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Customer Reviews (5)

Milnor's"Morse Theory"-Classic for its basic proofs
I gave this book a 5star because it does succeed in presenting the main ideas,theorems,and proofs in Morse theory. This book was given as a reference in V.I.Arnold's"Mathematical Methods Of Classical Mechanics" for further information on Riemannian curvature(AppendixI). It turns out that Arnold's book contains much material which is prerequisite to Milnor. Euler-Lagrange equations,vector fields on manifolds,Poisson Brackets,and more which you will encounter in Milnor are explained in Arnold. Another book which helps is Bishop and Crittendon's"Geometry Of Manifolds." The configuration space of a mechanical system can and does in many cases translate to a Riemannian manifold with a motion of the system necessarily translating to a geodesic of the manifold. An example is a double planar pendulum. Since each pendulum is free to rotate 360 degrees,its configuration space is a torus or donut. Geodesics are extremal paths,hopefully minimal. One possible path is a closed spiral on the donut. Is it a geodesic? What's the motion? This book answers a great many questions as to how the shape or curvature and topology of the manifold influences and determines its geodesics. A knowledge of homotopy theory,deformation retracts,cw complexes,etc. is needed. Not easy going but rewarding. I'm still working on it.

Good but old
This book is a classic. If your grandpa did math, he probably did it out of this book. I think maybe Gauss picked up a few of his tricks here.

The age of this book was an issue. Some of Milnor's words are not in common use any more. He doesn't phrase his results in the modern language of tensors, which was troubling for me. With that said, some of Milnor's proofs are so clear and readable that they can't be improved upon. This is a great place to start learning Morse theory, though I'd look at a more modern treatment too if you are serious.

A Gem of Exposition
This book needs no review, as it is so well-known. But reading the first critique about the need for a more intuitive development of the subject, perhaps one viewpoint is worth restating.This book is a model of concise exposition. All of Milnor's works are written in a fashion that "makes it clear", except that sometimes years of thought are really needed to see the essence of the arguments. The writing sets up the framework for understanding, and the reader must work to fill it in. This is what makes it great writing. The reader accepts the truth of the statements, but Milnor does not bludgeon the reader with details which can be filled in by a professional mathematician. Or as many of us understand it, when you can fill in all the details, you have developed geometric intuition and are on the way to a deeper understanding of the subject.

Each chapter of the book is a classic. Chapter 2 on Riemannian geometry gives an overview of the subject which can be used as a basis for teaching a course on the same. When the students can fill in the details, they understand the core of the subject.

The best
When I was just becoming a mathematician, my teachergave me this book, saying "You're not ready for thisyet, but you should have it --- it's the best piece of mathematical exposition there is." Maybe that claim's exaggerated, but I've yet to find one I prefer. Along with Milnor's Lectures on the h-Cobordism Theorem, and hisCharacteristic Classes, this book is a lesson not only in topology (and wonderful topology, too!), but in clear writing as well.

A real landmark in topology.
Perhaps everyone who has had a bite in topology feels that this book is too famous to be given any kind of reference. The above having been said, this book is really a gem, elegantly explaining the Bott periodicity in thespirit of the original article by Bott.Of course, a simpler proof usingK-theory has been available since the sixties, but that does notdeteriorate the value of this book. ... Read more

Product Description
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem. ... Read more

Customer Reviews (9)

it's ggrrrrrrrrrrreat!
I consider myself to be a pretty lousy graduate student and I still found this book to be very readable. This book is also cheap enough that you may want keep an extra copy around, as it makes a great gift item/stocking stuffer.

a must-read supplement for topology students
Milnor's "Topology from the Differentiable Viewpoint" is a brief sketch of differential topology, well written, as are all books by Milnor, with clear, concise explanations. For students who wish to learn the subject, it should be read as a companion to a more substantive text, such as Guillemin & Pollack's Differential Topology or Hirsch's Differential Topology, as too much of the material is left out for this to be adequate as a textbook. OTOH, it does make for good bedtime reading.

While this book is highly regarded among mathematicians, it is not without its faults, namely,
- it fails to cover many topics of importance, such as transversality (only mentioned in an exercise), embeddings, differential forms, integration, Morse theory, and the intersection form;
- it only cites some theorems without proving them, or it leaves the proofs to the reader;
- it offers proofs of many theorems that are really only sketches without all the details;
- manifolds are only defined as subsets of Euclidean spaces;
- there is only 1 collection of 17 problems at the end of the book, which are used to introduce important concepts; and
- it probably moves too quickly for true beginners, packing a lot into only 51 pages.

So don't buy this as your only, or even first, book on differential topology. Oddly, many of the faults that I listed above are simultaneously strengths, in that it can be read very quickly, with relatively little effort and a high rate of retention. Milnor really emphasizes the topology of the subject, giving applications such as the fundamental theorem of algebra, Brouwer's fixed point theorem, the hairy ball theorem, the Poincare-Hopf theorem, and Hopf's theorem. Most of the book focuses on degree theory, but there is also a nice introduction to framed cobordism, which is rare for an elementary book. Guillemin & Pollack's book was based in large part on this one, and could be read together, with G&P giving more elementary explanations and additional topics, while Milnor's book provides a proof of the Sard theorem and the Pontrjagin-Thom construction. The exercises, though not particularly difficult, do provide a good opportunity to practice proving theorems in the subject, as there are no hints for them, as one would find in many other differential topology books, and they are not separated by chapter.

Exactly would it should be
I would suggest to use this book as a companion to more serious books on topology. Weighing in at a mere 51 pages, this book accomplishes what it needs to: a brief, succinct introduction to topology mostly based on the work of Brouwer. There is a nice mixture of topics, ranging from Sard's theorem to Poincare-Hopf theorem. The proofs and ideas are not fully rigorous or developed, but that would be quite a bit to expect from such a short exposition.

best math book ever written

Despite the lovely subject matter covered in this book, it more importanty gives one a taste of Mathematics as an intellectual discipline. It in outline shows how a mathematical theory - in this case Differential Topology -is constructed and consquently what mathematicians actually do and think about.
Anyone who would like to appreciate Mathematics as a field of study rather than just learn some math should open this book.

Better still, the prerequisite is only multivariate calculus!I have long thought this book should be the third year of calculus rather than differential equations or complex analysis.

Additionally, for the novice it is the only entry I know of into the mysteries of high dimensional geometry, that amazing almost unbelieveable accomplishment of the human mind.

There is a Star Trek episode in which a blind woman wears a dress of sensors which enable her to know more about her environment than a person can know from seeing. She knows exact distances and dimensions, can detect minute movements, can process the complete spectrum of light. In some sense she sees better. Modern topology and geometry are like that sensor dress for seeing higher dimensions. While we can not visualize the sphere in 5 dimensions, we know more about it from these mathematical theories than a five dimensionally sighted being ever could.

Today, mathematics is often considered to be just a practical tool - like a spread sheet - or a toaster oven. We forget its power to widen our imagination, to frame the unimaginable. This book reminds us of this and shows why Mathematics is the Queen of Sciences.

Compact and useful
This book packs a lot of interesting material into a small volume. E.g., I picked up another book recently that started talking about cobordisms right off the bat; despite my having a couple of shelves full of well-known Dover, Springer, Cambridge UP etc. books on topology, differential geometry, mathematical physics, etc., Milnor's tiny book was the only one I found that could help me understand what cobordisms are right away. The book also uses many illustrations to help understanding.

I demote this to 4 stars only because Princeton UP's price is a bit high; many years ago I was lucky enough to find a used copy of the old U. Virginia edition, and paid much less. ... Read more

Customer Reviews (10)

Best, most easily understandable book he ever wrote.
This was topic for my 2nd oral exam at U of Chicago. Me and a couple of other fellows took turns lecturing on it to each other in preparation for same, to work out a few wrinkles of minor skips in proof which we found.

He's a great expositor, and I think this one is his crowning achievement for regular guys likeme.

great at what it covers, but doesn't cover enough
Milnor & Stasheff's "Characteristic Classes" is the standard reference for them. It includes a number of different, but equivalent, definitions and properties of the Stiefel-Whitney, Chern, Euler, and Pontrjagin classes, with a formal, heavily algebraic topological flavor. The material presented is all easy to follow and well explained, and there are problems included in every chapter, some of which are challenging, earning this work its high reputation. However, there is a dearth of geometric intuition and many important, basic facts about the classes are absent, so while a student with only a standard background in algebraic topology and differential topology could read and understand the book, to really gain a practical knowledge of characteristic classes as one would need in studying, say, low-dimensional topology (let alone physics), the book must be supplemented with other book(s) on the subject, such as Bott & Tu's Differential Forms in Algebraic Topology.

Characteristic classes associated to a fiber bundle are cohomology classes of the base manifold that behave naturally under pullbacks (i.e., the characteristic class of the pullback of a bundle is the pullback of the characteristic class of the bundle). In particular, the classic classes that this book deals with are associated to vector bundles, either real (the Stiefel-Whitney (S-W) and Pontrjagin classes), real orientable (the Euler class), or complex (Chern classes). There are several different ways of defining these classes, most of which are covered:

- As obstructions to the extension of a trivialization of the bundle over the k-skeleton of the base manifold to a trivialization over the (k+1)-skeleton (for some k). Alternatively, as the obstruction to the existence of a certain number of linearly independent, nonzero sections of the bundle. Most applications of characteristic classes in topology focus on these properties. Unfortunately, relatively little space is dedicated to this approach, with much of the technical details being left to Steenrod's The Topology of Fibre Bundles.

- As the pullback under the classifying map of the generators of the cohomology classes of the classifying space for the bundle. Since every bundle is isomorphic to the pullback under the classifying map of a universal bundle over such classifying space, this explains why characteristic classes have such significance - they are basic algebraic topological invariants for bundles that play a role similar to (co)homology groups for manifolds. Indeed, under certain circumstances, a few characteristic classes can uniquely specify a bundle (although the authors fail to mention this). Much of the book focuses on computing the cohomology rings of classifying spaces for real, real orientable, and complex vector bundles, but this unfortunately is not of much practical use.

- As certain functions of the curvature of a connection on the bundle (Chern-Weil theory). This approach includes, among other applications, the Gauss-Bonnet theorem (covered in the Appendix), and is central to gauge theory in both physics and mathematics (not mentioned in this book). The treatment of this facet is inadequate - see, e.g., Kobayashi & Nomizu's Foundations of Differential Geometry (Volume 2) or Chern's Complex Manifolds without Potential Theory (With an Appendix on the Geometry of Characteristic Classes) for more depth. Secondary characteristic classes, such as Chern-Simons classes, are only mentioned in an epilogue - see Morita's Geometry of Characteristic Classes.

- For Euler and S-W classes, the classes are intimately connected to the Thom isomorphism and Thom class of a vector bundle, which is one of the emphases of the book. The Thom Isomorphism Theorem is proved here as well.

- For Chern classes, an induction procedure is used to define all other (lower) classes once the top class is defined. (It is also pointed out that a similar procedure can be followed for S-W classes.) This differs from the usual induction procedure that starts from the 1st class and works up. In fact, in one of the most surprising omissions from the book, there is no mention of the Splitting Principle for Chern (or S-W) classes.

- The usual relations among the various classes are proved: The top S-W class is the mod 2 reduction of the Euler class, S-W classes are mod 2 reductions of Chern classes, etc. Pontrjagin classes are defined in terms of Chern classes.

- A formal definition of characteristic classes can be given, where one just lists the properties that are needed to uniquely specify them (similar to the approach of defining homology via the Eilenberg-Steenrod axioms). While this does allow one to immediately start using the properties of the classes to derive other results, it provides no intuition about where the classes come from or why they are so important. Unfortunately, the authors elected to define the S-W classes in this fashion, and then only slowly derive the alternative characterizations of them, which is one reason why so many reviewers here (especially physicists) find this book to be unhelpful. Some patience is required when reading the book, but there is a payoff later on.

The only examples for which these classes are actually computed are certain bundles over the standard projective spaces (for which this book is generally cited as a reference), (trivially) the spheres, and Grassmann manifolds.

Much of the rest of the book is focused on (1) S-W, Chern, and Pontrjagin numbers and their implications for cobordism theories, but they only scratch the surface, referring the reader instead to Stong's Notes on cobordism theory; and (2) multiplicative sequences, such as the L-genus and Todd classes, and in particular a proof of the Hirzebruch signature theorem, but no mention is made of the natural extension and application of these classes to the Atiyah-Singer Index theorem or the Riemann-Roch theorem.

The remaining material comprises preliminary chapters on smooth manifolds (like in Milnor's Topology from the Differentiable Viewpoint defined only as subsets in R^n), singular homology and cohomology, and vector bundles. The reader should already be well familiar with these topics before opening this book.

The biggest weaknesses of the book are the formal presentation, especially in the first chapter on S-W classes, and some glaring omissions, including not only the aforementioned ones, but also:
- spin structures - in particular, that the vanishing of the 2nd S-W class implies the existence of such;
- structure groups and transition functions for bundles - in particular, the concepts of characteristic classes being obstructions to liftings of bundles with one structure group to those of another and being expressible as cocyles in Cech cohomology (the authors acknowledge these omissions in the Epilogue);
- explicit discussion of line bundles - in particular, the description of the first Chern class as the Poincare dual to the zeros of a generic section;
- that the 2nd S-W class is a characteristic element for the intersection form for an oriented 4-manifold;
- the exact sequence expressions for 1st Chern class or 1st and 2nd S-W classes;
- that the 1st Chern class is an isomorphism between (isomorphism classes of) complex line bundles and the integers, and that the 1st S-W class is a similar isomorphism for real line bundles and Z/2Z;
- the Dold-Whitney theorem that an oriented real vector bundle over an oriented 4-manifold is uniquely determined by its 1st Pontrjagin, Euler, and 2nd S-W classes, or that 2-plane complex (U(2)) bundle over a 4-manifold is uniquely determined by its 1st and 2nd Chern class;
- differential-form expressions for any of these cohomology classes (except a little bit when discussing Chern-Weil theory).

In short, while much important material has been left out (after all, the lectures on which this book was based were given in 1957!), what is covered is done very well. So this book should be one of your references for characteristic classes, but you'll need to supplement it with, e.g., Bott & Tu or Madsen & Tornehave's From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes and possibly Scorpan's The Wild World of 4-Manifolds or Lawson & Michelson's Spin Geometry. Unfortunately, there doesn't seem to be any comprehensive book on even these classical characteristic classes that encompasses all the different aspects one would need to know.

Very Disappointed.
This item was totally misrepresented. I purchased from this seller because the item was listed as "Like New" and their listing read "ships same day". I even paid extra for priority shipping (it was intended as a special birthday surprise for my son). I also sent the seller an email asking them to confirm actual date of shipping and a follow up email when it didn't arrive on time. The seller did Not respond to either email. The item arrived almost a week late with no note of explanation for the delay. The Most disappointing part of this entire transaction was the total misrepresentation of the item itself. The cover was extremely faded and the binding split the moment the book was opened. This was NOT the special birthday surprise I had hoped to give my son. In all my years of online purchasing, I have not had a more disappointing experience.

Essential for any geometer
Milnor's writing is, as always, exceptionally clear and concise.Foundational material for any geometry student.Every mathematician should own this.Every geometer should study it.

how many stars??
I read this page to see how Milnor's book could average only 4 stars.I found two unfair, but intelligent, 2/3 star reviews apparently by physicists, miffed that a masterful 50 year old book on the foundations of the topic, does not provide a history of their invention, and a survey of their current use in physics.If a book serves its own and its author's purpose wonderfully well, but does not serve yours, that is your fault, not the author's.As a hint, it is in the Annals of Math series, not the Handbook for Physicists series.Please read the chapter on "obstructions", p. 139.There Milnor succintly provides exactly the interpretation requested, and a reference to the classic text by Steenrod.

The most important construction on a smooth manifold is its tangent bundle, and the basic question is whether smooth never zero vector fields exist.The subject begins with the theorem of Poincare & Hopf:a never zero vector field exists if and only if the topological euler characteristic of the underlying manifold is zero.For a polyhedron, this euler characteristic is the number V-E+F = vertices -edges + faces.Thus the most basic characteristic class is the euler class.Briefly, the others measure existence of sequences of independent vector fields.In 1957 their existence, construction and properties were clouded, and Milnor cleared this away once for all in these notes, published by demand and gratefully received by [almost] everyone.This is a great book, and a 2 star review only serves to rate ones own qualifications to appreciate it.I.e. these reviewers are rating not the book but its suitability for their own narrow interests.For another short introduction try the chapter in the book by Bott & Tu. ... Read more

Product Description
The development of algebraic topology in the 1950's and 1960's was deeply influenced by the work of Milnor. In this collection of papers the reader finds those original papers and some previously unpublished works. The book is divided into four parts: Homotopy Theory, Homology and Cohomology, Manifolds, and Expository Papers. Introductions to each part provide some historical context and subsequent development. Of particular interest are the articles on classifying spaces, the Steenrod algebra, the introductory notes on foliations and the surveys of work on the Poincare conjecture. Together with the previously published volumes I-III of the Collected Works by John Milnor, volume IV provides a rich portion of the most important developments in geometry and topology from those decades. This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing. ... Read more

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This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event.

Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference. ... Read more

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This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattés map has been made more inclusive, and the Écalle-Voronin theory of parabolic points is described. The résidu itératif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated.

Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

Customer Reviews (2)

Very good if..
you have a heavy package in
differentiel geometry
complex analysis
topological algebra
riemann geometry.

If not, forget it.

Great Book
This is a wonderful book by a master of the subject.
It is packed with penetrating insights, illuminating
some of the deepest results on dynamics. Its great
strength is the bird's-eye view it gives.
It is a great place to start the study of complex dynamics.
It is not self-contained, so to get the detail on essential
ingredients such as uniformization and solving the Beltrami
equation one has to go elsewhere. I recommend students
to read it alongside Carleson and Gamelin, who take pains
to supply full details. ... Read more

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This volume contains papers on geometry of one of the best modern geometers and topologists, John Milnor. This book covers a wide variety of topics and includes several previously unpublished works. It is delightful reading for any mathematician with an interest in geometry and topology and for any person with an interest in mathematics. (A number of papers in the collection, intended for a general mathematical audience, have been published in the American Mathematical Monthly.) Each paper is accompanied by the author's comments on further development of the subject.The volume contains twenty-one papers and is partitioned into three parts: Differential geometry and curvature, Algebraic geometry and topology, and Euclidean and non-Euclidean geometry. Although some of the papers were written quite a while ago, they appear more modern than many of today's publications. Milnor's excellent, clear, and laconic style makes the book a real treat.This volume is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing. ... Read more

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Chapters: Alexander Grothendieck, Paul Cohen, Atle Selberg, René Thom, Edward Witten, Enrico Bombieri, Alain Connes, John Milnor, William Thurston, Michael Atiyah, Lars Ahlfors, Stephen Smale, Heisuke Hironaka, Vladimir Voevodsky, Laurent Lafforgue, Maxim Kontsevich, Richard Borcherds, Grigori Perelman, Shing-Tung Yau, David Mumford, Terence Tao, Lars Hörmander, Jean-Pierre Serre, Grigory Margulis, Timothy Gowers, Simon Donaldson, Alan Baker, Laurent Schwartz, John G. Thompson, Vladimir Drinfel'd, Sergei Novikov, Pierre Deligne, Kunihiko Kodaira, Charles Fefferman, Michael Freedman, Daniel Quillen, Vaughan Jones, Wendelin Werner, Andrei Okounkov, Pierre-Louis Lions, Jesse Douglas, Jean Bourgain, Curtis T. Mcmullen, Efim Zelmanov, Gerd Faltings, Shigefumi Mori, Jean-Christophe Yoccoz, Klaus Roth. Source: Wikipedia. Pages: 229. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Sir Michael Francis Atiyah, OM, FRS, FRSE (born 22 April 1929) is a British mathematician, and one of the most influential mathematicians of the twentieth century. He grew up in Sudan and Egypt, and spent most of his academic life at Oxford, Cambridge, and the Institute for Advanced Study in Princeton. He has been President of the Royal Society (19901995), Master of Trinity College, Cambridge (19901997), Chancellor of the University of Leicester (19952005), and President of the Royal Society of Edinburgh (20052008). He is currently retired and an honorary professor at the University of Edinburgh. He has had many mathematical collaborations, in particular with Raoul Bott, Friedrich Hirzebruch and Isadore Singer, and his students include Graeme Segal, Nigel Hitchin and Simon Donaldson. With Hirzebruch he founded topological K-theory, a major tool in algebraic topology, that describes the ways in which high dimensional space...More: http://booksllc.net/?id=20698 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Wacław Sierpiński, René Thom, Henri Poincaré, Kazimierz Kuratowski, Felix Hausdorff, John Milnor, Vladimir Arnold, William Thurston, Michael Atiyah, Stephen Smale, Vladimir Voevodsky, Pavel Samuilovich Urysohn, Leopold Vietoris, Elmer Rees, Luitzen Egbertus Jan Brouwer, Grigori Perelman, Heinz Hopf, John R. Stallings, James W. Cannon, Brian Bowditch, Karen Vogtmann, Mladen Bestvina, Anatoly Fomenko, Erik Christopher Zeeman, Jean-Pierre Serre, Raymond Louis Wilder, Leonard Gillman, Robert Lee Moore, Hassler Whitney, Raoul Bott, Shaun Wylie, Edwin E. Moise, Johannes de Groot, George David Birkhoff, J. H. C. Whitehead, Andreas Floer, Peter Hilton, R. H. Bing, Henry Wallman, Solomon Lefschetz, Sergei Novikov, Louis Kauffman, Albert W. Tucker, Judith Roitman, Hing Tong, Cahit Arf, George Mackey, Samuel Eilenberg, Frank Adams, Clifford Taubes, Eberhard Hopf, Andrey Nikolayevich Tychonoff, Zygmunt Janiszewski, Greg Kuperberg, Colin Adams, John Morgan, Daniel Quillen, Víctor Neumann-Lara, Oswald Veblen, Max Dehn, Morwen Thistlethwaite, James Waddell Alexander Ii, Wu Wenjun, Armand Borel, Oleg Viro, C. T. C. Wall, Włodzimierz Kuperberg, Dennis Sullivan, Ruth Lawrence, Shmuel Weinberger, Klaus Wagner, Allen Hatcher, Alice T. Schafer, Jean Leray, Shlomo Sternberg, Curtis T. Mcmullen, Michel Kervaire, Christos Papakyriakopoulos, John L. Kelley, Victor Anatolyevich Vassiliev, Hans Freudenthal, Augustin Banyaga, Krystyna Kuperberg, Abram Ilyich Fet, Sylvain Cappell, Dušan Repovš, Karol Borsuk, Richard Davis Anderson, J. Hyam Rubinstein, David Epstein, Valentin Poénaru, Lev Schnirelmann, Peter Shalen, William Floyd, Arthur Milgram, Robion Kirby, W. B. R. Lickorish, Jack Morava, Mary Ellen Rudin, Georges de Rham, Ralph Fox, Viktor Buchstaber, Daina Taimina, F. Burton Jones, Tudor Ganea, Clifford ...More: http://booksllc.net/?id=20698 ... Read more

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Chapters: John Milnor, Warren Sturgis Mcculloch, George B. Mcclellan, Bobby Czyz, Roy Scheider, Thomas R. Pickering, Daniela Gioseffi, Sandra Boynton, Ray Heatherton, Al Harrington, George Huntington Hartford, Mark E. Kelly, Ken Blanchard, Jay Lynch, Christopher Collins, Anthony Accetturo, Dickinson W. Richards, Robert Adams, Peter S. Connor, James Smith Bush, Lowell Mason, John Batterson Stetson, Stephanie Adams, Chub Feeney, Jim Ringo, Eugene Nickerson, Peter Shapiro, John Harbison, Tony Galento, Gail Fisher, Ronald I. Spiers, Douglas J. Bennet, A. J. Price, Samuel P. Bush, Walter G. Alexander, Jay Alford, David Ackroyd, Scott J. Kelly, Stephen Dobyns, Mims Hackett, Tom O'malley, Frank Tallman, Morton Schindel, Jeff Zaun, Bobby Jones, John Mortimer Smith, Daniel Quillen, Steven A. Cohen, Peter Cain, N. J. Burkett, James J. Barry Jr, John Augustine Hartford, Cornelius Clarkson Vermeule Iii, Leroy Dubeck, Lynne Russell, Robert Hett Chapman, Charles Knox Robinson Iii, Beekman Winthrop, Aaron B. Tompkins, David Ferry, Dennis M. Cavanaugh, Edward Rafeedie, Thomas Aloysius Boland, Corinne Alsop Cole, Charles N. Fowler, Maria Jeritza, Karen Hunter, Steven Cramer, Ira Condict, Lesley Bush, Ray Yagiello, John Condit, Ernest Trow Carter, Marc Cartwright, Charles H. O'brien, Daniel F. Minahan, Stephen Hartke, Terie Norelli, Beatrice Hicks, Jim Collins, Silas Condit, Richard M. Freeland, John Crotty, Dickinson Richards Debevoise, Jim Trelease, Henry Graves, John L. Blake, Constance Adams Demille, James C. Condos, Isaac Pierson, James Girard Lindsley, Bruce Gray, Syd Kitson, Patrick E. Hobbs, Will Holder, Frank C. Stanley, Jack Robinson, Joe Duckworth, Daniel J. Shanefield, Hayward A. Harvey, Lloyd Conover. Source: Wikipedia. Pages: 398. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: George Brinton ...More: http://booksllc.net/?id=104977 ... Read more

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Chapters: Richard Feynman, John Milnor, Peter Shor, Elwyn Berlekamp, David Mumford, Vern Poythress, Barry Simon, Rohit Jivanlal Parikh, William Nierenberg, Arthur Rubin, Kenneth G. Wilson, Bjorn Poonen, George Mackey, Reid W. Barton, Daniel Quillen, Neal Koblitz, Noam Elkies, Irving Kaplansky, Melvin Hochster, Andreas Blass, Robert Mills, Melanie Wood, Richard M. Dudley, Karl Rubin, Ravi Vakil, Eugenio Calabi, Don Zagier, Andrew Gleason, Don Coppersmith, Richard Schroeppel, James Bjorken, Miller Puckette, Gabriel D. Carroll, Jeffrey Lagarias, Roger Evans Howe, Peter Montgomery, Joel Spencer, Abhinav Kumar, Stephen L. Adler, Arthur P. Dempster, Daniel Kane, David Vogan. Source: Wikipedia. Pages: 159. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Richard Phillips Feynman (pronounced ; May 11, 1918 February 15, 1988) was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics (he proposed the parton model). For his contributions to the development of quantum electrodynamics, Feynman, jointly with Julian Schwinger and Sin-Itiro Tomonaga, received the Nobel Prize in Physics in 1965. He developed a widely used pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his work in theoretical physics, Feynman has been credited with pioneering the field of quantum computing, and introducing the c...More: http://booksllc.net/?id=25523 ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 558 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more