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| 21. Euler : The Master of Us All (Dolciani Mathematical Expositions) | |
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our price: $33.95 (price subject to change: see help) Asin: 0883853280 Catlog: Book (1999-01-01) Publisher: The Mathematical Association of America Sales Rank: 93566 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description Reviews (11)
I hope Prof. Dunham will decide to write a sequel, and/or tackle the work of other prolific mathematicians, like the Indian Srinivasa Ramanujan, another one of my heroes. This is the third book by Prof. Dunham I've read. I have enjoyed them all and keep them handy to lift my spirits when I'm down -they're that much fun. I wish I'd had him as a teacher in college, and I envy his students at Muhlendorf. I just hope they appreciate how lucky they are!
The style in this book is both unusual and clever. Each of the eight chapters covers a different branch of mathematics and each begins with a prologue, then follows with some of Euler's contributions, and finishes with an epilogue. The prologues present the history of mathematics up to Euler's time, so the reader gets a feel of what this great mathematician had to work with. And the epilogues tell where we have come since Euler. This book is full of equations and expects some work (but not much mathematical background) from the reader. If you like mathematics or ever wondered how some of the great discoveries in this field were derived, do yourself a favor and buy, then carefully read, this wonderful book.
The book is not suitable for people who want to learn more about the person Euler, but do not have a math background, because 75% of the book is about real math (equations). So if you don't enjoy reading equations, do not buy the book. Summary: as enjoyable as the other Dunham books, although a bit more expensive (but still worth the money).
This book in many ways resembles Dunham's Journey Through Genius. As in that book, Dunham has selected 15 or so theorems to present in detail, and he makes an effort to keep the proofs similar in spirit to the original proofs. Although the proofs are complete and the book is full of equations, they are accessible to anyone with a high school level of mathematics education. But in addition to the proofs, Dunham also provides historical context, as well as commentary on how later mathematicians used and improved upon Euler's work. For example, we learn that Euler began to loose the sight in his right eye at the age of 32, and that despite his virtual blindness by the age of 65, he continued his prolific rate of output until his death at age 84. The book's title is taken from a quote by Laplace, who said, ``Read Euler, read Euler. He is the master of us all.'' Indeed, if you have any interest in mathematics, you will almost certainly find yourself in complete agreement with Laplace's sentiments by the time you finish reading this wonderful book. ...
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| 22. The Autobiography of Benjamin Franklin (Dover Thrift Editions) by Benjamin Franklin | |
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our price: $3.99 (price subject to change: see help) Asin: 0486290735 Catlog: Book (1996-05-01) Publisher: Dover Publications Sales Rank: 6150 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description Reviews (40)
As a serious reader, I was delighted in the way that Franklin is obsessed with the reading habits of other people. Over and over in the course of his memoir, he remarks that such and such a person was fond of reading, or owned a large number of books, or was a poet or author. Clearly, it is one of the qualities he most admires in others, and one of the qualities in a person that makes him want to know a person. He finds other readers to be kindred souls. If one is familiar with the Pragmatists, one finds many pragmatist tendencies in Franklin's thought. He is concerned less with ideals than with ideas that work and are functional. For instance, at one point he implies that while his own beliefs lean more towards the deistical, he sees formal religion as playing an important role in life and society, and he goes out of his way to never criticize the faith of another person. His pragmatism comes out also in list of the virtues, which is one of the more famous and striking parts of his book. As is well known, he compiled a list of 13 virtues, which he felt summed up all the virtues taught by all philosophers and religions. But they are practical, not abstract virtues. He states that he wanted to articulate virtues that possessed simple and not complex ideas. Why? The simpler the idea, the easier to apply. And in formulating his list of virtues, he is more concerned with the manner in which these virtues can be actualized in one's life. Franklin has utterly no interest in abstract morality. One of Franklin's virtues is humility, and his humility comes out in the form of his book. His narrative is exceedingly informal, not merely in the first part, which was ostensibly addressed to his son, but in the later sections (the autobiography was composed upon four separate occasions). The informal nature of the book displays Franklin's intended humility, and for Franklin, seeming to be so is nearly as important as actually being so. For part of the function of the virtues in an individual is not merely to make that particular person virtuous, but to function as an example to others. This notion of his being an example to other people is one of the major themes in his book. His life, he believes, is an exemplary one. And he believes that by sharing the details of his own life, he can serves as a template for other lives. One striking aspect of his book is what one could almost call Secular Puritanism. Although Franklin was hardly a prude, he was nonetheless very much a child of the Puritans. This is not displayed merely in his promotion of the virtues, but in his abstaining from excessiveness in eating, drinking, conversation, or whatever. Franklin is intensely concerned with self-governance. I think anyone not having read this before will be surprised at how readable and enjoyable this is. I think also one can only regret that Franklin was not able to write about the entirety of his life. He was a remarkable man with a remarkable story to tell.
Franklin did not have an easy life as the tenth son of a candle maker whose education ended at the age of ten. But by hard work and careful planning he was able to retire from business at the age of forty-two and devote his time to science and politics. He was sent to England in 1764 to petition the King to end the proprietary government of the colony. Soon after the Revolution began he was sent to France to negotiate an alliance with Louis XVI. He was a member of the committee that drafted the Declaration of Independence. It is difficult to image anyone not coming away richer from reading this book.
Written in several pieces, it takes his life just past his electrical experiments, ending with his ambassadorial trip to London in 1757 on behalf of the Pennsylvania Assembly to argue that the Proprietors (the descendants of William Penn) should accept a tax to fund the raising of a militia. Ben's early life story is familiar to all, coming penniless from Boston to Philadelphia, etc. particularly these days when new Franklin biographies seem to appear almost monthly. It is an interesting book, particularly because it was written by Franklin himself. But the breathless praise that is everywhere showered upon it seems a bit over done. First of all, it's incomplete, and secondly, it's not nearly as witty as Poor Richard.
Franklin recounts his family's modest life in England and the circumstances that brought them to Boston. He was among the youngest of a very large family, ultimately finding his way to Philadelphia to find work as a printer when an apprenticeship with an older brother turned sour. We always think of Franklin as being a slightly older statesman among the Founding Fathers, when in fact he was a full generation older than Washington or Jefferson. Unlike popular perception, he was an athletic and vibrant youth, who rescued a drowning Dutch companion and taught swimming to children of London's elite. Philadelphia in the 1720's and 1730's was a small town, never sure if it would really take off as a settlement. Franklin quickly befriended key politicians who felt Philadelphia had grown sufficiently to have a world-class print shop. He played a key role in the town's development, leading civic groups in establishing libraries, fire companies, meeting halls, and street cleaning services. Of course, he was also the consummate politician, serving in office, and networking his way to his first fortune by publishing government documents and printing the first paper currency. He also had a knack for working with the several important religious sects of that time and place, especially the pacifist Quakers, even though Franklin was a deist. Franklin was a clever businessman. In today's lexicon, he effectively franchised across the colonies his concept of the publisher/printer who would provide both the content and the ink on paper. By age 30, he had set up his business affairs so that his printing businesses in several colonies were operated by partners and he received a share of the profits, allowing him to pursue other interests. The autobiography is unfinished, so we don't hear his account of his pursuits of electricity, which made him as famous and well-known as Bill Gates is today, nor his thought on the Revolution. Franklin did play a key role in establishing logistical support to the British during their fight with the French in the New World. At that time and during his years in Europe, he was generally perceived as a Tory supporter. Read this book to learn how Franklin devoted himself to self-improvement by establishing clubs, lending libraries, a sober lifestyle allowing time for study, and his methods for measuring his personal performance against metrics he had established for a proper lifestyle. One will also gather a new appreciation for the fullness, utility, and richness of the English language when put on paper by a master.
Without the insight from Issacson, or, I suspect, from any decent biography of Franklin, the autobiography is disjointed, as he wrote different sections at different times of his life, and some time periods are eliminated completely. And it seems to have multiple personalities, struggling between the subjects of self-help, biography, history and simple meanderings and ruminations of an old man. As a companion book - 5 stars; as a standalone - 2-3 stars ... Read more | |
| 23. The Map That Changed the World : William Smith and the Birth of Modern Geology by Simon Winchester | |
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our price: $10.46 (price subject to change: see help) Asin: 0060931809 Catlog: Book (2002-08-01) Publisher: Perennial Sales Rank: 3241 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description In 1793, a canal digger named William Smith made a startling discovery. He found that by tracing the placement of fossils, which he uncovered in his excavations, one could follow layers of rocks as they dipped and rose and fell -- clear across England and, indeed, clear across the world -- making it possible, for the first time ever, to draw a chart of the hidden underside of the earth. Determined to expose what he realized was the landscape's secret fourth dimension, Smith spent twenty-two years piecing together the fragments of this unseen universe to create an epochal and remarkably beautiful hand-painted map. But instead of receiving accolades and honors, he ended up in debtors' prison, the victim of plagiarism, and virtually homeless for ten years more. Finally, in 1831, this quiet genius -- now known as the father of modern geology -- received the Geological Society of London's highest award and King William IV offered him a lifetime pension. The Map That Changed the World is a very human tale of endurance and achievement, of one man's dedication in the face of ruin. With a keen eye and thoughtful detail, Simon Winchester unfolds the poignant sacrifice behind this world-changing discovery. Reviews (76)
Smith also had an interesting personal history in that his great efforts for science were so unremunerative that he landed for some eleven weeks at the age of fifty in one of London's great debtors' prisons. Winchester makes much of this great irony in his book, that a monumental figure should be so ill-treated and so long unrespected during his lifetime. For all Smith's merits as a subject, however, Winchester's narrative is a bit of a slog. His emphasis is very often on the science of geology rather than the personality of Smith. This is reasonable enough given the subject matter of the book, but I, at least, frequently found the author's discussion difficult to follow. Winchester may, as a one-time student of geology at Oxford, have had too high an opinion of his layman readers' capacities. (Or I, of course, may not have been the proper audience for the book.) For those who are not geologically inclined, there may be more discussion of strata, however, than is palatable: "Below the 300 feet of chalk, Smith declaimed before the others, were first 70 feet of sand. Then 30 feet of clay. Then 30 more feet of clay and stone. And 15 feet of clay. Then 10 feet of the first of named rocks, forest marble. And 60 feet of freestone." And so on. Winchester's narrative does become more interesting toward the book's end, when Smith has, finally, published his map and he is imprisoned for debt--the great dramatic moment toward which the book has been leading. But Smith's stay in the King's Bench Prison is itself anticlimactic, because while Winchester alludes to its "horrors" earlier on, he finally describes debtors' prison as a sort of country club, where the indebted middle-class pass their time playing cards or bowling and drinking beer. Trying and embittering it may have been to be locked away while his possessions were riffled through and sold off, but it was evidently not horrific. Winchester's writing is at its most charming--and he does write charmingly--in the most personal section of the book, when he tells the story of his discovery at the age of six of an ammonite fossil. He and his fellow convent boys were led by the sisters of the Blessed Order of the Visitation on a miles-long walk to the sea, an expedition they undertook once a week. Winchester's account of the boys' riotous plunge into the sea shows just how nicely he can turn a phrase: "Up here there always seemed to be a cool onshore breeze blowing up and over the summit. It was tangy with salt and seaweed, and the way it cooled the perspiration was so blessed a feeling that we would race downhill into it with wing-wide arms, and it would muss our hair and tear at our uniform caps, and we would fly down toward the beach and to the surging Channel waves that chewed back and forth across the pebbles and the sand. "I seem to remember that by this point in the weekly expedition the dozen or so of us--all called by numbers, since the convent's peculiar regime forbade the use of names; I was simply 46--were well beyond caring what the nuns might think: The ocean was by now far too magnetic a temptation. Once in a while we might glance back at them as they stood, black and hooded like carrion crows, fingering their rosaries and muttering prayers or imprecations--but if they disapproved of us tearing off our gray uniforms and plunging headlong into the surf, so what? This was summer, here was the sea, and we were schoolboys--a combination of forces that even these storm troopers of the Blessed Visitation could not overwhelm." Perhaps Winchester will one day expand on this passage with further autobiographical fare.
The problem may be that Winchester is too good a writer, or too accurate a biographer, to put down any details of which he's not 100% certain. Add to that the fact that the source materials focus on William Smith's professional work almost to the exclusion of any personal detail, and you have what should be a compelling personal journey that winds up reading more like a geology text in too many chapters. Smith's place in history was assured by his 1815 publication of a map of England showing the geological strata and graphically demonstrating his theories that one could tell the age of the rocks from examining the fossils found within. This was radical stuff in 1815, and the work that led to this map took Smith some 30 years. Along the way he picked up a wife, who was possibly crazy, and adopted a nephew, who became his assistant, had business and financial troubles, which led to his being held in debtor's prison, and had a long running class-based feud with England's scientific establishment, which led to his works not being properly recognized for many years after their publication. Unfortunately, only the last aspect of Smith's life is covered in any detail because that's all he wrote about in his own journal, or is covered in other source material. About the wife we're told that she was a burden to him, often sick, probably crazy, and possibly even a nymphomaniac. We're told all that, but we're never given examples, or are told how Smith felt about her. Did he love her anyway? Did they ever try to have children of their own? Did she embarrass him publicly? We don't know. About the nephew we're told that Smith took over his care when his sister and brother-in-law died, and that he became his assistant, but we're told nothing of their personal relationship. Was their's a close, familial relationship, or only one of master or mentor to apprentice? We don't know. And such is the frustration with the book (mine, at least). What's left is endless descriptions of the various layers of the earth's crust, and how Smith could tell if an outcropping belonged to the Jurassic or Cretaceous periods. I picked up this book because I loved Winchester's previous "The Professor and the Madman" so much. That's a book that's rich in personal detail, and is as important and fascinating in the descriptions of the lives of the subjects as it is in the descriptions of their professional works. "The Map that Changed the World" is likely stunning for students of geology, but may bore beyond belief the reader who doesn't care or know about item one of earth science. So - In the end, I suppose a mixed review. If you get this joke (and think it's funny): "Subduction leads to orogeny" - or, if you have a bumper sticker that says "Stop Plate Tectonics" - Then this is a five star book that you will love every page of. If you don't even care to look up any of those words, then this is a three star book you should avoid. Which averages out to four stars: An occasionally fascinating and well-written book that is often dry and disappointing.
Winchester is a glorious writer in his twin histories of the Oxford English Dictionary. But here his subject is just too obscure and trivial, and try as he might, Winchester can't make it seem interesting.
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| 24. Alfred Tarski : Life and Logic by Anita Burdman Feferman, Solomon Feferman | |
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our price: $23.10 (price subject to change: see help) Asin: 0521802407 Catlog: Book (2004-10-04) Publisher: Cambridge University Press Sales Rank: 29398 US | Canada | United Kingdom | Germany | France | Japan |
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| 25. Alfred C. Kinsey : A Public/Private Life by James H. Jones | |
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(price subject to change: see help) Asin: 0393040860 Catlog: Book (1997-11-01) Publisher: W W Norton & Co Inc Sales Rank: 136462 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Amazon.com Reviews (7)
The Kinsey Institute revealed that Kinsey used pedophiles to document orgasms in hundreds of boys and girls as young a 5 months old. One of his favorites reported abusing at least 800 children. These Kinsey reclassified prostitutes as married woman when he could not find enough woman willing to submit to his questionnaire. He used child molesters, rapists, homosexuals, prostitutes,sadists, masochists, etc. to represent the average American. Kinsey would not allow anyone, even a janitor to work for him unless they submitted to a sexual history questionnaire. When applicants did not agree that adultery, pre-marital sex, and sex with animals was normal, he told them they would not fit in with his staff. The Rockafeller Foundation's records reveal that Kinsey's associates were unqualified. Not only were the histories unscientifically administered but the statistics were proven unreliable and inacurate. If you want to know the full truth of the Kinsey deception -- buy Reisman's well documented book.
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| 26. Dark Hero Of The Information Age: In Search of Norbert Wiener The Father of Cybernetics by Flo Conway, Jim Siegelman | |
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our price: $18.15 (price subject to change: see help) Asin: 0738203688 Catlog: Book (2004-12-14) Publisher: Basic Books Sales Rank: 19733 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description Reviews (5)
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| 27. Strange Angel : The Otherworldly Life of Rocket Scientist John Whiteside Parsons by George Pendle | |
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our price: $16.50 (price subject to change: see help) Asin: 015100997X Catlog: Book (2005-01-18) Publisher: Harcourt Sales Rank: 398778 US | Canada | United Kingdom | Germany | France | Japan |
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| 28. Naturalist by Edward O. Wilson | |
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our price: $10.17 (price subject to change: see help) Asin: 0446671991 Catlog: Book (1995-12-01) Publisher: Warner Books Sales Rank: 103118 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Amazon.com Reviews (15)
And like the good evolutionary biologist that he is, Wilson's life, its unpredictable twists and turns, parallel the randomness of natural selection. A bumpy family life meant that he moved frequently, and that he was often alone: in response, he took refuge in the wild places and the natural history institutions of the places where he found himself, thus focussing and increasing his love of nature and the sciences. An accident of early life caused him to become very nearsighted, and so he turned to the study of the ants: and on this subject he is a recognized authority. Even his will and his discipline were not characteristics he himself sought out or developed; rather, they were traits which were instilled in him early on. Random chance gave him the tools by which he would become a great naturalist. Wilson appears to be a man who knows not the word "problem," only "opportunity." The means by which he took advantage of his nearsightedness I have mentioned; he likewise learned to work with, instead of against, the unconscious muscle tremors which make dissection of very small objects difficult. Perhaps the greatest testimony to his ability to turn a problem into an opportunity is in this line: "Without a trace of irony I can say I have been blessed with brilliant enemies [...] I owe them a great debt, because they redoubled my energies and drove me in new directions." These words could be merely self-serving justifications for failure, if Wilson had not achieved in the eyes of others, or if he had not accomplished what he set out to do, which was to be as great a naturalist as he could be: that he did both reveals these sentiments to be the mature recognition of his hard work and dedication to the struggle in the face of adversity coming at him from unexpected directions. I must say that when I came to this book, I did not accept Wilson's sociobiology, and I still do not see that it is supported by solid proof. It is all the more amazing to me, then, that I am thoroughly moved by this account of his life, in its discovery of the natural world and in the author's sense of wonder at life around him. The lauds which Wilson has received, I suspect, are nothing compared to the joy he gains through his work and his studies. I don't know what Wilson reads in his spare time, but he has written a text with echoes of Wordsworth and Whitman: his life in nature is no mere analysis and dissection, but a glorious presentation of his wonder before the natural world. Wilson paraphrases Wordsworth's declaration that "the child is the father of the man" as "Most children have a bug period. I never outgrew mine." Wilson has followed his bliss into his adult life, and it has brought him fame and joy. The ultimate paragraphs of his book reveal that though he would change the focus of his studies, he would in no wise vary his field of study, nor the course of his life: he would be then, as he is now, a man who followed the dictates of his heart, who took the random events of his childhood and shaped them into a life that brought him great pleasure. It is fitting, then, that this book should do the same for the reader: out of his experiences, Wilson has created one of the most entertaining and moving autobiographies I have ever read. ... Read more | |
| 29. They Made America: Two Centuries of Innovators from the Steam Engine to the Search Engine by Harold Evans | |
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our price: $24.00 (price subject to change: see help) Asin: 0316277665 Catlog: Book (2004-10-12) Publisher: Little, Brown Sales Rank: 58 US | Canada | United Kingdom | Germany | France | Japan |
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| 30. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire | |
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our price: $18.45 (price subject to change: see help) Asin: 0309085497 Catlog: Book (2003-04-23) Publisher: Joseph Henry Press Sales Rank: 8375 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Amazon.com Reviews (38)
My math bakground is limited to 2 semesters of calculus 20 years ago and I haven't used it since. For me, John Derbyshire's approach was both refreshing and entertaining. If you've got even the faintest interest in math, you will find this book rewarding.
I found it very entertaining to read about the lives of the great mathematicians involved in developing the prime number theory and furthering the study of the Riemann Hypothesis. Mathematics is littered with such interesting characters that even a liberal arts major can enjoy these expository stories of their lives. The only downside to this whole book is that he takes too much time for the non-math inclined readers to get 'caught up' with their basic skills before he jumps to anything interesting. If you have a background that is strong through calculus, then you could probably avoid reading all the math-based chapters up through the end of the prime number theory section of the book, and you most likely woud not have missed a thing.
My formal math education ended after a standard introductory calculus course as an undergrad. However, I have always been, and remain, extremely interested in math -- a math aficianado if you will. As such, I've self-taught myself a lot of math -- including a lot of very advanced math -- over the past 40 years; ergo, my reading of a great many math books. And without doubt, Derbyshire's book is the finest math book I've yet to read. I suspect Derbyshire started with the hypothesis that his readers are not familiar (or only familiar in a passing sense) with high-level, advanced math, and perhaps might even suffer from math anxiety. Any such readers, however, should have absolutely no fears. Derbyshire's exposition is superb. He clearly defines everything the reader needs to know to grasp AND understand fully the more advanced parts of the book. The book is clearly well designed to convey the information he wants or needs of convey and masterfully explains what would otherwise be quite difficult to understand. Without any doubt this is by far the best book on any advanced and complicated subject -- the best book on ANY math subject (including a book on something as simple as how to add one and one) -- I have ever read. Without sacrificing the complexity of the subject, Derbyshire has written his book in a very readable and interesting manner. And he does all this while making the subject so interesting you can hardly wait for someone to finally prove Riemann's Hypothesis and Riemann's zeta function so we can read Derbyshire's account of that landmark event in the history of mathematics.
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| 31. Making the Mummies Dance : Inside The Metropolitan Museum Of Art by Thomas Hoving | |
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our price: $21.95 (price subject to change: see help) Asin: 0671880756 Catlog: Book (1994-02-15) Publisher: Touchstone Sales Rank: 125827 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description Reviews (6)
Hoving has a steam-roller personality, the energy of nuclear fission and no small amount of self-confidence. His educational background -- Princeton and an archeological expedition or two in Europe -- isn't as impressive as you'd expect, but he makes up any shortcomings with old-fashioned chutzpah. After some experience in minor jobs and a city job with the Parks Department, he's told he may be selected as director of the Metropolitan so he looks the place over and makes some notes: "The museum needs reform. Sprucing up. Dynamics. Electricity. The place is moribund. Gray. It's dying. The morale of staff is low. The energy seems to have vanished. You've been missing all the fine exhibits...." This book shows how MOMA gets from where it was then to what it is now -- the politics, infighting, backbiting, sneaking, smuggling and downright stealing it takes to make a museum one of the finest in the world. It's also a fairly realistic look at the glittering personalities and the haute monde of the New York City of a few decades ago. This is a rousing tale that should hold the interest of any reader, art lover or no. Never mind that Hoving doesn't hesitate to toot his own horn. This is, after all, his book. Even taking the stories with a massive grain of salt, they're always riveting and vastly amusing. No one will ever say of Thomas Hoving that he has no opinion on the people and the issues of the art world or that he hesitates to express them. I can't imagine anyone not being fascinated by this marvelous picture of the fabulous and often sham world of art museums and the people who support them and run them.
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| 32. The Man Behind the Microchip: Robert Noyce and the Invention of Silicon Valley by Leslie Berlin | |
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our price: $19.80 (price subject to change: see help) Asin: 0195163435 Catlog: Book (2005-06-01) Publisher: Oxford University Press Sales Rank: 23694 US | Canada | United Kingdom | Germany | France | Japan |
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| 33. The Essential John Nash by John Nash | |
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our price: $34.95 (price subject to change: see help) Asin: 0691095272 Catlog: Book (2001-11-19) Publisher: Princeton University Press Sales Rank: 55481 Average Customer Review: US | Canada | United Kingdom | Germany | France | Japan |
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Book Description From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness. In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography. The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from. Reviews (12)
This book is largely a collection of Dr. Nash's own writings, each a significant contribution to mathematics or economics. Nash's papers are thoughtfully introduced and explained - thankfully so given the complexity of Nash's writings. Also included is Nash's own touching and revealing autobiography. The result is a compelling glimpse inside the thought processes of a genius - a beautiful mind indeed. Thanks to Harold Kuhn and Sylvia Nasar for pulling this wonderful collection together.
It is always easy to dismiss ideas as trivial after they have been discovered and have been put into print. This is apparently what John von Neumann did after discussing with Nash his ideas on noncooperative games, dismissing his ideas as a mere "fixed point theorem". At the time of course, the only game-theoretic ideas that had any influence were those of von Neumann and his collaborator, the Princeton economist Oskar Morgenstern. The rejection of ideas by those whose who hold different ones is not uncommon in science and mathematics, and, from von Neumann's point of view at the time, he did not have the advantage that we do of examining the impact that Nash's ideas would have on economics and many other fields of endeavor. Therefore, von Neumann was somewhat justified, although not by a large measure, in dismissing what Nash was proposing. Nash's thesis was relatively short compared to the size on the average of Phd theses, but it has been applied to many areas, a lot of these listed in this book, and others that are not, such as QoS provisioning in telecommunication and packet networks. The thesis is very readable, and employs a few ideas from algebraic topology, such as the Brouwer fixed point theorem. The paper on real algebraic manifolds though is more formidable, and will require a solid background in differential geometry and algebraic geometry. However, from a modern point of view the paper is very readable, and is far from the sheaf and scheme-theoretic points of view that now dominate algebraic geometry. It is interesting that Nash was able to prove what he did with the concepts he used. The result could be characterized loosely as a representation theory employing algebraic analytic functions. These functions are defined on a closed analytic manifold and serve as well-behaved imbedding functions for the manifold, which is itself analytic and closed. These manifolds have been called 'Nash manifolds' in the literature, and have been studied extensively by a number of mathematicians. I first heard about John Nash by taking a course in algebraic topology and characteristic classes in graduate school. The instructor was discussing the imbedding problem for Riemannian manifolds, and mentioned that Nash was responsible for one of the major results in this area. His contribution is included in this book, and is the longest chapter therein. Here again, the language and flow of Nash's proof is very understandable. This is another example of the difference in the way mathematicians wrote back then versus the way they do now. Nash and other mathematicians of his time were more 'wordy' in their presentations, and this makes the reading of their works much more palatable. This is to be contrasted with the concisness and economy of thought expressed in modern papers on mathematics. These papers frequently employ a considerable amount of technical machinery, and thus the underlying conceptual foundations are masked. Nash explains what he is going to do before he does it, and this serves to motivate the constructions that he employs. His presentation is so good that one can read it and not have to ask anyone for assistance in the understanding of it. This is the way all mathematical papers should be written, so as to alleviate any dependence on an 'oral tradition' in mathematical developments. Nash's proof illuminates nicely just what happens to the derivatives of a function when the smoothing operation is applied. The smoothing operator consists of essentially of extending a function to Euclidean n-space, applying a convolution operator to the extended function, and then restricting the result to the given manifold. Nash gives an intuitive picture of this smoothing operator as a frequency filter, passing without attenuation all frequencies below a certain parameter, omitting all frequencies above twice this parameter, and acting as a variable attenuator between these two, resulting in infinitely smooth function of frequency. The next stage of the proof of the imbedding theorem is more tedious, and consists of using the smoothing operator and what Nash calls 'feed-back' to construct a 'perturbation device' in order to study the rate of change of the metric induced by the imbedding. Nash's description of the perturbation process is excellent, again for its clarity in motivating what he is going to do. The feed-back mechanism allows him to get a handle of the error term in the infinitesimal perturbation, isolating the smoother parts first, and handling the more difficult parts later. Nash reduces the perturbation process to a collection of integral equations, and then proves the existenc | |