series, and to me, this is one of the best.

Ethnomathematica and the universal language of maths as the tool of science
This book doesn't tutor you in mathematics so if that is what you want then go elsewhere now.

If you are looking to learn mathematics without a good cause then I would say that you better have the attention span to learn something absolutely mundane if you don't have a reason for it. A reason to learn mathematics is as vital to grasping mathematics as our brain needing a spinal cord to work. It would be best to begin with a cause to learn it and unfortunately just needing to know it for exams doesn't help matters either. I would suggest therefore that you turn to other books in this series like "Introducing Newton and classical physics" and "Introducing the Universe". "Introducing Quantum Theory" and "Introducing Relativity" are the big two science books that can be understood somewhat rudimentary outside of the developed mathematics to support it. I think trying to understand those topics provides enough motives to complete a full study and application of the language of mathematics. Then this book becomes an engrossing essential.

Mathematics is not hard if learned the correct way. Mathematics is easy if you spend the right amount of time (lifetime really but in a truly applied year you will have advanced dramatically) on it and know what to learn and in what order. Buy a calculator. Read and learn the manual. In the manual you will come across terminology that you would like to comprehend. This book lays it all out for you.

"Introducing Mathematics" explains the historical record for mathematics and its development. By the end of the journey you would have an overview that maps mathematics. Then you should go about learning about each part in other specialized books. The main maths to learn after this one are algebra, geometry, trigonometry, analytical mathematics and then the big calculus. Getting to calculus is what it is all about. There are then various laws and rules and applications like statistics after that but the goal here is a slow progressive study of the above maths topics before moving into calculus. This is what it is all about.

Core material:
History of Mathematics culminating in Ethnomathematics is covered in detail
Egyptian, Greek, Chinese, Hebrew, Middle Eastern and European contributions to maths
Counting
Representing numbers as figures
Zero
Special and large numbers
Powers
Logarithms (logs)
Calculation
Equations (linear, quadratic, cubic and degree equations)
Algebra
Simultaneous equations
Measurements, error bars and fridges
Pythagoras
Zeno's paradoxes
Geometry
Binomials
Pascal's triangle, Jain and Vedic and meru-prastara
Trigonometry
Integers
Analytics
Functions
Calculus
Differentiation
Derivatives
Integration
Berkeley
Euler
Non-Euclidean
N-Dimension spaces
Groups and sets
Boolean algebra
Cantor
Godel's theorem
Turning machine
Fractals
Chaos theory
Topology
Number theory
Statistics
P-values and outliners
Probability
Uncertainty principle
Policy numbers

Overall this is exactly the kind of book I wanted to read. A starter book that just covers all the stuff you need to learn for calculus. Some of the topics are explained harshly but study them enough and you will come around to appreciating the time spent for just getting the point the book makes. When it clicks the feeling is great. Enjoy mathematics. ... Read more

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How past attempts by scientists to discover the perfect circle led to major discoveries of the physical universe. ... Read more

Customer Reviews (5)

Zebrowski's History of the Circle is a great fun book.
This is not a text book, but an fun read that discusses
interesting topics from physics and math.
It explains things so well that I wish I had Zebrowski as a professor or could find textbooks written by him.
I think the lengthy first review below as well as examples from the other reviews give a good idea of the contents of this book.
It's a joy to read, and to use when explaining things correctly to others.

interesting but ...
An interesting read which could have benefited from the
attention of a diligent editor.Sadly, historical details
are often muddled and in the later chapters the author
indulges in some freewheeling speculation regarding high
energy physics while quoting undergraduate level journals
as sources.
Nevertheless, all of the subject matter and most of the
text is well worth a look.

Looking For Pi Info? Its Not Here.
The first chapter BREIFLY addresses pi, so this not a good source for those of you that may have drawn the same conclusions about the title that I did.However, if you've ever wondered why there are 360 degrees in a circle and how that relates to time or other interesting trivia, this is a great source.I do recomend it to anyone with an intrest in the basic concepts of Physics which somehow work themseves in everywhere.The title would be more acurate if it removed "A History of the Circle" and just left it with "Mathmatical Reasoning and the Physical Universe" because it lacks far to much of the first subject.

Just what I was looking for (and I didn't even know it!)
What a delightful discovery! This book served to effortlessly broaden my knowledge about applied mathematics. I have to recommend this book to all - and especially towards those, like myself, who are frustrated with our own mathematical ignorance... I am a bit of a compulsive book buyer and I don't always make an effort to read each book in my huge collection. I'm very happy I made the time to thoroughly read this one!

A DECIDEDLY PLEASANT JOURNEY INTO THE WORLD OF SCIENCE
The beauty of Ernest Zebrowski's book, A HISTORY OF THE CIRCLE, is that it was written for everyone, not just for science professors.The author never talks down to his readers.Clearly, Mr. Zebrowski is not just asuperb scientist and mathematician:he is also a skilled writer, teacher,philospher, and historian.Like Lewis Thomas, he has a wonderful way ofmaking science come alive.He transports you back into time and makes youfeel as if you are right there watching some of the most intriging momentsin human history unfold before your eyes.I learned so much from readingthis book.You can pick up any chapter at random and find yourselfcaptivated by a fascinating anecdote, a compelling biographical sketch, athought-provoking question, or a delightful little tidbit of information. The author made me think about things I have never thought about before. Reading this book has given me a newfound appreciation for the importanceof the circle as well as a newfound respect for the truly remarkable featsof our early scientists, mathematicians, and architects.So whether you'relearning about the life of Albert Einstein or the death of Archimedes;whether you're trying to figure out why old fenceposts were deliberatelyspaced 9.417 feet apart or how how the ancient Egyptians could havepossibly managed to erect thousands of 20-ton blocks 48 stories high; orwhether you are discovering that an experienced hunter is often smarterthan a computer or that terrified peasants rioted when the Gregoriancalendar was adopted because they believed that the pope was actuallystealing 10 days of their lives...you will enjoy reading, or even justskimming, A HISTORY OF THE CIRCLE.This book will change the way you lookat nature: you will see things you never saw before.It might even changethe way you look at yourself.I was delighted to discover, for example,that I was made of stardust, but I must say it was a bit unsettling tolearn that I am now a tad older than the sun which, according to Mr.Zebrowski, is "barely middle-aged." ... Read more

Product Description
Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students.

This captivating book gives voice to women mathematicians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring. The earlier parts of the book provide historical context and perspective, beginning with excursions into the lives of fifteen women born before 1920. Included are histories of collective efforts to improve women's opportunities in research mathematics. In addition, a photo essay puts a human face on the subject as it illustrates women's contributions in professional associations.

More than eighty women from academe, government, and the private sector provide a rich mélange of insights and strategies for creating workable career paths while maintaining rewarding personal lives. The book discusses related social and cultural issues, and includes a summary of recent comparative data relating to women and men in mathematics and women from other sciences. First-person accounts provide explicit how-tos; many narratives demonstrate great determination and perseverance. Talented women vividly portray their pleasure in discovering new mathematics. The senior among them speak out candidly, interweaving their mathematics with autobiographical detail. At the beginning of a new century, women at all stages of their careers share their outlooks and experiences.

Clear, engaging, and meticulously researched, Complexities will inspire young women who are contemplating careers in mathematics and will speak to women in many fields of endeavor and walks of life. ... Read more

Customer Reviews (1)

The recent accounts demonstrate how much progress women have made in the last half-century
While the opportunities for women still lag behind men in some areas, in general there are equal opportunities between the sexes. Most of the women under forty today have no idea how different it was for women thirty years ago. Before the twentieth century, it was even worse. Women such as Sophie Germain had to study mathematics in secret or publish their results under a male byline. This book starts with the biographies of fifteen female mathematicians born before 1920 and chronicles their struggles and achievements. While these biographies are interesting, they are probably too distant to be considered relevant by the modern student. In their other studies, they will have encountered facts such as women lacking the right to vote, so the fifteen women will simply be additional examples of women held in check by the prevailing social and legal norms.
The real power of the book is in the accounts that are much more recent. Less than fifty years ago, women were rare in mathematics and those who managed to succeed were often considered oddities. Many graduate programs had either formal or informal policies against admitting women and those accepted generally were given little encouragement. Nevertheless, determined women managed to succeed and provide inspiration to future generations of mathematicians. This is their story and they are all to be commended for their success and their willingness to encourage the next generation to succeed. It is largely due to their hard work and occasional suffering that there are now so many opportunities for women in all areas of mathematics. I strongly recommend this book as required reading in any history of mathematics class. It is also suitable as supplemental material for courses in women's studies and the history of education.

Published in Journal of Recreational Mathematics, reprinted with permission.
... Read more

Product Description
Dispelling some of the subject's alarming aspects, this book provides, in a witty and engaging style, the fundamentals of mathematical operations. Topics include system of tens and other number systems, symbols and commands, first steps in algebra and algebraic notation, common fractions and equations, irrational numbers, the binomial theorem, and much more. By the book's conclusion, readers will appreciate the compelling magic behind a subject they may have previously dreaded.
... Read more

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James Gow's A Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. Particular attention is given to Pythagorus, Euclid, Archimedes, and Ptolemy, but a host of lesser-known thinkers receive deserved attention as well. ... Read more

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Customer Reviews (9)

Treasure.
We do problems from this book in the math club at my college.
I wish there were more books like this one.

Excellent and fun book
This is a great resource for challenging math problems.After getting annoyed with newspaper "problem of the week" type books, this was a refreshing find.Don't let the "high school level" disclaimer fool you - there are some seriously difficult problems in here.

If you're the type to find logic and math problems fun, I would recommend dropping $15 for this text.It's well worth the time.

A Good Variety of Mind-Expanding Problems
This book consists of "320 unconventional problems in algebra, arithmetic, elementary number theory and trigonometry." The problems are mathematically accessible to students at the high school level or higher, as they call more upon analytical thinking than upon advanced mathematical techniques. There is a range of difficulties, with harder problems marked with stars in the book. (The hardest problems are marked with double stars.) The problems are divided into twelve sections: "Introductory Problems," "Alterations of Digits in Integers," "The Divisibility of Integers," "Some Problems from Arithmetic," "Equations Having Integer Solutions," "Evaluating Sums and Products," "Miscellaneous Problems from Algebra," "The Algebra of Polynomials," "Complex Numbers," "Some Problems of Number Theory," "Some Distinctive Inequalities," and "Difference Sequences and Sums." Much of the book is devoted to providing hints and solutions, which are both thorough and clear. This is a great resource for preparing for competition, for developing your analytical thinking, or just for having fun (that is, if you are the sort of person who finds solving math problems fun).

Good variety of problems
The reason I am giving 5 stars to this book is for its unique collection of problems. It has been very entertaining reading the book so far (I have not completed the book). There however are a few errors which can be easily figured out by the reader. The treatment of each problem is unique.

Very interesting book
I found this book very interesting, because it deals with many many problems of algebra and number theory. You can find many interesting and tough theorems (not all of them are widely known nor taught) with their demonstration. I particularily liked the section about "distinctive inequalities": it deals with a great number of inequalities and you can learn some new techniques for solving them. The book lacks of geometry, that's true (only some trig somewhere), but it gives (in my opinion) really a strong preparation on topics concerning algebra... try it! ... Read more

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A century and a half before the modern information technology revolution, machinists in the eastern United States created the nation's first high technology industries. In iron foundries and steam-engine works, locomotive works, machine and tool shops, textile-machinery firms, and firearms manufacturers, these resourceful workers pioneered the practice of dispersing technological expertise through communities of practice.

In the first book to study this phenomenon since the 1916 classic, English and American Tool Builders, David R. Meyer examines the development of skilled-labor exchange systems, showing how individual metalworking sectors grew and moved outward. He argues that the networked behavior of machinists within and across industries helps explain the rapid transformation of metalworking industries during the antebellum period, building a foundation for the sophisticated, mass production/consumer industries that figured so prominently in the later U.S. economy.

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The colorful lives of these women, who often traveled in the most avant-garde circles of their day, are presented in fascinating detail. The obstacles and censures that were also a part of their lives are a sobering reminder of the bias against women still present in this and other fields of academic endeavor. Mathematicians, science historians, and general readers will find this book a lively history; women will find it a reminder of a proud tradition and a challenge to take their rightful place in academic life today. ... Read more

Customer Reviews (3)

A perfect learning tool
A compelling story of the development of mathematics.If students were taught from Osen's book, they would have greater appreciation and interest in this mportant subject.Teachers, especially, couldn make the subject of mathematics considerably more interestin.

Fantastic.A "must read" for any aspiring mathematician.
This book examines the lives of women mathematicians from antiquity to the present.Osen describes the trials, tribulations, and triumphs of some of history's most fascinating people with a perspective no male could bring tothe subject.I'd love to discuss the matter with the author.

Profiles women mathemeticians, lives and contributions
Traces the lives of notable women whose work in mathematics is best appreciated through an under standing of the societies that shaped their lives. Traces the impact of their work; reinforces women's participation in enduring intellectual achievements and discounts the popular notion that we value mathematical ignorance as a social grace.Explains the power full satisfactions and aesthetic values which equal any other branch of knowledge. ... Read more

Product Description
This book is a collection of papers presented at the conference New Trends in the History and Philosophy of Mathematics held at the University of Roskilde, Denmark, 6-8 August 1998. The purpose of the meeting was to present some of the new ideas on the study of mathematics, its character and the nature of its development. During the last decades work in history and philosophy of mathematics has led to several new original views on mathematics. Both new methods and angles of study have been introduced, and old views of, say, the nature of mathematical theories and proofs have been challenged.For instance, disciplines as etnohistorical studies of mathematics and the sociology of mathematics have resulted in several new insights, and classical historians of mathematics are also experimenting with new perspectives. In a similar way, philosophy of mathematics has witnessed rather deep changes. Classical foundational studies have been challenged by new broader perspectives. The aim was to provide a forum within which historians of mathematics, philosophers, and mathematicians could exchange ideas and discuss different new approaches in the history and philosophy of mathematics.The book includes papers by Joan Richards, Henk J. M. Bos, Donald MacKenzie, Arthur Jaffe, Jody Azzouni and Paulus Gerdes. It also includes an extended introduction. ... Read more

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Taking seminal mathematical concepts and theories as their starting point, the contributors to this volume define myriad forms of interaction between mathematical research and historiographical problems. In the process, they pose such important questions as "Can an independent historian of mathematics make fruitful contributions to the development of mathematics?" and "Where did twentieth-century mathematics go wrong?" This collection of papers evolved from a History of Mathematics Symposium organized in Tokyo in conjuctions with the International Conaress of Mathematics held in Kyoto, Japan. The venue gave excellent cause to develop yet a further line of study rarely given its due in such anthologies: the mathematical traditions in the East. On this subject, papers discuss how to intermingling of cultures contributed to the introduction of Indian mathematics to the Islamic world, and Western mathematics to Japan. ... Read more

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Customer Reviews (4)

Good Sources, but...
This is a good source book in general, but some chapters are much better than others. The book is a collection of chapters written by different experts in the different historical areas. Some of the chapters are really good while others are mediocre.

I liked the Egypt and China chapters the best.

I found the India chapter with its repeated use of [...] in the source material to be irritating at times. As to all the [...]'s, I went to Google Books and found Colebrooke's Algebra 1817 book to fill in the missing [....]'s with Colebrooke's stilted 1800's British translation.

I did not like the selection of Babylonian tablets. There are tablets after tablets after tablets with no real coherent theme. A bit of the "Chinese style commentary" would have been greatly appreciated to help figure out what is actually going on in some of these tablets. There are a lot of good tablets shown, but there are also a lot of questionable choices for the tablets shown. Plimpton 322 is dealt with in all of half a page (p151) while there follow shortly after no less than fourteen pages of times tables and conversion rates: Ash 1924.796, W23273, W23283+22905, W23021. I question if this is really an appropriate choice of materials and wonder what were the editors thinking on this selection of materials?

These two chapters could be better, but even in these weaker chapters there are some good parts. I used the tablet Ash 1922.168, with the areas left out, as a homework for my History of Math class. I was quite happy to finally figure out the "pulverizer" when I came to the note on page 416.

Overall I give the book 4 stars and am happy with my purchase.

Disorderly
This bulky, slapdash collection of source texts will hopefully be made superfluous by a better and more stringently organised one quite soon. Until then it is the only one of its kind so we have to read it anyway. Although many, many pages are devoted to elementary arithmetic and other trivialities of no historico-cultural interest, there are also a few occasions where cultural contextualisation is enjoyable. As illustrations of this, I shall summarise two selections on the use of similar triangles to measure heaven and earth.

Chinese measurements of the heavens relied crucially on two cultural contingencies: that China is big and that it has bamboos in it.

As Chen Zi says, "16,000 li to the south at the summer solstice, and 135,000 li to the south at the winter solstice, if one sets up a post at noon it casts no shadow. This single [fact is the basis of] the numbers of the Way of Heaven." (p. 219, from The book of Chen Zi, in the Mathematical Classics of the Zhou Gnomon, compiled around the first century BCE.)

Chen Zi is referring to the point S' on the earth's surface perpendicularly beneath the sun S. Now, standing somewhere else, we erect a bamboo tube BB' so that its shadow falls at our feet O. Then (assuming that the earth is flat) OBB' is similar to OSS', so by measuring OBB' and knowing OS' we can calculate the distance to the sun from the earth, SS'. The value for SS' reported by Chen Zi is 80,000 li, which is obviously ludicrous, suggesting that it was the cool idea rather than the actual result that interested him.

Now, Chen Zi continues, pick up the bamboo tube you used as the post and point it towards the sun. Suppose its diameter is just big enough for you to see the whole sun through the tube (otherwise go get a longer or shorter tube). Then (length of bamboo):(bamboo diameter)::(distance to the sun):(diameter of the sun), where everything is know except the diameter of the sun,so now we know how big the sun is.

While the Chinese thus utilised their benefit of having vast land and bamboo sticks at their disposal, the Muslims faced other circumstances in response to which they devised other methods. Al-Biruni (Book of the Determination of the Coordinates of Localities, c. 1025, chapter 5) discusses a method for measuring the circumference of the earth akin to the Chinese method above, but does not find it feasible:

"Who is prepared to help me in this [project]? It requires strong command over a vast tract of land and extreme caution is needed from the dangerous treacheries of those spread over it. I once chose for this project the localities between Dahistan, in the vicinity of Jurjan and the land of the Chuzz (Turks), but the findings were not encouraging, and then the patrons who financed the project lost interest in it." (p. 628)

Instead:

"Here is another method for the determination of the circumference of the earth. It does not require walking in deserts." (p. 628)

The method is this. Climb a mountain. Let M be the mountain top, E its base, and C the centre of the earth. Now look towards the horizon and let H be the point furthest away from you that you can see. Then your line of sight is tangent to the earth's surface, so the angle MHC is a right angle. Thus since we can measure the angle CMH we know all the angles of this triangle. We also know that CH = CE = radius of the earth, and we can measure EM, so we can solve for the radius of the earth.

Al-Biruni did indeed carry this out:

"When I happened to be living in the fort of Nandana in the land of India, I observed from an adjacent high mountain standing west from the fort, a large plain lying south of the mountain. It occurred to me that I should examine this method there. So, from the top of the mountain, I made an empirical measurement of the contact between the earth and the blue sky. I found that the line of sight had dropped below the reference line by the amount 0;34°. Then I measured the perpendicular of the mountain and found it to be 652;3,18 cubits, where the cubit is a standard of length used in that region for measuring cloth." (p. 631) Al-Biruni goes on to calculate the circumference of the earth from this data, which comes out as 12,803,337;2,9 cubits.

The downside of this method is of course that it requires "a high mountain close to the seashore, or close to a large level desert." Thus, coming across such a mountain is an opportunity too good to pass up even if you are in the middle of a war:

"Abu al-Tayyib Sanad bin 'Ali has narrated that he was in the company of al-Ma'mun when he made his campaign against the Byzantines, and that on his way he passed by a high mountain close to the sea. Then al-Ma'mun summoned him to his presence and ordered him to climb that mountain, and to measure at its summit the dip of the sun." (p. 629)

Why did the Chinese measure the heavens and the Muslims the earth? Shang Gao expresses the Chinese attitude: "he who knows Earth is wise, but one who knows Heaves is a sage" (p. 217). But in the Muslim world, different cultural circumstances conferred a higher status on earth-measurements:

"If the investigation of distances between towns, and the mapping of the habitable world, ... serve none of our needs except the need for correcting the direction of the qibla we should find it our duty to pay all our attention and energy for that investigation. The faith of Islam has spread over most parts of the earth, and its kingdom has extended to the farthest west; and every Muslim has to perform his prayers and to propagate the call of Islam for prayer in the direction of the qibla." (Al-Biruni, p. 635)

Note however the conditional "if...", which is perhaps another hint that al-Biruni, like Chen Zi, does not consider practical gains to be the primary purpose of mathematics.

Excellent
Excellent service AND book condition. Very fast delivery. 100% Satisfied as allways with Amazon services.No further words need. Just excellent!

The Untold History of Math
This book is a must-have for teachers. It gives a comprehensive history of mathematics that every teacher should know. The book itself is well-written and moderately easy to follow, though some of the examples are advanced. It is a great reference and worth its price. ... Read more

Product Description
Discover the many ways mathematics is relevant to your life with MATHEMATICS: A PRACTICAL ODYSSEY and its accompanying online resources. You'll master problem solving skills in such areas as calculating interest and understanding voting systems and come to recognize the relevance of mathematics and to appreciate its human aspect. Included with your purchase is access to the CengageNOW, an online tutorial that allows you to work with real math notation in real time, with unlimited practice problems, instant analysis and feedback, and streaming video to illustrate key concepts and Personal Tutor with SMARTHINKING a live, online mathematics tutor. ... Read more

Customer Reviews (7)

AWFUL
I ordered this book along with three others and only this book has been a nightmare. It took two emails for the man selling this book to respond with the fact that he was "out of town" and hadn't recieved money yet even though i have a receipt and the other books i ordered came and were paid for properly. Really scethcy experience when i need the book in a timely manner for class. I would recommend all students buying from this seller beware, might just get the book NEXT semester.

Very pleased!
I was very pleases with my order, it was exactly as discribed and came quickly.

Good purchase choice!
THe book was sent to me in even better condition than expected. It also came about a week earlier than the expected delivery date so all in all a very good purchase choice.

Pages books
Terrible customer service...they never contacted me after I emailed them several times. I also never received the book that I ordered. I actually had to file a claim with Amazon.

Excellant Math Book
This book is well written and easy to use, well organized and easy to use. ... Read more

Product Description
This magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900.

Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galton's probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century?

Stigler's emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs.

Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.

Customer Reviews (6)

Excellent Coverage of the History of Statistics Before 1900
This is an outstanding book.As a Statistics student, I can't imagine reading anything better on this subject.The math in the book is in-depth enough such that I can relate historical developments of various statistical theory and technique to what I have done (and, for that matter, that which I have yet to do) and it was possible to reproduce some of the calculations on my own (which was quite enjoyable).Overall, this is an excellent book--I can't recommend it enough.

Statistics and Its History
Excellent book.To me, this book is not simply an exposition of the history of statistics, but a way to understand statistics better via the challenges which historically motivated its development.The writing is clear, precise, and insightful.

great perspective on a key period in the development of statistical science
Stigler is unrivaled as a statistician who researches the history of statistics. This covers the famous mathematicians and statisticians who developed the foundation on which probability and statistics blossomed in the 20th Century. He is thorough and accurate and his writing is always clear and interesting. After reading this try Salsburg's "Lady Tasting Tea" to see how Fisher, Cramer, Neyman and Pearson and Kolmogorov and others formally developed probabilty and mathematical statistics as important disciplines in the 20th Century.

Always enjoyable and enlightening, Stigler brings an unparalleled degree of scholarship to the essays.

Great background for students
I love history of mathematics books like this one that have the guts to delve into the actual mathematics involved while retaining a narrative thread. I use it with my children to illustrate why mathematics is important. What problems were people trying to solve? How solutions were arrived at in steps over time rather than as deus ex machina. This is much more effective than presenting mathematics as most schools, out of context as a series of recipes. The book is divided into three main parts:

The Development of Mathematical Statistics in Astronomy and Geodesy before 1827

The Struggle to Extend a Calculus of Probabilities to the Social Sciences

A Breakthorugh in Studies of Heredity

Excellent content, turgid prose
Professor Stigler is an academic, and writes like one. He is obviously knowledgeable; this book will appeal to professional statisticians.

For intelligent laymen with a general interest in the history of statistics, Against the Gods: The Remarkable Story of Risk by Peter Bernstein and The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by David Salsburg will be equally informative and far more enjoyable. Both authors are as knowledgeable as Professor Stigler, but write more clearly. ... Read more

Product Description
The mysterious tally sticks of prehistoric peoples and the terrestrial maps used for trade, exploration, and warfare; the perennial fascination with the motions of heavenly bodies and changed perspectives on the art and science of vision: all are testament to a mathematics at the heart of history. This visually stunning volume takes the reader on an illustrated tour of mathematics across cultures and civilizations, bringing to life a world of important ideas and-rarely supposed-great intrigue and charm.

The development of mathematics can be seen in a wealth of images, from the richly illuminated manuscripts of the Middle Ages to the deeply unsettling art of Dali and Duchamp, from the austere beauty of Babylonian clay tablets to the delicate complexity of computer-generated pictures. These images, and many others, are lavishly reproduced to accompany a text that travels from the dawn of Chinese and Indian civilizations to the scientific and digital revolutions of our day.

Including portraits of household names such as Kepler and Copernicus as well as lesser-known but equally compelling figures like Niels Henrik Abel and Leonhard Euler, The Story of Mathematics is a rich amalgam of history, biography, and popular science. Readers will come away understanding how and why mathematics evolved as it did--of how it entered and remained close to the center of every area of human activity. Explaining mathematical concepts without equations, Richard Mankiewicz enables us to appreciate this essential intellectual occupation without "doing the math."Amazon.com Review
"The evolution of science, philosophy, and mathematics, all related, is far more important to the history of humanity than a parade of rulers and aprocession of wars." Strong words, but Richard Mankiewicz comes mightyclose to backing them up in his fascinating book, The Story ofMathematics.

Divided into brief chapters, the book traces the development of mathematicsfrom a baboon's fibula with 29 clearly visible notches (from Swaziland,circa 35,000 B.C.) to the Babylonian sexagesimal--or base 60--numbersystem, which survives to this day in our method of timekeeping, to Euclid'sElements, described as "the most important textbook of all time," tofractals and other Mandelbrot sets. Along the way, Mankiewicz pays tributeto the men and women at the forefront of mathematics, though he's notafraid to dispel some myths: the Pythagorean theorem was widely known inantiquity before Pythagoras was even born, and a 14th-century Chinesemanuscript clearly depicts what is now known as "Pascal's Triangle," a goodthree centuries before Pascal was born. Most entertaining are the chapters onpractical applications of mathematics: astronomy, codemaking and -breaking,military strategy, modern art, and navigation.

At times, it is difficult to follow the actual complex mathematics, but thevast majority of the book is readily accessible to the general reader.Filled with beautiful illustrations taken from ancient papyri, medieval manuscripts, scientific instruments, Renaissance painting, andcomputer-generated art, The Story of Mathematics is a singularlyhandsome volume and a pleasure to read. --Sunny Delaney ... Read more

Customer Reviews (7)

A Balanced and Well-Told Story
Mankiewicz has given his readers exactly what the title promises -- The *Story* of Mathematics. As such the book doesn't bog itself down with illustrating the very mathematics it talks about. This might seem like a major absence for a book about mathematics, and maybe it is, but I get the feeling that the book assumes that the reader doesn't need or want a refresher. I appreciate the approach taken by Mankiewicz because it successfully keeps the story moving forward...as all good stories are inclined to do.

More commendable is that Mankiewicz's book gives the most historically balanced view of the early origins of mathematics that I've yet encountered. I am, of course, referring to the controversy that still surrounds Egypt's influence in the subject. I've read an entire spectrum of biased claims. Some of them over-crediting Egypt's contributions, but most of them under-crediting her legacy. Mankiewicz's view that "Our knowledge of Egyptian mathematics is necessarily limited by a genuine lack of artefacts" resonates as both sincere and true. He goes on to write that "It is therefore tempting to see the mathematics of the Egyptians as a step backward from the level reached by the Babylonians. But this probably unwarranted, especially given their precision in pyramid-building and their management of such a vast empire....the ancient Greeks widely acknowledged that their mathematics, especially their geometry, originated in Egypt." Those words seem to avoid the usual sensationalizing that I've encountered in other works on the topic.

This balanced reportage precipitates throughout the rest of the book, giving due space to all the key players, regardless of their geographic origins, in the story of numbers. The writing style is very accessible and, thankfully, with personality. Hopefully, this book is a hallmark of more to come. I think the world deserves a proper and balanced view of mathematics.

High on illustrations, low on math... and very small print
As another of the reviewers remarked, this book was obviously originally designed to be a "coffee-table" book on math for casual browsing... lots of beautiful illustrations (ranging from Michaelangelo pictures employing the use of perspective, right through to computer-generated fractal patterns), a chatty but superficial perusal through the history of mathematics, and very little in the way of actual mathematics content.

Unfortunately it seems the publisher slashed the printing budget for this book, and instead of being published in its originally designed "coffee-table book" dimensions, the book has been reduced in physical size with the result that the text is pretty small, and the print on the pages looks very cramped.

Informative, but not terribly interesting
I read this book because math is one of my favorite subjects and it seemed to be full of inforamtion. And it was full of information which stretched from discussing math in Pythagoras's times all the way up to modern chaos theory, but as I read it I just didn't find that it captured my attention as I had hoped. As I read through this novel I felt that only a small portion of what I was reading was really going to stay with me. I often felt my mind wandering as I just didn't find myself completely interested and sometimes I had to remind myself to pay attention.I would have liked a little bit more discussion on the importance and applications of the mathematics that was being developed. There wasn't as much depth as I yearned for, but perhaps this can be forgiven to some extent considering how much the author was attempting to discuss.

Despite all of the aforementioned, I'm still giving this book 3 stars(although I'd prefer to give it 2.5 if I could). It was a very easy read and certainly didn't get particularly complicated. Plus, there were some pretty nice illustrations. Overall, I'd say that although I don't regret having read the book, I probably wouldn't read it again.

Good text, terrible production
As far as the text goes, this is a pretty nice book. But the publishers have done the author a disservice in how they produced the book (maybe over-produced is a better term). It looks to me as if the book was intended to be a coffee-table sized book, then, when that turned out to be too expensive, the size was reduced. So we get tiny print, small pictures, and an over-dense page layout. Plus, there's one of the most irritating typos I've ever seen: the splash page for chapter three says it is about the Pythagorean "theorum"!!

The actual content is competently done, for the most part reflecting what is in the standard references and not taking any big interpretive risks. There is more coverage of recent mathematics than is common on books aimed at the "general reader." The bibliography is much too short, but it points to other books that do have more extensive references. There are better short histories of mathematics, but this one won't lead you astray... provided your eyes are good and small sans-serif type doesn't bother you!

It's OK.Just know what you're getting.
I was under the impression when I ordered this that it was an ordinary book you could read straight through.It's actually more of a general reference book of math history, organized in subtopics with really tiny, dense print written with little flair. ... Read more

Product Description
This epoch-making and monumental work on Vedic Mathematics unfolds a new method of approach. It relates to the truth of numbers and magnitudes equally to all sciences and arts. The book brings to light how great and true knowledge is born of intuition, quite different from modern Western method. The ancient Indian method and its secret techniques are examined and shown to be capable of solving various problems of mathematics. ... Read more

Customer Reviews (12)

to complex
Buy Vedic Mathematics Made Easy by Dhaval Bathia. much easier fun to read and understand.

Good but not that easy!
While the subject matter is covered in the text I would not refer to it as "simple".The author is obviously a highly advanced mathatician and the material is presented with highly advanced terminologies that to some laypeople may be a little difficult to understand.That being said, if you stick with it you will learn different methods of doing advanced mathmatics in a much easier way than taught in the Western world.

vedic maths
great book - my teenager is working his way through it in his spare time - wants to be able to wow his math teacher with doing difficult math in his head

Amazing Book for Mathematics
It is really amazing book of mathematics. I never knew that mathematics is so simple. Even it gave me explaination about current mathematic principles. After reading this book, I am able to solve equations very easily. This should be teach in every school. It is very easy and very interesting. I am shocked to realize that I did not knew about this book.

Faster than Calculator!!!!!
This book makes "promblems" rename to "FUN."I never imaged math can be as fun and easy, but this book made it so.I gurantee it will make your brain work faster then the calculators.Shock your co-workers or professor with this methods and over smart your friends. ... Read more