Product Description
Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: People From Vigevano, Gian-Carlo Rota, Eleonora Duse, Ludovico Sforza, Bona Sforza, Andrea Soncin, Guido Da Vigevano, Carlo Barone, Vigevano Calcio, Gravati. Excerpt: Eleonora Duse (October 3, 1858April 21, 1924) was an Italian actress, often known simply as Duse. Duse was born in Vigevano, Lombardy, and began acting as a child. Both her father and her grandfather were actors, and she joined the troupe at age four. Due to poverty, she initially worked continually, traveling from city to city with whichever troupe her family was currently engaged. She came to fame in Italian versions of rôles made famous by Sarah Bernhardt. She gained her first major success in Europe, then toured South America, Russia and the United States; beginning the tours as a virtual unknown but leaving in her wake a general recognition of her genius. While she made her career and fame performing in the theatrical "warhorses" of her day, she is today remembered more for her association with the plays of Gabriele d'Annunzio and Henrik Ibsen. In 1879, while in Naples, she met journalist Mattino Cafiero, and became involved in a fast paced love affair with him. However, less than a year later, while she was in mid-pregnancy, he left her. The baby did not survive birth, and shortly thereafter Cafiero died as well. Duse then joined Cesare Rossi's theater company, and met actor Teobaldo Checchi. The two married in 1881. By 1885, the couple had one daughter, Enrichetta, but divorced after Duse became involved with another actor, Flavio Ando. Eleonora Duse portrayed by Franz von Lenbach.By this time, her career was in full swing and her popularity began to climb. She travelled on tour to South America, and upon her return a year later she formed her own company, meaning that s... More: http://booksllc.net/?id=523019 ... Read more

Product Description
Chapters: Donald Knuth, George Pólya, John Horton Conway, Srinivasa Ramanujan, Gian-Carlo Rota, James Stirling, W. T. Tutte, Bartel Leendert Van Der Waerden, Paul Erdős, Frank P. Ramsey, András Hajnal, Terence Tao, James Joseph Sylvester, Marcel-Paul Schützenberger, Pál Turán, Timothy Gowers, Eric Temple Bell, Percy Alexander Macmahon, Václav Chvátal, Michel Deza, John Howard Redfield, Julian West, Béla Bollobás, George Szekeres, Ronald Graham, Heiko Harborth, Øystein Ore, László Lovász, Sharadchandra Shankar Shrikhande, Ben J. Green, Judith Q. Longyear, Víctor Neumann-Lara, Solomon W. Golomb, David B. Weinberger, Ernst G. Straus, Issai Schur, Percy John Heawood, Doron Zeilberger, Alfréd Rényi, Ken Ono, Jaroslav Nešetřil, Fred S. Roberts, Victor Anatolyevich Vassiliev, Neil Sloane, Eugène Charles Catalan, Fan Chung, Herbert Wilf, Noga Alon, D. Raghavarao, Arthur Milgram, Endre Szemerédi, Igor Pak, Gil Kalai, László Pyber, Branko Grünbaum, László Babai, Jack Edmonds, Richard K. Guy, George Andrews, Alexandre-Théophile Vandermonde, Richard P. Stanley, Emanuel Sperner, Paul Seymour, Vera T. Sós, András Frank, Imre Leader, John Riordan, D. K. Ray-Chaudhuri, Michele Mosca, Naum Vilenkin, M. N. Vartak, Michael H. Albert, Vance Faber, Gábor Tardos, Cheryl Praeger, Jim Geelen, Sun Zhiwei, Tatyana Pavlovna Ehrenfest, Brendan Mckay, Aviezri Fraenkel, Daniel Kleitman, Karl Mahlburg, Yousef Alavi, Péter Frankl, Fred Galvin, Jeong Han Kim, Norman Macleod Ferrers, Lajos Pósa, D. R. Fulkerson, Rosemary A. Bailey, Richard Rado, Peter Cameron, Gyula O. H. Katona, Stefan Burr, Doug Stinson, Navin M. Singhi, Chris Godsil, Nicolaas Govert de Bruijn, Anatoly Vershik, Vasanti N. Bhat-Nayak, Bernard Frénicle de Bessy, Ron Aharoni, Dénes Kőnig, W. H. Clatworthy, David Shane Gunderson, Zoltán Füredi, Jack Van Lint, Alfred Young, Joel Spencer, Helge Tverberg, Tibor Gallai, David P. Robbins, Alan Hoffman, Thomas Zaslavsky, R. M. Wilson, Walther Von Dyc...More: http://booksllc.net/?id=47717 ... Read more

Product Description
The work presented in this volume spans a period of some 40 years. In addition to more than 30 papers, a reprint of a 250-page book is also included—the much-admired A Collection of Mathematical Problems.

The papers were selected on the basis of their individual significance, but taken together, they incidentally exhibit the broad range of fields to which Ulam has contributed. Among them are studies on the foundations of mathematics, set theory, measure theory, topology, probability theory, the Monte Carlo method (which was initiated by Ulam), the theory of computation, the use of computers for mathematical experimentation, and the applications of mathematics to astronomy, physics, and biology. Some of the papers cannot be categorized as belonging to any specific field: they are concerned with the cross-relationships between the methods of one field and those of another. ... Read more

Product Description
This volume completes the publication of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974.

Volume IV presents 20 papers on probability, 17 on combinatorics, and 18 on the teaching and learning of mathematics. Pólya has made a number of fundamental contributions to the first two fields, including perhaps the first use of the term "central limit theorem," but his major influence on mathematics has clearly been his approach to pedagogy. Many of the papers throughout these volumes have a strongly pedagogical flavor, but the papers in the third section of this volume focus squarely on the real business of how to do mathematics—how to formulate a problem and then create a solution.

This volume is the twenty-third in the series Mathematicians of Our Time, edited by Gian-Carlo Rota. ... Read more

Product Description
In this volume, the editor presents reprints of most of the fundamental papers of Gian-Carlo Rota in the classical core of cominatorics. These include Part I, III, IV, VI and VII of the Foundation series on Mobius fuction, polynomials of binomial type, counting in vector spaces, generating functions and symmetric functions. Also reprinted are papers which are derived or related to the themes explored in these central papers. Rota's work, starting with the paper, "On the Foundations of Combinatorial Theory: I - Theory of Mobius Functions" (1964) has revolutionized the way we approach combinatorics; this volume is intended to be an introduction to his way of thinking about that subject. Kung has provided a substantial amount of new material on the impact that Rota's papers have had on combinatorics. Extensive survey articles are included in each chapter to guide the reader, both to the reprinted papers and to the works of others which have been inspired by these papers. There are also four prefatory essays describing Rota's special influence on combinatorics, particularly at the historical Bowdoin conference in 1970.This book is intended for experts as well as beginning graduate students (particularly as a source for research problems). ... Read more

Product Description
This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.Amazon.com Review
We tend to think of mathematics as uniquely rigorous, and ofmathematicians as supremely smart. In his introduction to TheMathematical Experience, Gian-Carlo Rota notes that instead, "amathematician's work is mostly a tangle of guesswork, analogy, wishfulthinking and frustration, and proof ... is more often than not a wayof making sure that our minds are not playing tricks." PhilipDavis and Reuben Hersh discuss everything from the nature of proof tothe Euclid myth, and mathematical aesthetics to non-Cantorian settheory. They make a convincing case for the idea that mathematics isnot about eternal reality, but comprises "true facts aboutimaginary objects" and belongs among the human sciences. ... Read more

Customer Reviews (16)

Says nothing new for somebody who has been in the field for a while
I'm not sure how The Mathematical Experience ended up in my library, but I read it anyway. I was expecting a very good reading experience out of the book, and the first two chapters proved to be so. When chapter three came along, it went downhill from thereafter, only to be revived for one more time by chapter six. The authors brought out theorems and mathematical entities in The Mathematical Experience including the Riemann Hypothesis, the Four Color problem, Euclid's proof of infinity of prime numbers, the Fourier series, and others. The biggest problem in this manner is that I have seen them brought up so many times in other books that there is nothing new to be said. While the comments written in first two chapters felt to be highly relevant and true to the core (I recommend Morris Kline's Why Johnny Can't Add: The Failure of New Math over this book), I found, also in chapter six, the tone and attitude by the authors to be pessimistic and very condescending. Although I am an experienced mathematician, I actually sympathize with others who struggle with mathematics largely because of the amount of misunderstanding and lack of proper guidance. This is a very prevalent problem among high school and college students due to little pedagogy espoused by the teachers. Once I observed a student teacher instructing a class of six graders in mathematics, I found a total of nine errors in a span of forty-five minutes, and I saw the look of a student's facial expression when one of the errors appeared that said it all for me. In chapter six, the authors somewhat painted the prep school teacher as an ignorant of the subject that he teaches yet he is absolutely right in one thing: math ought to be fun. Taking that out of the equation while inserting very little pedagogy, drones of college students are in fearful state of mathematics and avoid the subject as much as possible, and those who wish to major in mathematics, it becomes a survival of the fittest from day one of Calculus class to the last day of third course of Real Analysis. Probably, to my best estimation, less than 10% of the original students from day one will go on to have a true math degree. Understandably, mathematics contains a lot of useless information that has little applicable value to the real world, but that hasn't stopped me from enjoying doing it for countless hours every day. When thinking of the outside mathematical world, practically not one mathematician is famous enough as Einstein is. The closest figure to achieve this immortality is probably Pythagoras solely because of his famous and most memorized equation with Euclid a close second for having written a book that has been claimed to be the second most read book ever next to the Bible. Having said that, nobody really cares, but people who use mathematics are doing it for practical purposes. While reading The Mathematical Experience, I felt my mind to be wandering and skimmed a lot of parts, remarking on how sometimes outdated the book is and how negative the authors can be at times. Touching on religion, I was very surprised to read the statement that most mathematicians are probably agnostic. Hey, I thought mathematicians are foolproof, so shouldn't they be atheistic as I am? The debate of this topic is absolutely meaningless anyway. All in all, The Mathematical Experience brings out the same old stuff as in other books, is interesting when conversations are shown, and will be relevant when it happens but not too often. But I truly wasted my time.

My Mathematical Experience
I'm into philosophy and literature but have always been interested in science. I was looking for a good introduction to the world of mathematics and I did a lot of research that pointed to this book. It's a perfect book for the intelligent layman interested in the subject but it gets really difficult about half-way through.

The fact that the book became incomprehensible to me when I got to a certain point is not the reason why I have given it 4 stars. It doesn't get 5 stars because it deserves a revision; Fermat's Last Theorem, for example, has been proved already.

The book is also very beautiful, it's full of interesting illustrations and is very pleasing to the eye. I recommend it highly.

Good approach and selection, mathematical aspect uneven
In my view, this book (which looks like a collection of articles gathered up under several rubrics) shares typical achievements and flaws of all popular-math literature; namely, it's enjoyable and enlightening as far as historical and philosophical aspects of the material presented, yet when they authors actually get to mathematics, it becomes fragmeted, jerky, and confused. Symptomatic of this is the chapter on nonstandard calculus: the historical narrative is very interesting, yet the math proper is confused and incomprehensible. Perhaps that is because it's impossible to express it fully and right in a popularizing context; perhaps it is so because I'm too obtuse to have understood it (but then the most of the target audience is probably no better); or maybe it's because the authors didn't do a terribly good job of it. The next chapter (Fourier analysis) suffers from the same.

Overall, I say, it's a good, although overrated, book. Read it, get what you can out of it and don't fret about the rest: the book is really a collection of articles, apparently written for different purposes, at different times, and for different publications; the quality of writing varies from section to section, although the overall structure and topicality are unquestionably very good. The book has an extensive and diverse bibliography along with a rather mediocre (close to names-only) index. Well, no book is perfect, including this one: overall it's solid four stars -- recommended.

Informative and engaging
The authors deal with various important aspects of mathematics and about practising mathematics. They also deal with the philosophy of mathematics. By and large, they do it engagingly. Specifically, they tackle why mathematics seems to 'work'; how a mathematician actually goes about doing mathematics; they offer some light treatment of a few mathematical topics, and they illustrate mathematical thinking as well.

This book is best read by students thinking about choosing mathematics as a career, or even just as a field of study. Although, any layperson will come off with a greater appreciation of what mathematics is, and what mathematicians do.

Philosophy, History and Myths of Mathematics
The Mathematical Experience by Philip J. Davis and Reuben Hersh
1981 Houghton Mifflin Company, Boston

Is all of pure mathematics a meaningless game? What are the contradictions that upset the very foundations of mathematics? If a can of tuna cost $1.05 how much does two cans of tuna cost (Pg. 71)?If you think you know the answer, don't be so sure.How old are the oldest mathematical tables? What is mathematics anyway, and why does it work?Can anyone prove that 1 + 1 = 2?
This is a book about the history and philosophy of mathematics. I'm certainly not a mathematician, and there are parts of the book I will never understand, yet the balance of it made the experience well worth while.The authors presented the material so that it is interesting and (mostly) easily understood.They have a creative way of making a difficult subject exciting. They do this by giving us insights into how mathematicians work and create.They live up to the title making mathematics a human experience by adding fascinating history.Frankly I was shocked when they pointing out how even mathematicians have made questionable assumptions and taken some basic "truths" on faith.They show the beauty of math in the "Aesthetic Component" chapter. Ultimately the question that comes up again and again is the question of whether or not we can really know anything about time and space independent of our own experience to make an adequate foundation for a complete system in mathematics. If you have ever wondered about the world of mathematics and the personalities involved you might consider this book.If you are a mathematics teacher you should read this book. If you are a mathematician you could find it quite unsettling.
It contains eight chapters, each one broken up into many subtitles so if you do get bogged down in the mathematics it isn't for long. There are 440 pages.I'd like to see a much more complete glossary for people like me who need it. ... Read more

Product Description
This book, the first of a two-volume basic introduction to enumerative combinatorics, concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. Richard Stanley covers those parts of enumerative combinatorics with the greatest applications to other areas of mathematics. The four chapters are devoted to an accessible introduction to enumeration, sieve methods--including the Principle of Inclusion-Exclusion, partially ordered sets, and rational generating functions. A large number of exercises, almost all with solutions, augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. ... Read more

Customer Reviews (6)

Excellent!
I am what one of the reviewers called an arm-chair mathematician..

While I do not believe, that this book is suitable as a first introduction to combinatorics, it is a great book for anyone, who is interested in the subject and has had some prior exposure.
The formal mathematical prerequisites are quite minimal. The proofs are such, that after some thinking one can understand them - and they are always rigorous.
If one some occasions, the author would have given a short hint, instead of simply saying "it is easily seen" this would have made the book even more readable (but even then, after enough thinking one does see, albeit maybe not easily...)

All in all, very recommendable
(I am referring to volume 1 only, I did not read volume 2)

Very challenging, very deep
This is an excellent book on combinatorics, but it is quite difficult to understand--written for experts, not novices.The author often chooses a more general framework in which to present things, and this can make the material quite difficult to follow.But the rewards for the diligent reader are great.Occasionally I question how Stanley chooses to present a certain topic, but usually if I look closely enough, I see that there are deep reasons for his choice of notation or presentation.

Some of the material in this book is easier than others; some of it depends on earlier chapters, but some stands on its own.People interested in partially ordered sets and lattices may want to jump ahead to that chapter--much of this chapter stands on its own, and it is an excellent exposition of that topic, and I think somewhat easier to understand than the rest of the book.

The most precious thing about this book is that the author manages to provide several comprehensive frameworks for solving large classes of enumeration problems.Combinatorics seems a hodge-podge subject to many mathematicians, but Stanley manages to see it as a unified subject with a number of general theories and common techniques.This book is truly the only text I have ever read that has this perspective on the subject.

I would recommend this book only to someone who has a strong background in mathematics and wants a challenging text that can take them to a deeper level of understanding.Students of combinatorics may want to take this book out of the library and read the introductory pages; there are some particularly useful comments right at the beginning.As a final note, the exercises in this book are also helpful and of diverse difficulty levels--and Stanley classifies the exercises by their difficulty level.People who find this book difficult to follow may want still benefit from some of the easier exercises.Students wanting an easier-to-follow text might want to check out Cameron's "Combinatorics", or Wilf's "Generatingfunctionology".As a final note I would like to remark that this book is very reasonably priced, especially when you consider the wealth of material it contains.

A Masterpiece on Enumerative Combinatorics
I agree with the other reviewers.The book is a masterpiece on enumerative combinatorics.However, I am not so sure that it is a good book for a beginner.If you are a beginner, then you should read another book first, like John Riordan's book on "Combinatorial Analysis."Stanley's book is best suited for an advanced student who has a high level of mathematical mental maturity.The reason I say this is that in a few places Stanley's formalism, which is entirely appropriate for professional exposition, actually obscures the underlying simplicity of the mathematical ideas.We have all seen this in research papers, where a mathematician takes a trivial idea and "obsures" the underlying simplicity with too much formalism.However, for an advanced student, the book has a high density of important ideas and methods.

This is for people who likes to COUNT
Gosh! This is for people who count, what else does a combinatorist do? Before people dismiss me as somebody who don't know hoot about math: I took a class with Prof. Stanley (the author) in college, and I had actually used vol 1 as a text. The material is highbrow (I agree on the 'hardcore' math observation) but the main theme of the book is how to 'count' -- needless to say not in the sense of everyday counting, but in the sense that 'topology' is 'coffee-to-donut transformation' and 'analysis' is 'honors calculus'. You have to know how to count, and comfortable with combinatorial proof to actually learn from this. I like the fact that Prof. Stanley asks for combinatorial proof to some known results, marking them as unsolved -- he really elevates the status of combinatorial proof, a method many dismiss as 'handwaving'. There is a number given to each exercise, according to the level of difficulty: [1] for trivial, [5] unsolved. I saw a professor who worked in differential topology for 40 years refer to this book -- and first year undergrads thumbing through the pages for exercises marked [1] and [2] to solve in spare time. This is a book for all levels of mathematicians: I am sure even the armchair amateur mathematicians can grasp some of the materials after a hard day's thought. I dont see this book as any less than a definitive text on enumerative combinatiorics.

People who like to COUNT?!? People who like hard-core math.
There was an earier review that claimed this book is for "people who like to count." That's a little silly. This book is a rigorous math text. And it's glorious. It's probably my favorite text. But it's not light reading at all.

I spent a semester actively reading and working on this book with my advisor. I read this book and worked on research, 50/50 split on my time. I got through 2.5 of the 4 chapters, and I'm damn proud of myself. It's a great book, but if you didn't know that 'enumerative' was for "people who like to count", you probably want a different text. ... Read more