Customer Reviews (6)

A Gem in Modern Math
It is a shame that I found this book 30 years too late. Though written in 1970, this book is still by far the best Modern Math book in both historical and technical details. I bought it at a local second-hand bookshop 1 week ago, and I have not stopped reading the thick 760-page book since then.

The book has 30 chapters, but one can read any chapter in silo. I found fresh ideas and in-depth explanations on Galois Group & Theory of equations, Felix Klein's Geometry, Emile Noether's Ideal in Rings... nowhere I could find such lucid explanations.

As the Author said in Preface, any man on the street deserves to know what Modern Math is about and how it affects our life and our universe. Modern Math should not be kept in the ivory tower of the universities, be the privileged treasure of the mathematians. It belongs to the enthusiates, the curious students & the engineers who, by far, ignorant of this fascinating "New" Math which dates since 4,000 years ago.

A great history book!
Edna Kramer's is perhaps the best of the genre of books on the History of Mathematics.

The most pleasing feature about this book is that it is a fine balance between the mathematical ideas and the lives of the mathematicians. Best of all, it paints a sympathetic history of the times in which the discoveries were made. The use of anecdotes and "little" events in the lives of the men and women really brings to life both the subjects and their work.

Although my particular favourite sections are on the achievements of Euler, Gauss, Lagrange, d'Alambert, Ricci, Levi Civita, and Riemann, the book is truly an expansive landscape - there is coverage of virtually all the greats from the 16th century onwards. There are numerous examples from which to learn the basics of the mathematics. For instance, the sections on the history of the calculus are interwoven with simple, yet lucid examples. Equally, the more complex ideas like integral equations and partial differential equations are illustrated by examples drawn from the physical world.

All this makes the book worthwhile - it DOES NOT skirt over the Mathematics, but rather, makes an active attempt at imparting knowledge and understanding. This makes the book ideal for both the Maths specialist who is interested in history and for the generalist seeking a broad understanding without being daunted by the Maths. Kramer has done a marvellous job in meeting this tough challenge.

If this book has one failing, it is the way it skims over mathematical contributions from non-western societies, but it balances this somewhat by not overplaying the "Greek card". Some books do go on about Euclid as if he was the Newton of the ancients! Having said this, it can be excused since the book is quite old and much new knowledge has been gained on contributions from India and China in the last couple of decades. The interested reader may also wish to look up George Joseph's book, "The flight of the Peacock" for this.

An ideal book for both history and mathematics. I have had my copy for 20 years and it keeps my interest, still. Thoroughly recommended!

Thirty Years and Still the Best
I first read "The Nature and Growth of Modern Mathematics" in1970 as an engineering student with minors in math and physics. This book,over the course of a summer, provided me with the history of mathematicaldevelopment at the same time leaving me with the elementals of math areasin which I had not submerged myself. The effect was a tremendous weavingtogether of mathematical knowledge - both the rudiments of theory andsimple examples of applications - which has served me well in the decadessince.

There is a great deal of power in the present era from being ableto recognize the appropriate techniques from a more wide knowledge base, attimes, yes, to synthesize two or more techniques to solve a potent problemor develop an application. Edna Kramers book gave me a great deal, and itis written in a way that could assist people in all occupations and withall interests.

It is a fascinating and at times awe inspring overview ofmath.

The best of the Math History books
Edna Kramer's book has 30 chapters.Each one starts with an odd bit of history.Then Edna explains the critical impact this nugget had.After that, she does an excellent write up of the mathematics involved, completewith formulas and proofs.Each chapter is then rounded out with morefacts, more history, and more math. Every chapter is superbly structured. I would recommend this book for anyone who enjoys mathematics.

Excellent text for those interested in advanced mathematics
This book gives a detailed view of the who and why in the world of mathematics.Included are the actual concepts and proofs on a simplified level.I have taken advanced courses in math but only after I read thisbook did I understand the reasons for the way mathematics developed and theway mathematicians answered their critics, which is never covered in formalcollege cources.Highly recomended, easy to read. ... Read more

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Praise for Hal Hellman

Great Feuds in Mathematics

"Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments."
-Professor Dirk van Dalen, Philosophy Department, Utrecht University

Great Feuds in Technology

"There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master."
-New Scientist

Great Feuds in Science

"Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences."
-American Scientist

"Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time."
-Nature

Great Feuds in Medicine

"This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here."
-The New York Times

"Stimulating."
-Journal of the American Medical Association ... Read more

Customer Reviews (4)

David Foster Wallace's Righteous Twin
Wallace's seriously flawed Everything and More: A Compact History of Infinity (Great Discoveries) made me wary of buying another pop math book by a non-mathematician, so I put off buying _Great Feuds_ for some time, but eventually I gave in, and I'm glad I did.Hellman's cautious approach contrasts nicely with Wallace's bombast, and, unlike Wallace, Hellman gets almost all of the details right, with a notable exception being his claim that having a smallest element (rather than each of its nonempty subsets having smallest elements) is what makes a set well-ordered.

There's a lot of quoting of the opinions of professional historians, which is probably appropriate for a book written by an outsider, but I found it a bit tiresome after a while (just as I did when Peter Ackroyd took a similar approach in Albion: The Origins of the English Imagination).Also, I felt that Hellman didn't make it as clear as he could have who ended up winning the war of which these feuds were battles.21st century mathematics is overwhelmingly Cantorian, Zermeloian, and Hilbertian, in the sense that the existence of actual infinities and the appropriateness of using the Law of the Excluded Middle and the Axiom of Choice are all taken for granted by mainstream practitioners.There are respected researchers probing the effects of rejecting these principles, but they are few in number and those who do reject them are definitely working in the margins.

Don't let these quibbles or my 4-star rating keep you from buying this book.Within its genre, it's about as good as they come.

Readable Math
After seeing Mr. Hellman on CBS Sunday Morning News recently, I picked up his newest book, Great Feuds in Mathematics. A most enjoyable book. Although I am not a mathematician I was able to read "around" the few equations and enjoy the insight he brought to the math and its place in history. A good read.

Math is math
This book would be of most interest to advanced mathematicians and some philosophy initiates. I am a lay person with a large curiosity, however not being a math college major, limited my enjoyment of the "feuds."
Antonio Gonzalez

Fascinating Disputes But Beware The Challenging Arguments
This is an excellent book. The prose is clear and engaging and, despite the title, there are very few equations such that those who are equation-phobic have little to fear. However, many of the disputes center on nineteenth to twentieth century front-line research in pure mathematics - areas such as set theory, concepts of infinity, etc. These early ideas were prone to heated discussion and, in many cases, led to feuds. In order to allow the reader to understand the basis for these feuds, the author has included the essence of some of the key contentious mathematical arguments, often directly quoting members of each camp. I found that carefully following these arguments in detail could be difficult at times, but I certainly agree that pondering them is important if one is to clearly understand the position of each side. The final chapter poses the fascinating question: Are mathematical advances discoveries or inventions?" And here again, there are avid supporters of each side. I gave the book five stars because of the interesting subject matter and because I feel that the author has done a truly excellent job in presenting such a potentially difficult subject to as broad an audience as possible. Nevertheless, I still believe that I would benefit from reading some chapters a second time. Although anyone reading this book could learn much from it, I believe that it would be most enjoyed by serious math buffs. ... Read more

Product Description
Based on course material used by the author at Yale University,this practical text addresses the widening gap found between themathematics required for upper-level courses in the physical sciencesand the knowledge of incoming students. This superb book offersstudents an excellent opportunity to strengthen their mathematicalskills by solving various problems in differential calculus. Bycovering material in its simplest form, students can look forward to asmooth entry into any course in the physical sciences. Ideal forself-study! ... Read more

Customer Reviews (14)

Good, but falls short
The book is pretty good if you have seen the material before and you just need a review. If, however, you haven't seen a certain topic (say, Fourier series) then you're pretty screwed. General introductions are pretty loose (again, because this is only for review). I don't read it much, probably because of that.

Kindle disappointment
This is the first time I'm going to complain about my Kindle.I simple cannot read the equations in this book as reproduced on the Kindle.I bought it on Kindle to save money but I regret my choice.

Looks ok but is wrong on page 1
Well, the book looks useful and the author's online introductory physics lectures (at Yale Open Courses) are very good but on page one he states: "a function f(x)...is a machine that takes in a value of x and spits out a value f which depends on x".

Wrong!

It should read: "a function f...is a machine that takes in a value of x and spits out a value f(x) which depends on x".

That is, f names the function, not the value returned by it, e.g. compare sin and sin(45).

Toward what end?...
...basically stacks of higher level theorems with proofs but with no clearly apparent purpose...the author claims that working through the book will make a student more prepared...however, at no point does he offer proof or even an explanation of how...he doesn't even offer relevance to any particular area of science...suggested alternatives are texts by Boas, Sneider, and Arfken/Weber...

This is an excelent texbook
I'm surly learning a lot of calculus in this text, but it's really slow going for me. I've studied calculus 20 years ago receiving an A after the third Quarter, but this book is really revolutionary. I'm reviewing calculus in order to take the third semester soon, and I bought this book as a help. It's a big help, but it goes extremely quickly and requires an excellent grasp of algebra. I really like the book. It's very profound--but it's deep. I highly recommend it for a math or engineering student. ... Read more

Product Description
A Passion for Mathematics is an educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mind-bending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike. In each chapter, Clifford Pickover provides factoids, anecdotes, definitions, quotations, and captivating challenges that range from fun, quirky puzzles to insanely difficult problems. Readers will encounter mad mathematicians, strange number sequences, obstinate numbers, curious constants, magic squares, fractal geese, monkeys typing Hamlet, infinity, and much, much more. A Passion for Mathematics will feed readers’ fascination while giving them problem-solving skills a great workout! ... Read more

Customer Reviews (18)

Wonderful, the human side of math
Loved the stories behind the mathematician's lives. Very easy to read for anyone interested in math.

Keeping us interested. . .
Keep your math students excited!This book offers fascinating facts and great puzzles - super for end-of-year awards, and fun in the classroom.

It is fun!
The book's title is "A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality" is very accurate.
This is not a text book where you must to read page n-1 in order to understand page n. It is more like the Guinness Book of Records which you can open on any page and find something fascinating.
I found this book in our local library, but already after a couple of days I knew that I wanted this book. This was the only book I took with me on my recent trip overseas, and now it lying around in the kitchen and as I look into it at my leisure I find most fascinating anecdotes and problems.
Right from the onset the book captured me with the story of Ramanujan, a barefooted South Indian young man writing to a famous English mathematician. The mathematician (Hardy) first looked at it and threw the letter in the garbage, but then later took it out of, read it again and realized that the author must be a rare genius. Ramanujan was invited to England where he continue stunning his contemporaries with most unusual original discoveries. No mathematicians could follow Ramanujan's reasoning, but could see that his formulas were correct. Ramanujan himself explained that he received his formulas from an Indian Goddess while he was sleeping!

If you have a few mathematical programs such as Excel, Graph, Mathematica, or GSP, you can check out many of the problems, play with them, change them around or produces some pretty pictures like for example the "Schmidhuber Circles" on page 206.

The book does not require any deep knowledge of mathematics. This book can be equally enjoyed by highschool kids and university graduates.

Please don't believe me, check it out: The chances are that you will love it.

A most remarkable and enjoyable book
I have read hundreds of recreational math books over the years, and this recent addition has become my all time favorite -- a veritable smorgasbord of mathematical puzzles, factoids, amusing anecdotes about famous mathematicians, and insights into all nature of things. There is something for everyone, and the material is presented in a concise and entertaining way. As one example, you will learn the origin and orginator of most of the symbols we use -- e, pi, +, -, the factorial sign (!), etc.The book also shows a large number of delightful formulas by the Indian math protegy Ramanujan that are rare to see collected in a book for the general reader. Even the type font and layout makes for an easy read. Strongly recommended and a great gift for anyone with an interest in math.

mathematical Champagne
Sparkling, fascinating and creatively stimulating: the next best thing to a Brain Stimulator. A must have. Pickover as usual which means at his best. ... Read more

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Customer Reviews (8)

A Concise History of Mathematics

This is little more than a sketch of the history of mathematics. In broad strokes, it outlines the relationships among mathematicians and some of their texts, but says almost nothing of substance about the content of their work. Each chapter has a short bibliography, but since the last edition was in 1987 (1st ed. 1948), they are of limited value.

Mathematics Hystorical Development

When I was student ( from elementary school to university level ), I was never taught of history of mathematics ( at least in an organized and formalized way,sometimes there were references to singular and surprising anecdote as Gauss child summing up the first 100 natural numbers in few seconds). I think this is a lack ( probably it is not possible to teach everything in the already rich school program ) of the educational system. For this reason , enjoying mathematics ( especially the simplest one ), I was looking for something to explain and describe how the mathematical thinking developped with time. At the same time, I did not have much time, so I thought from the title that this book was the right one for my needs. Although all the history of mathematics from its dawn to about 1950and written in a short book is something very difficult to realize ( if not impossible ), I very reccomend this beautiful book, where the history of mathematics is well explained in terms of main thinking lines. Furthermore this book is rich of interesting anecdotes and details on personal and accademic relations among the greatest mathematicians of all time.

A Brief Outline of the History of Mathematics
In "A Concise History of Mathematics," Dirk J. Struik succinctly surveys the progression of mathematics: its discoveries, breakthroughs, and distinct personalities. If you enjoy the history of mathematics or if you dislike math (it will help infuse a sense of delight in math) you will find this book very useful. This little volume doesn't cover the subject or any prominent feature of mathematics in exhaustive detail, but it is a precise book with research touching on the foremost pioneers, originators, and timelines caught up in the development of mathematics from their earliest genesis until the start of the last century.

Chapters include:

- The beginnings
- The ancient orient
- Greece
- The beginnings of Western Europe
- 17th century
- 18th century
- 19th century
- First half of 20th century
- And more.

Simple to read and it will help elicit more affection for mathematics as it enlightens the reader in a historical outline regarding this essential subject.

Within this outstanding book is:

- A fine bibliography
- Numerous references (English and various languages).
- A few nice illustrations and pictures
- Many of the most significant details of the history of the mathematics.

Frege, Russell and other important figures are only mentioned in passing. Thus I prefer James Nickel's exhaustive and compelling volume on mathematics. I delight in mathematical truths because they reflect theism as the epistemic foundation. Without the infinite ontic ground of theism and without affirming a wellspring who is the foundation for infinite numbers, the non-theist cannot solve the paradox of infinite immaterial numbers within a finite material world. This is not a problem for the person who ascribes a theistic epistemic source whereas he believes in an infinite, immaterial, and eternal being as the infinite source of mathematics. Non-theists use infinite numbers, yet these numbers have no end, hence they do not comport with their worldview. One must presuppose theism to account for infinite numbers.

"A Concise History of Mathematics" is a marvelous fact-filled book, written in a lucid and crisp style.
The Necessary Existence of God: The Proof of Christianity Through Presuppositional Apologetics

Good infromation - Bad english
I bought the book for a class on history of math, and it covered that topic well.The issue I had was the usage of words only a PHD in English would use. The book lead me to the Internet to find more information about the period that was easier to understand.

Brief History of Mathematics,perhaps too concise.
I rather enjoyed reading this Dover classic on mathematics.Yet,there were some problems with the book.It's a vast topic,that's condensed into a rather small book.The author,Dirk J. Struik,did a wonderful job explaining the great giants of global historical mathematics.Now,if you're looking for the math geniuses of the twentith century,however,you'll miss them here.There is an excellent bibliograghy and many important basic formulas presented.The sketch portraits and rare photograghs add an insightful picture of the character of these esteemed numerologists.After reading this text,I found myself wanting to research more about their contributions to mathematics.Eventhough,i may be more advanced at understanding higher math concepts.This book presents a clear philosophical foundation,often skipped by math instructors today,because of time considerations. So, this book is the ideal text for any fellow math neophyte,who may cringe at the broad scope of classical mathematics. ... Read more

Product Description
Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free.This is an OCR edition with typos.Excerpt from book:THE GREEKS Greek Geometry About the seventh century B. c. an active commercial intercourse sprang up between Greece and Egypt. Naturally there arose an interchange of ideas as well as of merchandise. Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, CEnopides, Plato, Democritus, Eudoxus, all visited the land of the pyramids. Egyptian ideas were thus transplanted across the sea and there stimulated Greek thought, directed it into new lines, and gave to it a basis to work upon. Greek culture, therefore, is not primitive. Not only in mathematics, but also in mythology and art, Hellas owes a debt to older countries. To Egypt Greece is indebted, among other things, for its elementary geometry. But this does not lessen our admiration for the Greek mind. From the moment that Hellenic philosophers applied themselves to the study of Egyptian geometry, this science assumed a radically different aspect. "Whatever we Greeks receive, we improve and perfect," says Plato. The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the other hand, had within them a strong speculative tendency. They felt a craving to discover the reasons for things. They found pleasure in the contemplation of ideal relations, and loved science as science.Our sources of information on the history of Greek geometry before Euclid consist merely of scattered notices in ancient writeis. The early mathematicians, Thales and Pythagoras, left behind no written records of their discoveries. A full history of Greek geometry and astronomy during this period, written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abst... ... Read more

Customer Reviews (2)

A History of Mathematics

The Encyclopædia Britannica entry on Florian Cajori says, in part:

Cajori, Florian
born Feb. 28, 1859, St. Aignan, Switz.
died Aug. 14, 1930, Berkeley, Calif., U.S

"Cajori emigrated to the United States in 1875 and taught at Tulane University in New Orleans (1885-88) and at Colorado College (1889-1918), where he also served as dean of the department of engineering (1903-18). In 1918 he became professor of the history of mathematics at the University of California, Berkeley."

Reference: "Cajori, Florian." Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate Reference Suite DVD.

The first edition of this History of Mathematics occurred in 1893. Subsequent editions were in 1919, 1980, 1985, and this 5th edition in 1991. Apart from stylistic changes and minor corrections, the main revisions in the 3rd and later editions are said by the editor to be concerned with the eight page chapter on Babylonian mathematics, which was rewritten for the 4th edition and partly rewritten for the 5th. A book of similar title by Cajori, A History of Elementary Mathematics, although based upon this book under review, is a different work.

This is a densely written book, and especially in its later chapters assumes a mathematical background consonant with the period in which it was originally published. This is not a textbook. It is a scholarly discussion on the history of its subject. The historical limit of Cajori's discussion, mentioned in the preface to the 3rd edition and operative still in the current edition, is "the close of World War I." His viewpoint is not that of a modern reader. He is writing during the first blooms of 20th century abstract mathematics. The 1st edition of Whitehead and Russell's Principia Mathematica, which he mentions, occurred over the course of the years 1910 to 1913. The 1st edition of Felix Hausdorff's Grundzüge der Mengenlehre, which he doesn't mention, occurred in 1914. Emmy Noether (1882-1935) didn't arrive at Göttingen until 1915. Bourbaki's first book wasn't published until 1939.

Although Cajori lived until 1930, in revising his book for the 2nd edition (later editions occurred after his death), he could not know where mathematics was going in its methods of abstraction or how educational reforms and popular culture would affect the intellectual background and concerns of future readers, and so he could not write his history to speak to the viewpoint and expectations of a reader in the 21st century. But if you enjoy this sort of thing, this book is worth your attention, regardless of how well you understand everything in it.

The editor of the 3rd edition remarks: "With so vast and complex a subject to set forth within so small a compass, the author of a one-volume history of Mathematics must decide what facts to select, what interrelations to point out, whom to name, how much to explain, and the like. There is no optimum, no one way of doing this. Every one-volume history of mathematics is therefore necessarily very different. Indeed, each of the few that exist are, as the reader can easily verify, strikingly different." (p. iii)

Content may be good but Kindle version is useless
This isn't a proper e-book. It obviously is just a raw OCR scan without any human 'cleaning up'. I feel I should be given a proper copy for my Kindle when it's appropriately formatted. Riddled with misspellings and 'junk'. Especially when dealing with mathematics formatting is key, otherwise the book is unreadable.

Because of this, I am unable to review the actual content of the book. ... Read more

Product Description
Key Message: The third book of a three-part series, Algebraic, Graphics, and Trigonometric Problem Solving, Second Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and the accompanying practice exercises. Along with the activities and the exercises within the text, MathXL^® and MyMathLab^® have been enhanced to create a better overall learning experience for the reader. Technology integrated throughout the text helps readers interpret real-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops readers' mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines.

Key Topics: Function Sense and Linear Functions; Introduction to Functions; Linear Functions; Systems of Linear Equations and Absolute Value Functions; The Algebra of Functions; Addition, Subtraction, and Multiplication of Functions; Composition and Inverse of Functions; Exponential and Logarithmic Functions; Exponential Functions; Logarithmic Functions; Quadratic and Higher Order Polynomial Functions; Introduction to Quadratic Functions; Complex Numbers and Problem Solving Using Quadratic Functions; Curve Fitting and Higher Order Polynomial Functions; Rational and Radical Functions; Rational Functions; Radical Functions and Equations; An Introduction to the Trigonometric Functions; Introducing the Sine, Cosine, and Tangent Functions; Why are the Trigonometric Functions Called Circular?

Market: For all readers interested in Algebra, Trigonometry.

... Read more

Customer Reviews (3)

No good for distance learning
This text may be fine for classroom study but if you intend to use it for online or telecourses keep in mind that the reading includes examples without answers. I understand that the appendix contains answers to some of the end of chapter review questions (although some of the ones in this book are marked incorrectly e.g. question 3 is blue because the answer is in the back but actually question 4 is answered), my issue is that as you read the chapter example questions are given but no answers. How can I know if I am understanding if I am not given the answer? I am a seasoned distance learner and have a very hard time getting anything worthwhile from this text.

Excelloent Condition
This book was in perfect condition and actually better than described.Great service, no worries at all.Thanks very much!

chapter1: answer
i need to help this chapter 1 so i not understand this book but i need you explain me this clear this chapter 1 about f(x)numbers. Please answer me to explain me this chapter 1 from algebraic, graphical, and trigonometricproblem solving on mathematics in action. i need easily answer and explainthis chapter 1 as for example. Thankss Christy Gasch ... Read more

Product Description
This lucid presentation examines how mathematics shaped and was shaped by the course of human events. Authors Resnikoff and Wells explore the growth, development and far-reaching applications of trigonometry, navigation, cartography, logarithms, algebra, and calculus through ancient, medieval, post-Renaissance and modern times. Preface. Index. Bibliography. 203 black-and-white figures. 7 tables. 14 photos.
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Customer Reviews (2)

A few interesting applications
The first half of the book is a fairly interesting discussion of astronomy and its applications to cartography and navigation. Aristarchus calculated the distance to the moon and the sun from three easy measurements: the shadow of the earth is about two moon radii wide at the distance of the moon (observable at lunar eclipses, of course), both the moon and the sun subtend and angle of about half a degree when viewed from the earth, and we can calculate the ratio of the distance to the sun and the distance to the moon by measuring the angle between the sun and the moon at half moon. But to carry out these calculations we need to know values of trigonometric functions, so we go on to tackle this problem from first principles by deducing Aristarchus' approximation 1/60tan(y)/y where x>y applied to a 30-60-90 triangle. The section ends with an interesting exercise: "Could the 'size of the universe' have been reasonably estimated in early times if the earth had no moon?" Astronomical observations are also crucial for navigation, of course, and then we are led to map making. We study the usual Mercator projection (x=longitude, y=log(tan(latitude/2 + 45))), but unfortunately we cannot prove its key property of being conformal (instead the authors present a "slightly involved" proof that stereographic projection is conformal, which they say is a step in the right direction because then the rest can be done by complex function theory). It follows that a constant compass course will be a straight line in the Mercator projection; on the surface of the earth itself it will be a complicated "loxodromic" curve, although later we shall see that it becomes an equiangular spiral when projected onto the equatorial plane. After having seen that both astronomy and navigation calls for quite extensive calculations we look at how the invention of logarithms reduced this burden dramatically. Again there are some interesting exercises along the way, such as "Can a table of values of the function x^2/4 be used to convert division [and multiplication] to addition and/or subtraction?" (There are Babylonian clay tablets relevant in this context.) The second half of the book is a very dumb presentation of the calculus and a few applications. For instance, one supposed application is a better way of calculating logarithms through infinite series expansion. But the series expansion is derived from Taylor's theorem (which is unnecessary and historically backwards) and thus relies on appeal to the "formula" for the derivative of the logarithm function which is stated in a table without the least indication of proof. Even if the authors had told us that we can understand the logarithm as the integral of 1/x this would not have done us any good since the one insight on which all understanding of this and a million other things rest---the fundamental theorem of calculus---is simply stated without any indication of why it is true. Thus the useful series for the logarithm, which would have been very interesting to derive from first principles, is instead derived by three layers of appeal to authority.

Entertaining and puts math in context
This book is easy and entertaining to read. It puts mathematics in context and motivates to study mathematics. The book also teaches to respect the work of all those mathematicians that have made it possible for us to reach the current level of civilization. ... Read more

Product Description
A straightforward explanation of the abstract principles common to science and mathematics, this helpful volume enables scientists and mathematicians to read and appreciate papers in fields different from their own. It also offers other readers an improved understanding of subjects employing mathematical principles. Topics include Euclid's algorithm; congruences; polynomials; complex numbers and algebraic fields; algebraic integers, ideals, and p-adic numbers; groups; the Galois theory of equations; algebraic geometry; matrices and determinants; invariants and tensors; algebras; group algebras; and more. "Unreservedly recommended"--Journal of the Institute of Actuaries Students' Society. 1960 ed. (1949 pub.)"Clever and well-written, the book would make a worthwhile and inexpensive addition to any mathematics collection."--Book News, Inc.
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Customer Reviews (3)

Outstanding, compressed overview
This book, covers just about everything important in algebra from basic operations on numbers to groups and tensors, both pure and applied, and all in less than 150 pages!

Given, the above scope, it moves quickly, but should be completely comprehensible to anyone with a strong High School math background, as long as the student reads slowly and carefully.The advantage of the compression is that it is possible to see the whole field and its connections without getting mired in the details.

Fantastic for a broad overview of algebra, prior to studying in more detail (or afterwards, to see how it all fits together).Don't be put off by the age of the book and, for the money, unbeatable.

Good pocketbook of algebras
This is an old, elegantly presented, reminder of algebraic theories which should be general knowledge of the mathematics and physics students now. Disgracefully, they are not, and a short, concise review is something which could be readen in a pair of afternoons for the mere pleasure of adquiring a general idea of many theories. This book provides that, if one is prepared to cope with a little antique names. Dr. Littlewoods "Simple Account" should be amply recommended.

very helpful
I used the chapter on Galois Theory as a reference for a course I was in because it had such a concrete explanation on how Galois Theory works. However, it didn't mention anything about field extensions & barely mentioned groups. That's why I liked this book, it gives concrete versions of things like (off the top of my head) complex variables, matrices, Galois Theory, polynomials, tensors & more. There's a chapter on each subject & treats it in a very concrete manner. Any math student not totally comfortable with abstractness (as I was, with Galois Theory of equations anyway) would find this book helpful, imo. ... Read more

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Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content.

New to the Third Edition
In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors.

Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

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Presenting the various approaches to the study of integration, well-known mathematics professor Angus E. Taylor brings together in one volume "a blend of the particular and the general, of the concrete and the abstract"—an invaluable study aid for beginning graduate students. 38 diagrams. Introduction. List of Special Symbols. Index.
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Customer Reviews (1)

Gotta Be Nuts To Use Anything Else.
I have many friends who are graduate students or upper level undergrads in mathematics at Columbia and Yale who are suffering in their Real Variables courses because their arrogant,aloof instructors are using overpriced,ultra-TERSE higher analysis texts like Rudin's Real And Complex Analysis or Royden's incomprehensibly "classic" text.(For those of you who are using Royden and spent the insane cover price on it,you should realize there are a TON of errors in it.)I feel so bad for them because they really got taken for a ride-for a fraction of the cost,they could have had this GEM of a text.Taylor,famous for his Advanced Calculus,developed this text as a series of lecture notes at UCLA in the 1950's.Taylor rightly realizes the key to understanding mathematical analysis/measure theory at this level is a firm grip of point-set theory and abstract topologicalspaces-of which the real and complex numbers systems are but special cases.He then proceeds to develop the metric and topological properties of the number systems in this abstract setting-focusing on the rigorous set-theoretic foundations. Critical to analysis(and pure math in general) are PRECISE DEFINITIONS-and this is what makes Taylor's approach to the subject so beautiful and crystal clear,without sacrificingrigor or exposition of challenging theories.How many analysis text do you know develop BOTH the classical Lesbegue approachto modern integration as well as the Daniell approach for functional analysis-without losing an ounce of clarity?Run-don't-walk to your bookstore and order this if you're in upper level analysis courses. This will become a standard reference throughout you're career-I promise. ... Read more

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Practice: Word Problems mimics the verbal problems in each lesson at an average level. ... Read more

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V. 3. other two volumes, one and two, available. The set is in 3 volues. a complete guide to a unique system of mathematics. ... Read more

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Progress in Mathematics Grade 2
This transaction was great.The book was just as the seller described.I would buy from this seller again! ... Read more

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This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added as well as commentary that helps place the exercises in context.

Customer Reviews (4)

An intellectually satisfying history of mathematics
This is a brilliant book that conveys a beautiful, unified picture of mathematics. It is not an encyclopedic history, it is history for the sake of understanding mathematics. There is an idea behind every topic, every section makes a mathematical point, showing how the mathematical theories of today has grown inevitably from the natural problems studied by the masters of the past.

Math history textbooks of today are often enslaved by the modern curriculum, which means that they spend lots of time on the question of rigor in analysis and they feel obliged to deal with boring technicalities of the history of matrix theory and so on. This is of course the wrong way to study history. Instead, one of the great virtues of a history such as Stillwell's is that it studies mathematics the way mathematics wants to be studied, which gives a very healthy perspective on the modern customs. Again and again topics which are treated unnaturally in the usual courses are seen here in their proper setting.This makes this book a very valuable companion over the years.

Another flaw of many standard history textbooks is that they spend too much time on trivial things like elementary arithmetic, because they think it is good for aspiring teachers and, I think, because it is fashionable to deal with non-western civilisations. It gives an unsound picture of mathematics if Gauss receives as much attention as abacuses, and it makes these books useless for understanding any of the really interesting mathematics, say after 1800. Here Stillwell saves us again. The chapter on calculus is done by page 170, which is about a third of the book. A comparable point in the more mainstream book of Katz, for instance, is page 596 of my edition, which is more than two thirds into that book.

Petty details aside, the main point is the following: This is the single best book I have ever seen for truly understanding mathematics as a whole.

Relationship between algebra and geometry
It is a very good book.It has presented very clearly some difficult-to-understand relationship especially the link between algebra and geometry.It is a very good balance - history, Mathmatics, biography all mixed very well together.Highly recommended.

concise and well written summary of mathematics
Stillwell covers a lot of ground in a short undergraduate text intended to unify various mathematical disciplines.Naturally, _Mathematics_and_its_History_ begins with the early Greeks and in particular geometry (which is how mathematics was typically expressed then).The development of algebra and polynomial forms is described followed by perspective geometry.The invention of calculus and the closely related discovery of infinite series provide the backdrop for short biographies of prominent mathematicians (mostly dead white males to multicultural deconstructionists).The development of elliptic integrals (used in solving functions with specified boundary conditions such as a Neumann problem found in fluid mechanics).The treatment then diverges to physical problems including the vibrating string and hydrodynamics, together with a note on the renown Bernoulli family.Then Stillwell returns to the esoteric in complex numbers, topology, group theory and logic with some comments on computation at the end.Some mathematicians may find the overview to lack comprehensiveness, but the book's brevity for each topic and biographical notes present a balanced approach to the more casual reader about this important field of study and how it developed.

see below
This is an overall good text. It offers a very in depth history of many many mathematical ideas.It gets quite technical at times, which can be a good or bad thing, depending on what you are looking for. ... Read more

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This consumable book provides lesson support material for students to analyze and complete.It provides a long-term record of each student's mathematical development. ... Read more

Customer Reviews (2)

It's just okay
It should be used only as a supplement to a textbook.I bought this but it seem to have no order.Strange exercises.

Excellent.
Excellent. The book is brand new as expected. Received the book a few days after I placed the order.Will definitely order from this vendor again. ... Read more

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The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics. ... Read more

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The "little red book" that beats the others
Prof. Gowers packs only the most essentially juicy pieces of mathematics between the covers of this small book that fits comfortably into the back pocket of your jeans.This book is deceptively small and curiously strong.Only dedicated self learners need buy this book; as it is not written with any type of entertaining prose--it's "all business" from page 1.However, this "teaspoon of rigor" helps the rest of math go down.Oddly, Amazon.com does not include a preview for it but here is the table of contents as copied from Oxford's site for the Very Short Introduction series.(To: Prof. Gowers & OUP--outstanding job, keep it up)

Table of Contents
1. Models
2. Numbers and Abstraction
3. Proofs
4. Limits and Infinity
5. Dimension
6. Geometry
7. Estimates and Approximations
8. Some Frequently Asked Questions

Concise, not Simple - Elegant like a simple black dress
Professor Timothy Gowers starts with the need for models and ends with the usefulness and necessity of estimation.The body of the book gives the flavor, the value and the connectedness of Proofs, the calm resolutions of infinity and the impact of changes in dimension and Geometry.

No.Not a problem-based course.Not a history lesson.No sexy examples.Little mention of the titans.Yet the point of doing math, its constraints and pathways, would strike anyone who reads the book.Whether high school students would get it.I'm not sure.The maturity in the words and the totality of the immersion within its few pages is sublime.In knowing that exact answers are rarely found, but knowing the boundaries of the answers and their closeness to actual mimics our own lives.

This would be a must read in a non-ADHD world.

Gowers also wrote the Princeton book on Math.The professor is a Fields medal winner.

Great Insights to Math
I've always loved math, but I've always had difficulties explaining to people why they should care about math.While this is by no means a complete overview of the basics of the subject since there is far too much to cover, it does provide a lot of meaningful insights as to why Mathematics is interesting.It's a very pragmatic approach that does away with romanticism while not condensing the material to something overly dense.This book is a great little book on the wonders of math.

nice introduction
it helps me to link some topics together and understand some points from a wider perspective. the size of the book is excelent you can take it with you anywhere.

This book gives hints of what advanced maths is about
When I started reading this book I kept putting it down to extend the pleasure of reading it. It makes sense of why some things don't matter in maths. It even seems to confirm that infinity does not exist, while still being a powerful tool. Any person who wants to gain an insight of mathematical knowledge could not do better than read this book. They will gain an appreciation of advanced maths without having to believe or understand it. I don't think the concepts could be expressed more clearly or more simply. However even the unquestionable ability of Timothy Gowers could present hyperbolic geometry in a form that gives credibility to the topic. Of course he is only telling us, he didn't invent it.
I have found if a student can understand fractions, they can understand geometry,trigonometry, algebra and calculus. I don't think any one knows how people lift their skills from tangible to abstract mathematics but this book makes ordinary people aware of the vast challenges and beautiful fields. But beauty is like the numbers, they are both abstract adjectives and can not exist by them selves. This book shows us that that doesn't matter.
After this the next step to enlightenment is The Princeton Companion to Mathematics which was edited by Timothy and displays the same simple clarity. It has also been reduced from $142 to $66 ... Read more

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Paperback grade 2 volume 2 Everyday Mathematics Student Math Journal, copyright 2001.Package of five paperback This book contains Units 7-12 in the grade 2 Everyday Math curriculum. ... Read more

Customer Reviews (2)

Excellent Math program workbook
My husband is a retired NYC school principal. An award-winning educator with Fordham University and New York University and he wants you to know that this is a great book for practicing math skills. If he says it's good, believe it. He's from Brooklyn, he was everything from a teacher to principal and everything in between and he knows education books, what works and what doesn't. He said it was good even for the person who just wants to improve and practice basic math skills. Like me. He handed it to me. Hint. Nudge.
Everyday Mathematics: Student MathVolume 2 (Grade 4)

Item not in good condition
This workbook had a torn page, 15 of the pages had been completed (some in pencil, others in crayon and ink) and several of the pages had been graded by a teacher with a red ink pen. The spine was torn and the name "David" was written on the cover of the journal in permanent market. This information should have been posted in the description, and if it would have been I would not have purchased this book since it is a workbook. ... Read more

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Geometry is probably the most accessible branch of mathematics, and can provide an easy route to understanding some of the more complex ideas that mathematics can present. This book is intended to introduce readers to the major geometrical topics taught at undergraduate level, in a manner that is both accessible and rigorous. The author uses world measurement as a synonym for geometry - hence the importance of numbers, coordinates and their manipulation - and has included over 300 exercises, with answers to most of them. The text includes such topics as: - Coordinates - Euclidean plane geometry - Complex numbers - Solid geometry - Conics and quadratic surfaces - Spherical geometry - Quaternions It is suitable for all undergraduate geometry courses, but it is also a useful resource for advanced sixth formers, research mathematicians, and those taking courses in physics, introductory astronomy and other science subjects. ... Read more

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Excellent
The best geometry book available for someone who has a working knowledge algebra.Well written and moves from the basic to the intermediate at a measured pace.HIGHLY recommended. ... Read more