Posted in History-Mathematics (Friday, September 5, 2008)
Written by Barry M. Katz. By Stanford Alumni Assn.
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No comments about Technology and Culture: A Historical Romance (Portable Stanford).
Posted in History-Mathematics (Friday, September 5, 2008)
Written by Feng-Hsiung Hsu. By Princeton University Press.
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5 comments about Behind Deep Blue: Building the Computer that Defeated the World Chess Champion.
- Feng-Hsiung Hsu's story will appeal to anyone who enjoyed Tracy Kidder's Soul of a New Machine or Steven Levy's Hackers. The book captures the thrills and spills of an intellectual steeplechase. Along the way, it reveals the inner workings of the computer science department at Carnegie Mellon University. It's a great read. Feng-Hsiung Hsu, if you're reading this and you ever find yourself in Hortonville, Wisconsin, the first cup of coffee is on me.
- I have prurchased this book to improve my english language.
Yhe same talks about two subjects that I know: computers and chess.
It was a good surprise read this enjoyable work which offers information, stories and knowledge.
The author explains very clear the roots of Deep Blue and reflects the environment of Top chess.
Read it!
- Behind Deep Blue was written by the man who lead the research and development team which created the chess computer that beat the World Chess Champion, Gary Kasparov. Hsu tells a lot of fascinating stories about his involvement with IBM, academia and the world of computer-vs-computer chess tournaments. It never got too bogged down in computer or chess jargon.
Some interesting things concerning the identity of Deep Blue (or computers in general) emerge from Hsu's story. Hsu speaks of his computers' identities in ways which facilitate his sportsmanship. So for instance, almost every time one of Hsu's computers loses a game it is retrospectively explained by reminding the reader that the computer had been regrettably forced to play when it still needed a few more weeks of software or hardware tweaking. It never lost because it was an inferior machine - it lost because its superiority could not manifest because its update/debugging had been interrupted by the tournament schedule. As the book makes clear, Hsu's computers were continuously undergoing relentless tweaking, providing Hsu with this excuse every single time one lost. This may be par for the course when diagnosing machines - since any sub-desired performance which can be corrected can, therefore, be "explained" as the unfortunate consequence of the machine's present uncorrected state. For humans it's different. When I lose a foot-race I can't say, "Well the only reason I lost is because this race was scheduled a few years before my training made me fast enough to win it."
Another fascinating element of the book is Hsu's recounting of Deep Blue's now-famous rejection of 36. Qb6 in game two against Kasparov in the 1997 match. Kasparov broadly hinted that the computer's decision not to move that way was a human decision - implying that the IBM team had cheated. Hsu's defense of Deep Blue is convincing. But there is raised an interesting point regarding computer intelligence. If Deep Blue did in fact choose to avoid 36. Qb6 without human intervention then Kasparov's heartfelt identification of the move as cheating has Deep Blue passing a simple version of a Turing Test.
- Feng-Hsiung Hsu's story will appeal to anyone who enjoyed Tracy Kidder's Soul of a New Machine or Steven Levy's Hackers. The book captures the thrills and spills of an intellectual steeplechase. Along the way, it reveals the inner workings of the computer science department at Carnegie Mellon University. It's a great read. Feng-Hsiung Hsu, if you're reading this and you ever find yourself in Hortonville, Wisconsin, the first cup of coffee is on me.
- Conceit and self-righteousness have become the calling cards of anyone who can outdo someone or something with computers. Big deal. All the self adulation that has gone into this tacky piece of work can't hold a candle to the fact that Gary Kasparov can play chess (and think!) Which is more than I can say about the vanity displayed by the author. Anyone who sets out to humiliate or bring down a champion by using questionable means has zero integrity. However, it's to be expected from this kind of individual.
It is singularly unimpressive; vain and self indulgent.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by David Eugene Smith. By Dover Publications.
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2 comments about A Source Book in Mathematics.
- For students of the history of maths, Smith provides you with a very convenient reference. He has gone back to many of the original papers by Newton, Pascal and others, and gathered 125 of these into this book. You can search for insight into how those luminaries made their important discoveries. As an added utility, the papers have been translated into English.
An amazing time saver. For he lets you access the papers without any intermediary. The alternative would be to spend months searching in some large research library. And also probably having to order copies made from other libraries. At non-trivial cost in time and money.
- Mathematics was never easy and looking at these classic
reproductions you really get a feel of the ignorance
of even the greatest men in mathematics.
Here you can see them struggle to invent new ideas
that made possible our scientific and technical culture.
I think this kind of book is invaluable to the student
who wishes to actually understand.
Some of the papers are almost impossibly difficult.
It is a very good book!
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by Arun J. Prakash and Gordon V. Karels and Ray Fernandez. By Praeger Publishers.
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No comments about Financial, Commercial, and Mortgage Mathematics and Their Applications.
Posted in History-Mathematics (Friday, September 5, 2008)
Written by Ziauddin Sardar. By Totem Books.
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5 comments about Introducing Mathematics, New Edition (Introducing... S.).
- I found this book to be quite enjoyable. The section on Muslim mathematicians was particularly interesting. Did you know that Muslim mathematics made great contributions to trigonometry?
Buy this book if you want an overview of mathematics -- including the history of mathematics. The visual treatment make this book fun to read and attractive to all ages.
- This book briefly touches on many areas of maths, some old and some new, often uses the passive voice in regards to historically significant theorems in math without reference to the fuller context or reasons why they were deemed significant or who proved them and how. Being an "introducing" of course the book is limited in its scope and can only scratch the surface for most of its topics, of which it does an Ok job with.
But the bigger bone I have to pick is with the cultural studies stuff towards the end. Mathematics IS a cultural activity, and is what it is today, not stricly because of Eurocentric hegemony and cultural domination with value-laden theorems, but because mathematical ideas and approaches to proof are "traded" amongst cultures in a broader and larger Marketplace of Ideas.
Some recent books challenging Platonism (Where Mathematics Comes From, The Mathematical Experience) are better constructed with more limited theses.
- 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.
- I'm a big fan of the Introducing... series, and to me, this is one of the best.
- 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.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by Georges Ifrah. By Wiley.
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4 comments about The Universal History of Computing: From the Abacus to the Quantum Computer.
- This book is really fascinating, especially if you are interested in scientific and technical achievements. Read this book and you'll find out how the computer can be traced to the Renaissance, and how Word War II influenced the development of analytical calculation. The epic tale of computing comes to life in these pages.
- I would have expected from the title that this book might have started in the 1940s (or at the earliest with Babbage and the Difference Engine) and told the story of the development of computers from there. No, as the subtitle indicates, this book goes way back. In fact, the first section is a summary of number systems going back to the age of the Egyptians and before. It's a very methodical and somewhat dry tale, not helped by being translated from the French by translators who feel compelled to insert their own comments at intervals.
When it does get going, it provides a history of the relevant mathematics as well as automata from the Islamic era forward. The actual computer era is touched on mostly in its early stages, with the first computers of the forties and fifties. And it concludes with about sixty pages that have nothing to do with history but rather attempt to define key words such as "information" and "computer." All in all, it is a methodical and thorough book, perhaps a little dry but not as much as some books I have read. The author muses on the implications of various stages of discovery rather than simply relating the facts (and the translators chime in as well), which enlivens the story. Still, this book is probably for the more interested rather than the casual reader.
- Until recently, the history of computing has tended to be tied to the goals of mathematicians, as they struggled to keep up with the increasing demands of a society growing more technical. As nations began to trade with other nations, the necessity of performing computations on larger numbers very quickly forced changes in the notation. When first introduced into Europe, the modern decimal system of notation was greeted with skepticism and some hostility. However, as is nearly always the case in human endeavors, it was accepted rather quickly, as it was so much more efficient than other systems such as Roman numerals. Therefore, the history of computing devices is bound very tightly with improvements in representation, and the historical changes in notation are the topic of the first section of the book.
Ifrah does an excellent job in recapitulating the history of the notation of computation, covering the entire world, ending up with the modern notation and the efficiency of binary numbers. Nearly forty pages are devoted to explanations of many ancient numerical notations, and many figures are included. It is this approach that differentiates this book from other histories of computing. Other authors concentrate on the history of the evolving architectures of the computing devices, ignoring the necessary precondition of a compact and efficient notation. It is very difficult to imagine computing devices that could easily perform arithmetic on Roman numerals. The second section is a two track treatment of the development of computing devices. One track covers the mathematical preliminaries and the second the mechanical advances that led to the construction of accurate computers. Most of the early improvements were done by mathematicians, and it was not until the late nineteenth century that governments started to be interested in computers. The primary event was the work of Charles Babbage, who showed that computers were possible and how valuable they could be in performing routine computations that were highly prone to error. In many ways, this history of computing is more a history of the requisite mathematics rather than a history of hardware. This is a second way in which this book differs from other histories. One of the reasons why computers have improved so quickly is that much of the theoretical background for their actions were developed before the machines were. Ifrah explains that in great detail, describing how some of the principles of abstract mathematics have been applied to the building of computers. The final section is very small and deals with the future of computing. This is a wise move, as this book is a history and one thing we have learned from the recent history of computers is that predicting the future is largely impossible. We know that they will get faster, have more memory and the usage will increase, but the consequences of this are difficult to predict. If your interest is in the preconditions necessary for computers to be widely used, then this is the book for you. Ifrah covers all of the notational and mathematical background necessary for computers to be useful, for without that, they would probably have been little more than intellectual toys.Published in the recreational mathematics e-mail newsletter, preprinted with permission.
- If you have been looking for a more academic approach to the history of computing then this is the book for you.
The book is divided into three parts. Part One contains a very comprehensive taxonomy/chronology showing the evolution of human number systems.
Part Two is where you will find the core "History of Computing" bit: tables, logarithms, analogue/digital, mechanical calculators, automatic calculation, electronic machines etc. It also includes an interleaved, and detailed, explanation of how computing has evolved from basic number crunching into abstract information processing.
Part Three reads like a long philosophical conclusion and contains some excellent material on ethics and artificial intelligence.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by William P. Berlinghoff and Fernando Q. Gouvea. By Oxton House Pub.
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5 comments about Math Through the Ages: A Gentle History for Teachers and Others.
- Most of the texts available for history of mathematics courses are aimed at upper-level undergraduate students and try to be encyclopedic. This book fills a needed hole in the offerings through its accessibility to freshmen, and its explicit aim not to cover everything. It contains a 56-page snapshot overview followed by 25 articles on particular topics, ideal jumping-off points for student presentations and/or research projects. The articles are clearly written, not intimidating yet accurate and sensitive to the current state of the art in the field. The references to further reading are useful and reliable sources.
After 13 years of frustration, I may finally have found a book that works with my course. Highly recommended!
- This book is a resource that all high school teachers should have. It begins with a relatively short (about 60 pages) history of mathematics and then diverges into a series of indepth explorations of particular mathematical topics.
The history section at the beginning has many small tidbits which will enhance the learning experience. The indepth explorations, which range from Pythagorus to geometry, will nicely enhance your lesson plans. Most of them can serve as the theme that particular lessons can be built around. I am currently working on my practicum at a local highschool and I am using the book regularly.
- As students struggle through their mathematics lessons, it is sometimes helpful for them to understand that the creators of their torment often struggled as well. Furthermore, when we present the polished mathematics of calculus, linear algebra and so forth, educators often forget the long historical road that led to the material that we handle so well. In this excellent book covering the history of mathematics, the authors demonstrate a competency of exposition and a focus on the key points that students and teachers can both appreciate.
It begins with a short and rapid recapitulation of mathematics from the first primitive scratches in the dust to the role of computers in solving problems. After this whirlwind beginning, you are subjected to twenty-five short essays, each about a specific point in mathematical history. By point, I don't mean in time, rather a point as in a position in a discussion. These essays are very well written and each would be excellent fodder for a one-hour class lecture or presentation. Questions for discussion and material for projects are included with each of the short essays. Topics covered in the essays include: the development of the zero, the story of pi, writing fractions, negative numbers, the development of coordinate geometry, complex numbers, Non-Euclidean geometry, probability theory and Boolean algebra. This is by far the best book I have seen for courses in the history of mathematics. With the essays, problems and ideas for projects, all an instructor needs to do is read, discuss and enjoy. If your interest is in learning a bit more about the history of mathematics, it will also serve you well in that capacity.Published in the recreational mathematics e-mail newsletter, reprinted with permission.
- For math teachers at the high school or college level, or anyone else interested in math, this is an ideal introduction to the history of math. Start with the 55-page overview. Then read any or all of the articles that follow, on a variety of topics such as negative numbers, pi, quadratic equations, the Pythagorean theorem, the history of probability theory, and infinity, all around five pages each. Once you're finished with that, there's an extensive bibliography with plenty of suggestions for further reading on the topics that have piqued your interest.
Throughout, the authors have striven for (and succeeded at attaining) readability, accessibility, and historical accuracy. The result is a book that scores high marks for being both interesting and informative.
- I came across this book because a friend of mine uses it in a college class for math ed. It's really well written and makes the material accessible for people whose math background isn't necessarily very strong. I bet it could even be used for high school students. The exercises and projects are really good, too.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by Stephen M. Stigler. By Belknap Press.
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5 comments about The History of Statistics: The Measurement of Uncertainty before 1900.
- This book is THE definitive work on the early development of statistics. Obviously written by a man in love with his subject. Bernoulli, de Moivre, Bayes, Laplace, Gauss, Quetelet, Lexis, Galton, Edgeworth and Pearson all but come alive. I particularly enjoyed the reproductions of first sources included that you would otherwise have to travel to Paris to see.
- 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.
- 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 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.
- 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
- 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.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by Alexander J. Hahn. By Key College.
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5 comments about Basic Calculus: From Archimedes to Newton to its Role in Science.
- If you are deeply curious about the amazing ability of mathematics to define, describe and predict the physical world and its behavior (incl. the solar system) you will be thrilled with this book. It concentrates on the essence of the matter, basic calculus, and includes real-world applications set within the context of some of history's most important scientific questions.
The author clearly demonstrates that he not only possesses a great curiosity, fluency, and appreciation for the subject but also thrives on imparting these things to others. He has provided a great deal of supplementary information on his web site including a detailed description of the contents, scope and focus of the book. The Solution Manuals ARE available from the author simply by e-mailing him at: hahn.1@nd.edu Most calculus books make some compromise in presenting the material. In the case of a thoroughly rigorous text, that compromise most often means sacrificing historical context, intuitive understanding, and real-world application (even though the book may be "exercise-rich" with contrived examples). Basic Calculus successfully navigates a difficult (and different) course, focusing on these commonly sacrificed areas and effectively presenting the pearls of calculus knowledge without delving too deeply into eye-glazing minutiae. In lucid and interesting style, it accomplishes exactly what it sets out to do - it imparts the essence of the matter, in context.
- This splendid book aims to develop calculus from within its rich historical context and to demonstrate its power across a range of disciplines. The author succeeds admirably. Two hundred pages devoted to key ideas in the history of mathematics and science lead smoothly into calculus as we know it today. The remaining three hundred plus pages cover the usual topics, but with attention given to an extraordinary spread of interesting problems in science and business. The explanations of concepts and notation are as lucid as any I have encountered in a basic calculus book.
Because one of the distinguishing features of Basic Calculus from Archimedes to Newton to its Role in Science is its historical dimension, something should be said about the criticism of one reviewer that the book oversimplifies the history by using modern notation. Yes, Hahn does tidy things up. (Very nicely, I might add.) But what else can anyone really do? As Hahn notes, Leibniz's cryptic first work on calculus - Nova methodus pro maximis et minimis, itemque tangentibus...calculi genus - bewildered even his friends, the brothers Bernoulli. These famous mathematicians found Leibniz's article "an enigma rather than an explication." Hahn could try to unriddle the Nova methodus for us, explaining in detail all the fuzzy concepts and strange notation that baffled the Bernoullis. But that hardly seems the thing to do in a basic calculus book. Better to do just what Hahn does - seize on the essential ideas and use everything now at a mathematician's command to bring them into a clear light. Hahn has an excellent sense of just how far to go. The result is a truly extraordinary book that will amply reward readers looking for something special.
- How can we say that introductory courses in calculus at universities are meaningful if the students are never involved in math as professionals? What motivation can we offer them for studying it? This textbook, by Alexander J. Hahn, provides an outstanding answer to the question backed up by the author's precious teaching experience at the University of Notre Dame.
After reading the text, the reader will start to see calculus as a gift by our ancestors that helps us to analyze practical daily problems: calculus as a culture to be passed on to the next generation. Firstly, as the author says, "this text could as well have the title The Story of Calculus." As we read it, we find ourselves reliving history with the great persons like Archimedes, Descartes, Leibniz and Newton. We feel the activity and wisdom of the characters close-up, and we even experience their joys and sorrows as if they were our own. In a way, this book is a historical novel. It shows what calculus looks like as a critical tool that has helped to clear up the mysteries of the universe. Secondly, "the purpose of this text is to demonstrate its broad and formidable informative power." As the author explains, calculus enables us to designing telescopes, to read nuclear clocks, to design suspension bridges, and to understand the interior ballistics of rifles, the rocket equation, gravity, and the expanding universe. Economic subjects, such as banking, CPI, market mechanisms, cost analysis are also covered with full explanations. Books with such range and depth are rare indeed. It is easy to understand why the author received an award for teaching excellence. Of course, "the emphasis is always on the careful development of the mathematics and information that it provides", and most of the topics of first-year calculus courses (including differential equations) are covered (but partial differentials and double/triple integrals are not). The exercise section of each chapter contains advanced explanations of historical, scientific, and mathematical topics, and is organically integrated with the text. The total number of the problems in all the 15 chapters is close to 700. With its many figures and illustrations, as well as full derivations of the equations, this text is also suitable as a supplementary or a self-study manual. I strongly recommend Basic Calculus to those who have doubts about "the usual math training" which sometimes makes us feel like machines (not humans), as a rare and engaging view of mathematics from a different angle. I have found the contents of Hahn's textbook ideal for my students in general physics and calculus courses at Hosei University, Tokyo, and I am now completing a translation of this book into Japanese in collaboration with my colleague Professor Ichimura.
- What this book is not is a traditional calculus text. It covers a lot of traditional topics, but not in a familiar way. It is not terribly rigorous, nor does it need to be. It is designed to fill the first two semesters of calculus. There are a LOT of books that do this in the traditional way, that is they scare the life out of the student :-). It is my belief that this book will take a lot of the mystery out of calculus, since it develops the subject in the context of applications. I also think that most students will find the approach engaging. There are plenty of practice problems at the ends of the chapters, and some are quite challenging.
The focus of this book is not to present calculus as a theory, a thing which most students are simply not prepared for at this level. Rather it is to present calculus as the pragmatic development of methods to solve certain classes of problems. In this regard it does a fantastic job. Along the way the students's algebraic, geometric, and trigonometric skills are all tested and firmed up. The notion of the limit, such a mystery to most freshmen (and, truth-be-told, to many upper-level undergrads) is given a strong intuitive thrust right from the beginning. If you want more problems, get the Schaum's outline book and read them side-by-side.
- Basic Calculus: From Archimedes to Newton to Its Role in Science
is a beautifully done text. It is very clearly written and logically organized, tracing the development of calculus with many interesting examples from the physical world and man's quest to understand the physical world. The text is concise and so readily understood as to be elegant. Finally, all of the solutions to the exercises are given at Professor Hahn's internet site. Its address is www.nd.edu/~hahn/ One way to remember the website is that the letters "nd" are for Notre Dame, where Dr. Hahn teaches.
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Posted in History-Mathematics (Friday, September 5, 2008)
Written by Saul Stahl. By Wiley-Interscience.
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No comments about Real Analysis: A Historical Approach.
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