Book Description
This is the first volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variations in one and several dimensions, and geometric field theory. This material is explained in as simple and concrete a language as possible, in a terminology acceptable to physicists. The text for the second edition has been substantially revised.
Customer Reviews:
Best book to begin differential geometry with .........2004-12-09
Written by prominent mathematicians it is the one of the best books on the topic .
The language of the book is very simple so it is suitable for physics ...
Required background reading..........2004-01-21
..if you want to understand the much of Arnol'd's book on classical mechanics. Written for physicists in language that physicists can follow, the book starts with advanced calculus (geometry of surfaces and curves in 2D and 3D) and provides a readable and informative introduction to Riemannian geometry, including connections defined by structure coefficients of a Lie algebra, all the way through gauge theories. However, the books by Schutz and by Nakahara cover interesting topics not included here, so see them as well.
Customer Reviews:
Written for the physicist in mind.......2001-08-19
This book, written by some of the master expositors of modern mathematics, is an introduction to modern differential geometry with emphasis on concrete examples and concepts, and it is also targeted to a physics audience. Each topic is motivated with examples that help the reader appreciate the essentials of the subject, but rigor is not sacrificed in the book.
In the first chapter the reader gets a taste of differentiable manifolds and Lie groups, the later gving rise to a discussion of Lie algebras by considering, as usual, the tangent space at the identity of the Lie group. Projective space is shown to be a manifold and the transition functions explicitly written down. The authors give a neat example of a Lie group that is not a matrix group. A rather quick introduction to complex manifolds and Riemann surfaces is given, perhaps too quick for the reader requiring more details. Homogeneous and symmetric spaces are also discussed, and the authors plunge right into the theory of vector bundles on manifolds. Thus there is a lot packed into this chapter, and the authors should have considered spreading out the discussion more, as it leaves the reader wanting for more detail.
The authors consider more fundamental questions in smooth manifolds in chapter 3, with partitions of unity used to prove the existence of Riemannian metrics and connections on manifolds. They also prove Stokes formula, and prove the existence of a smooth embedding of any compact manifold into Euclidean space of dimension 2n + 1. Properties of smooth maps, such as the ability to approximate a continuous mapping by a smooth mapping, are also discussed. A proof of Sard's theorem is given, thus enabling the study of singularities of a mapping. The reader does get a taste of Morse theory here also, along with transversality, and thus a look at some elementary notions of differential topology. An interesting discussion is given on how to obtain Morse functions on smooth manifolds by using focal points.
Notions of homotopy are introduced in chapter 3, along with more concepts from differential topology, such as the degree of a map. A very interesting discussion is given on the relation between the Whitney number of a plane closed curve and the degree of the Gauss map. This leads to a proof of the important Gauss-Bonnet theorem. Degree theory is also applied to vector fields and then to an application for differential equations, namely the Poincare-Bendixson theorem. The index theory of vector fields is also shown to lead to the Hopf result on the Euler characteristic of a closed orientable surface and to the Brouwer fixed-point theorem.
Chapter 4 considers the orientability of manifolds, with the authors showing how orientation can be transported along a path, thus giving a non-traditional characterization as to when a connected manifold is orientable, namely if this transport around any closed path preserves the orientation class. More homotopy theory, via the fundamental group, is also discussed, with a few examples being computed and the connection of the fundamental group with orientability. It is shown that the fundamental group of a non-orientable manifold is homomorphic onto the cyclic group of order 2. Fiber bundles with discrete fiber, also known as covering spaces, are also discussed, along with their connections to the theory of Riemann surfaces via branched coverings. The authors show the utility of covering maps in the calculation of the fundamental group, and use this connection to introduce homology groups. A very detailed discussion of the action of the discrete group on the Lobachevskian plane is given.
Absolute and relative homotopy groups are introduced in chapter 5, and many examples are given of their calculation. The idea of a covering homotopy leads to a discussion of fiber spaces. The most interesting discussion in this chapter is the one on Whitehead multiplication, as this is usually not covered in introductory books such as this one, and since it has become important in physics applications. The authors do take a stab at the problem of computing homotopy groups of spheres, and the discussion is a bit unorthodox since it depends on using framed normal bundles.
The theory of smooth fiber bundles is considered in the next chapter. The physicist reader should pay close attention to this chapter is it gives many insights into the homotopy theory of fiber bundles that cannot be found in the usual books on the subject. The discussion of the classification theory of fiber bundles is very dense but worth the time reading. Interestingly, the authors include a discussion of the Picard-Lefschetz formula, as an example of a class of "fiber bundles with singularities". Those interested in the geometry of gauge field theories will appreciate the discussion on the differential geometry of fiber bundles.
Dynamical systems are introduced in chapter 7, first as defined over manifolds, and then in the context of symplectic manifolds via Hamaltonian mechanics. Liouville's theorem is proven, and a few examples are given from relativistic point mechanics. The theory of foliations is also discussed, although the discussion is too brief to be of much use. The authors also consider variational problems, and given its importance in physics, they continue the treatment in the last chapter of the book, giving several examples in general relativity, and in gauge theory via a consideration of the vacuum solutions of the Yang-Mills equation. The physicist reader will appreciate this discussion of the classical theory of gauge fields, as it is good preparation for further reading on instantons and the eventual quantization of gauge fields.
A masterful sequel!.......2000-01-22
Novikov et al's first volume was the defining book on differential geometry (S-V 93). The second volume picks up on the detailed theory of manifolds and topology and other advanced theories of differential geometry, including homotopy groups, Lie algebras and digressing into physical theories as well (eg.Yang-Mills) giving one of the juciest books on the subject - an utter delight!
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Emerson's Fall: A New Interpretation of the Major Essays
Barbara L. Packer
Manufacturer: Continuum Intl Pub Group
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- Gun-Running has Changed but not that Much
- Quality
- Poverty's a crime
- Interesting and worth reading and seeing.
- A deluge of brilliance, wit, political nonsense
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Major Barbara (Penguin Classics)
George Bernard Shaw , and
Elizabeth T. Forter
Manufacturer: Penguin Classics
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ASIN: 0140437908 |
Book Description
In this sparkling comedy, originally staged in 1905, Andrew Undershaft, a millionaire armaments dealer, loves money and despises poverty. His energetic daughter Barbara, however, is a devout major in the Salvation Army. She sees her father as just another soul to be saved. But when the Salvation Army needs funds to keep going, it is Undershaft who saves the day.
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LADY BRITOMART. Charles Lomax's exertions are much more likely to decrease his income than to increase it. Sarah will have to find at least another £800 a year for the next ten years; and even then they will be as poor as church mice. And what about Barbara? I thought Barbara was going to make the most brilliant career of all of you. And what does she do? Joins the Salvation Army; discharges her maid; lives on a pound a week.
Customer Reviews:
Gun-Running has Changed but not that Much.......2006-02-14
"Major Barbara" is a morality tale of a young woman, a Major in the Salvation Army, who finds her work supported by an arms dealer. Surprisingly, the arms dealer in the play, Undershaft, is witty, urbane, generous, industrious, and ruthless. He has some of the same rationalizations for what he does that contemporary arms dealers still use. He does not kill anyone. He does not start wars. He is in business. He creates jobs. If he did not do it, someone else would. Everyone does it, including governments. Poverty is the crime. Industry, including making armaaments, is the cure.
So, not much has changed. The world of the play is a complex web of moral ambiguity, hiding the most murderous of crimes. Or, are they really crimes at all? You be the judge.
This is a play worth reading. But if you are interested in the morals, or lack of them, in gun-running, and don't like reading plays, try "Lord of War," the film with Nicholas Cage.
Quality.......2005-09-30
I'm pleased with the purchase, I got what I expected and for little money. The delivery was timely and the product was in good shape.
Poverty's a crime.......2004-04-29
So says Andrew Undershaft, the extremely wealthy owner of a tremendously successful English armaments business, in George Bernard Shaw's play "Major Barbara." Undershaft, whose self-proclaimed religion is his wealth and his industry, inherited the business from a long line of Andrew Undershafts, each of whom was a foundling adopted by the corresponding previous Andrew Undershaft. This is not to say that the Undershafts don't marry and have families -- the current Andrew Undershaft has married the aristocratic Lady Britomart and has three children by her; he just doesn't let them have anything to do with the family business, preferring to stick to the tradition of bringing in an outsider to perpetuate the Andrew Undershaft dynasty.
Indeed, Undershaft feels that poverty is the primordial crime from which all other crimes -- burglary, murder -- spring, and that it is better to give a poor man a job so he can afford to live rather than spend public money on methods of punishing him should he violate the law in his efforts to afford to live. Undershaft moralizes when he speaks, but in actuality he scoffs at what he considers ordinary Christian morals of the kind professed by his daughter Barbara, who has joined the Salvation Army in her fervid desire to help the poor and has attained the rank of major. She works at a shelter doling out bread and milk to the downtrodden and trying to find work for the unemployed, but her real goal is to bring them to "salvation" by raising them to a higher state of spirituality. When her fiance, a scholar of Greek named Adolphus Cusins, who by a certain twist of logic happens to be his own cousin, reveals himself to be a foundling, Undershaft decides he's found his heir.
Although the play reflects the perspectives that Shaw, as a Socialist, had on the effects of poverty on morality and society, he doesn't seem to take sides with his characters and instead lets them be funny within the context of their respective social classes. His idle rich characters are lovably comical, like the mentally vapid trio of Undershaft's son Stephen (who wouldn't know what to do with his father's armaments business even if he were qualified to inherit it), daughter Sarah, and her fiance Charles Lomax. His impoverished characters -- those who come to the Salvation Army shelter for handouts -- can be honorably industrious like Peter Shirley or pugnacious and troublesome like Bill Walker. If Undershaft, for all his willingness to feed his fortune by manufacturing items that shed the blood of millions, represents the right way to fix poverty and Barbara the wrong way, why is the play named after her? I think it's possibly because her morality is one with which most theatergoers of the day could identify, while Undershaft's is idiosyncratic to say the least.
Interesting and worth reading and seeing........2002-10-04
GBS wrote play with "approaching audiences as citizens capable of thought and prompting them to think imaginatively to some purpose" in mind, as Margery Morgan says. And there are plenty for one to think seriously about in Major Barbara.
The most interesting is his conviction that no money is untainted. That's interesting because it means the donations and public fundings the environmentalists take in come from no less than the evil polluters themselves, perhaps feeling, which GBS rightly agreed, as the Salvation Army would that they "...will take money from the Devil himself sooner than abandon the work of Salvation." But GBS also wrote in the preface that while he is okay to accept tainted money, "He must either share the world's guilt or go to another planet." From what I can gather from the preface and play, GBS believed money is the key to solve all the problems we have, hence his mentioning of Samuel Butler and his "constant sense of the importance of money," and his low opinion of Ruskin and Kroptokin, for whom, "law is consequence of the tendency of human beings to oppress fellow humans; it is reinforced by violence." Kropotkin also "provides evidence from the animal kingdom to prove that species which practices mutual aid multiply faster than others. Opposing all State power, he advocates the abolition of states, and of private property, and the transforming of humankind into a federation of mutual aid communities. According to him, capitalism cannot achieve full productivity, for it amis at maximum profits instead of production for human needs. All persons, including intellectuals, should practice manual labor. Goods should be distributed according to individual needs." (Guy de Mallac, The Widsom of Humankind by Leo Tolstoy.)
If GBS wasn't joking, then the following should be one of the most controversial ideas he raised in the preface to the play. I quote: "It would be far more sensible to put up with their vices...until they give more trouble than they are worth, at which point we should, with many apologies and expressions of sympathy and some generosity in complying with their last wishes, place them in the lethal chamber and get rid of them." Did he really mean that if you are a rapist once, you can be free and "put up with," but if you keep getting drunk (a vice), or slightly more seriously, stealing, you should be beheaded?
A deluge of brilliance, wit, political nonsense.......2001-12-19
Shaw can be absolutely captivating even when he is being an evangelist for political philosophies that the twentieth century has proven to be nothing but vehicles for repression and mass murder (Communism - Shaw approved of Lenin even when the evidence showed him to be pure evil). This play-among his best (if you can see the movie with Rex Harrison, do not miss it)- has such brilliant dialogue and sparkling humor that it is easy to forget that one is being preached to. Shaw thinks human evil is due to socially deprived environments. Ergo, pour money into poor neighborhoods and social evils will vanish. Unfortunately for Shaw's argument, poverty and human evil are two different things entirely and only intersect occasionally and coincidently. The poor can be poor due to lack of opportunity or due to a culture of self-destructiveness (illegitmacy, drug/alcohol use, disdain for values that lead to achievement, disdain for skills that lead to steady employability). It is difficult to sustain an argument that the poor in the USA are so due to a lack of opportunity when recent immigrants have pretty much taken the available opportunities and ran with them, rapidly entering the middle classes within a generation of arriving here. Shaw simply cannot believe that anyone would choose to remain poor. Well, they can and do, when getting ahead means putting in 40+ hours a week, and not loafing all day on a street corner in an inebriated/stoned condition. Accepting that fact would have saved millions of lives that were sacrificed in the last century in the attempt to build a perfect "worker's paradise".
Leaving the silly premise behind the play aside, Shaw has crafted a startling piece of theatre and uses his magisterial command of the English language to amuse, provoke, and amaze the audience.
Book Description
A Financial Road Map for Women
Whether you're single or married, a career woman or a full-time mother, young or mature, your financial future is vitally important to you. Ernst & Young's Financial Planning for Women draws on the experience of the nation's premier tax and financial planners. This accessible guide addresses the unique money issues related to the major events of a woman's life, including:
- Being single
- Getting married or living together
- Caring for children or parents
- Dealing with divorce or widowhood
- Being an entrepreneur
- Planning for retirement
You'll find practical, easy-to-understand explanations of important financial planning concepts; real-life examples of financial success; and personal advice based on the authors' collective experiences. Plus, there are worksheets and checklists, and a handy resource guide to books and Web sites for women.
The authors of Ernst & Young's Financial Planning for Women: (seated left to right) Barbara J. Raasch, Sylvia Pozarnsky, Paula Boyer Kennedy; (standing left to right) Andrea S. Markezin, Elda Di Re, Freida Kavouras.
ERNST & YOUNG LLP's personal financial counseling practice tailors financial strategies for people at all income levels. The firm is the author of the bestselling Ernst & Young Tax Guide as well as a wide array of books on business and money management. Visit the firm's Web site at www.ey.com/pfc.
Customer Reviews:
Manipulation in the name of science..........2004-01-26
Before I read Pygmalion everythin I knew was, that is was connected to the musical 'My fair lady'. So first of all I was scared because musicals arer not the kind of entertainment I prefer. But while reading it the manipulation of a poor an first mentally weak girl in the name of science an in a sadistic and somehow abusing way kept me in suspense to go on reading. And beside that human-despising experiment a little love story evolved to a happy end. To conclude I want to justify the 'just' three stars: I don't like love stories.
Praise for Shaw's Voice.......2002-02-01
Shaw masters satire in Pymalion his play with a double edged sword. A superficial examination of the play reveals it to be a self-rightoues lesson in grammar. But a deeper inspection shows it tobe a toungue in cheek comedy (albeit a critical one) that reveals much about the British society of the time (particularly linguistically speaking). Henry Higgin's unabashed condescending attitude provide many laughs while Eliza's emotion filled responses are also humorous and no less insightful. The prolougue although irritating to most, gives the play a unique voice and the epilogue although considered by many to be a literary fallacy says true to Shaw's style. I have only one complaint about this book that I can rant on about to no end, that fact that he say's English is the language of the Bible. Is English the lanuguage of Crime and Punishment or Metamorphosis because it was translated in English? Please, don't insult us. But aside from that it is a Brilliant play!
The Pygmalion was wonderful, but Major Barbara...?.......2000-02-25
This was, all in all, a charming little book. I loved the Pygmalion and the manipulative male lead, Professor Higgins. Major Barbara, on the other hand, was as boring as could be. The preface? Don't even bother reading. It was absolute boredom, and completely unaffective on the reading of Major Barbara. The Pygmalion, while I did not particularly enjoy the epilogue (I'm a romantic), was very clever and yes, probably the real aspect of how things turn out. So, all being said, read the book! It is a delightful little sample of Shaw's work.
Witty compositions but unable to escape parochialism.......1998-10-09
The worst thing I found was Shaw's ending epilogue after the Pygmalion. He went too far, too deep and too preachy in his imagination of how things were to turn out. His lengthy preface to Major Barbara may well reflect sentiments at the turn of the century, but he never looked at the question "whether he imagined the impoverished becoming like him or him becoming like the impoverished" when he talked idealistically against the tyranny of poverty. He showed no comprehension of basic economics, social evolution nor human nature. Had he lived longer, he might have seen it in the collapse of communism in eastern Europe. That is not to say Shaw was espousing communism, and it can be argued that the communism was an imperfect implementation of a perfect solution. The same then can be said of a lot of other things, including Christianity, the Church, the Salvation Army, nationhood, law enforcement as well as the judiciary. None set out to commit the sins they did. At the end of the day, helping feed a single individual may cause no more harm than helping no individuals but sitting down and espousing fine rhetorics and theories and ideals which lead to establishment of institutions modelled after them which affect thousands instead.
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Bernard Shaw's plays: Major Barbara, Heartbreak House, Saint Joan, Too true to be good; (Norton critical editions)
Bernard Shaw
Manufacturer: Norton
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ASIN: 0393043231 |
Customer Reviews:
A "Heartbreaking" Separation.......2001-12-23
Having read the criticism by another online reviewer that "Saint Joan" is misleading, I wondered if we had read the same play. So I had a look at this book and the problem is obvious: no prefaces! Shaw's plays are meant to be read with his prefaces and they shouldn't be separated. Shaw himself intentionally wrote in that mode, noting at one point, "I would give six of the plays that Shakespeare did write for one of the prefaces he ought to have written." That's a little extreme, but the point is taken, and I believe that the general reasoning is valid. Shaw's complete plays with prefaces run to six volumes or so. Take that kind of route if you can; you'll be well rewarded with edification and entertainment.
Disappointing.......2000-02-18
While Shaw may have been a gifted playwright, his "Saint Joan" did an enormous disservice to the subject: the view it presents of Joan of Arc conflicts with the historical evidence on nearly every point, echoing instead the propaganda of her enemies. In truth, her trial was orchestrated by the English and their clerical allies (and even Shaw admits that the Inquisition overturned the verdict in 1456, shortly after the English were finally driven out of Rouen); nor was Joan a "rebel" except in the minds of her political opponents. By dredging up this fraudulent view of La Pucelle, Shaw's play was among the first popular works to undermine the efforts of countless scholars whose research had brought a more truthful view of the issue to light.
Shaw is hilariously one of the most thoughtful playwrites.......1999-04-05
I think that Shaw is generally misread in this part of the twentieth century. In particular, Too Good to be True, is highly outdated, and therefore highly incomprehensible. That makes it even funnier, and more enjoyable to think about. In every one of these plays, Shaw more or less, in different ways, concludes that the world is coming to an end. The death in the Doctors Dilema, the Dynamite in Major Barbara, The depression and outright declaration that "The world...is falling down, down, into the abyss" in Too Good to be True, and the war and sort of joke of war in Saint Joan, not to mention the portrayal of a Saint, all relate to that dire, but humorous topic. I especially recommend Too Good to be True. Featuring a measles microbe and the Union of Socially Federated States, this is an excellent read.
Shaw: Self-contradicting ýSupermaný
.......1996-09-06
A bundle of baffling contradictions, G. B. Shaw is a dogmatist's nightmare. Anyone expecting to mimic this sometimes-feminist, sometimes-philosophical playwright has bought one ticket to a wild ride.
"The Doctor's Dilemma," "Major Barbara" and "Heartbreak House" are good examples -- particularly when peppered by his own commentary, appendices and introductions. Without discussing the literary merits of his work - each play is a good read, a thrilling suspense and a small surprise - Shaw's best asset is not his politics, but his sense of humor.
Example:
"That any sane nation, having observed that you could provide for the supply of bread by giving bakers a pecuniary interest in baking for you, should go on to give a surgeon a pecuniary interest in cutting off your leg, is enough to make one despair of political humanity." [from the introduction to "The Doctor's Dilemma"]
Sure, Shaw thinks he's God's gift to philosophy. And believe you me, he's no Nietzsche. However, it's a lot better bet that he'll make you laugh.
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