These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory.
The volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view - some geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry.
" notation, vector space, and Boolean Algebra. Fortunately for me, I have a fairly extensive math education, and self-studied Functional Analysis, so I wasn't thrown for a loop; but for many others -- brace yourselves!
Regarding point two, Here are two examples:
1) Here is a quote: "The collection of all open sets in any metric space is called the topology associated with the space." Sounds like a definition to me! Fortunately the author gives a (sloppy) definition a few lines later. By the way, the only thing the reader learns about what an 'open set' is, is that it contains none of its boundary points. All the topology books I have read define open sets to be those in the topology. This is another point of confusion for the reader. In fact, points of confusion abound in that portion of the book.
2) On page, 17, trying somewhat haphazardly to explain the concept of a neighborhood, the author defines N as "N := {N(x) | x is an element of X}" This is already a little disconcerting: x is already understood to be an element of X. So he is saying that N is defined as N(x) (which he defines to be a collection of subsets of X). This is all he has to say on the matter until, on page 26, he writes "each N, an element of N(x)". Now N isn't both N(x) and an element of N(x). This is a point which the author does not clear up. He then starts using N all over the place, yet the reader isn't sure of what he's refering to.
A couple of other things:
-When he defines terms, they is not highlighted, and are embedded in a sentence, making it difficult to find them later.
- The index is pitifully small. Typical for English texts, I know; but this *is* the 3rd millinium!
On the other hand, I have good things to say about the book, too.
I like his style of writing. If it were just more precise, it would be fine for me. I like it better than the normal higher math texts, which tend to be too laconic for me. Notice that I make a distinction between the somewhat chatty style, which I like, and the sloppiness, which is confusing. One can be chatty, yet clear. So far, the undefined math terms which I listed above were not central to the text; and one would not miss much by just reading past them. The author includes many 'comments' sections throughout the book. These are wonderful so far. They are full of comments and examples which really clear up a lot of points. His examples are very good, too, although he is very terse in stating them. The paperback is nice looking. The paper, font, etc. make for easy reading (except for the sub/super-script font, which is too small for me).
To wrap this review up, I had already pretty much learned the stuff covered in the book so far, but judging from what I have read, I will be able to learn a lot from the rest of it; and, unlike some other math books I have studied, the experience won't be too painful.
p.s. See other reviews of it on the UK Amazon site.
Very readable presentation of diff. geometry.......2000-08-18
I have found Isham's treatment of differential geometry very clear, while maintaining quite an abstract nature. Isham takes care to motivate his definitions and include comments where comments are due. No problems are included but the book sometimes omits the simpler results and lets you work them out by yourself. A very readable introduction indeed.
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Modern Mathematical Methods for Physicists and Engineers
C. D. Cantrell
Manufacturer: Cambridge University Press
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The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. This up-to-date volume provides the essential mathematical and computational education for students, researchers, and practicing engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. He concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers.
Customer Reviews:
Highly recommended.......2004-03-12
Of all the "mathematical methods" or "applied mathematics" books
on my shelf, this is the one I find myself turning to most often.
There are many other books where you can look up, say, the
orthogonality properties of some "special function," but for an
authoritative explanation of fundamental mathematics as used
in physics today -- especially computational physics -- Cantrell
is excellent.
I often have to check with Cantrell to get an answer to questions
like "Is this result in this other text true in general, or only
in the special case that its author describes?". I never have
to double check to see to what extent the results in Cantrell
apply -- he makes things like that quite clear.
Cantrell has included a healthy dose of linear algebra and
functional analysis in his text, at the expense of some of the
chapters in more traditional mathematical physics texts, such as
those on contour integration or special functions.
However, examples of the use of special functions are sprinkled
liberally thoughout the text. And although the chapter on that
subject is mostly about Bessel functions, Cantrell's discussion
of Bessel functions is, typically, different from and more
insightful than conventional treatments.
My quibbles with the book have to do not with its content, but
with "first edition" glitches -- a figure here or a typo there.
And some sort of bug in the index preparation process left many
of the page numbers referred to in the index "off" by a page
or two. On the other hand, the hardcover edition that I have
lays open nicely on my desk, and after heavy use the binding
has not broken, and no pages have fallen out.
It would be nice if there were an appendix of "Answers to Exercises,"
or maybe a "Student's Guide." However, many of the exercises
are of the "Show that ..." variety, so the lack of such an appendix
is not nearly the drawback that it might be.
Overall: Excellent book, highly recommended.
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The Language of Physics.(Review): An article from: American Scientist
William J. Thompson
Manufacturer: Sigma Xi, The Scientific Research Society
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Release Date: 2005-07-28 |
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When Jim Hawkins uncovers the key to a pirate's treasure map he sets out on a quest to find the buried treasure with the help of pirate captain Long John Silver. Artist Tim Hamilton brings the pirates and villains to life in this graphic novel adaptation of Robert Louis Stevenson's classic.
Customer Reviews:
Treasure Island comes alive!.......2007-08-23
Treasure Island is my favorite book. I look for things like this graphic novel variation. First the art is great. It captures the feel of the story. It's dark and erie. The story is well paced and stays true to the original source material. The characters come alive before the reader's eye's. This is great reading for youths or adults.
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Treasure Island (Graphic Classics)
Robert Louis Stevenson
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Oliver Twist (Graphic Classics)
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Kidnapped (Graphic Classics)
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Moby Dick (Graphic Classics)
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The Hunchback of Notre Dame (Graphic Classics)
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Oliver Twist (Graphic Classics)
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Journey to the Center of the Earth (Graphic Classics)
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Kidnapped (Graphic Classics)
ASIN: 0764134914 |
Book Description
Young Jim Hawkins is the son of an innkeeper. When his father dies, Jim joins the crew of a sailing ship bound from the English port of Bristol to a distant island where a fabulous pirate's treasure is buried. In each of Barron's Graphic Classics, an English literary classic is transformed into a dramatic graphic novel with superb, atmospheric color illustrations and a finely-paced narrative. The tale—chosen from among important novels in the literary canon— ill keep young readers fascinated from first page to last. Graphic Classics make fine introductions for young readers to the riches of English literature. Books are available in both paperback and hardcover editions. In addition to the stories, each title features a brief biography and time line of its author, a list of his important works, a glossary, and an index. As such, these books are suitable for classroom use on junior and senior high school levels.
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Great Stories of Courage: The Call of the Wild/ the Red Badge of Courage/Treasure Island (Bank Street Graphic Novels)
Jack London ,
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Robert Louis Stevenson
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Comic book style art interspersed with black and white text. Page of questions about the book inside the back cover.
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Marvel Illustrated : Robin Louis Stevenson's Treasure Island #3 (Marvel Comics)
Roy Thomas
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Realizing that he shares lodging on the ship Hispaniola with mutineers, young Jim Hawkins makes his escape to shore and plunges deep into the island. Elsewhere, the mutineers battle the loyal sailors to the death! When Jim rejoins his shipmates, the head of the mutineers, Long John Silver, offers a ceasefire in exchange for the map showing where the buried treasure is located. And if Jim and company dont accept, they may be maroonedor worse.
Product Description
While the mutineers are ashore on Treasure Island, young Jim Hawkins climbs aboard the near-deserted ship, the Hispaniola...but, there is one last mutineer who has stowed aboard the vessel and stalks Jim with a very long, very sharp knife.
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Robert Louis Stevenson's Treasure Island (Graphic Revolve)
Robert Louis Stevenson ,
Wim (RTL) Coleman , and
Pat (RTL) Perrin
Manufacturer: Stone Arch Books
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Treasure Island
Robert Louis Stevenson
Manufacturer: BBC Audiobooks America
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ASIN: 0792743385 |
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Treasure Island (Graphic Classics)
Robert Louis Stevenson
Manufacturer: Barron's Educational Series
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Binding: Hardcover
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Accessories:
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Oliver Twist (Graphic Classics)
-
Journey to the Center of the Earth (Graphic Classics)
-
Kidnapped (Graphic Classics)
ASIN: 0764159763 |
Book Description
Young Jim Hawkins is the son of an innkeeper. When his father dies, Jim joins the crew of a sailing ship bound from the English port of Bristol to a distant island where a fabulous pirate's treasure is buried. In each of Barron's Graphic Classics, an English literary classic is transformed into a dramatic graphic novel with superb, atmospheric color illustrations and a finely-paced narrative. The tale—chosen from among important novels in the literary canon— ill keep young readers fascinated from first page to last. Graphic Classics make fine introductions for young readers to the riches of English literature. Books are available in both paperback and hardcover editions. In addition to the stories, each title features a brief biography and time line of its author, a list of his important works, a glossary, and an index. As such, these books are suitable for classroom use on junior and senior high school levels.
Books:
- Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications)
- Nonlinear Dynamical Systems and Chaos (Progress in Nonlinear Differential Equations and Their Applications)
- Nonlinear Dynamics and Statistics
- Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems (Pitman Monographs & Surveys in Pure & Applied Mathematics.)
- Optimal Control (Systems & Control: Foundations & Applications)
- Optimal Control Theory: An Introduction
- Optimization: Algorithms and Consistent Approximations (Applied Mathematical Sciences)
- Optimization Theory for Large Systems
- Practical Time-Frequency Analysis: Gabor & Wavelet Transforms with An Implementation in S (Wavelet Analysis and Its Applications, Vol 9)
- Principles of Combustion
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Good, with problems.......2006-01-02
