Buy used:
$6.21
FREE delivery July 2 - 8. Details
Or fastest delivery July 1 - 3. Details
Used: Very Good | Details
Sold by ThriftBooks-Phoenix
Condition: Used: Very Good
Comment: May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less
Access codes and supplements are not guaranteed with used items.
In stock
Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Follow the authors

John L. Casti
Follow
John L. Casti
Follow
Something went wrong. Please try your request again later.

Five Golden Rules: Great Theories of 20th-Century Mathematics--and Why They Matter First Edition

by John Casti (Author)
4.1 4.1 out of 5 stars 22 ratings
See all formats and editions
Praise for Five Golden Rules

"Casti is one of the great science writers of the 1990s. . . . If you'd like to have fun while giving your brain a first-class workout, then check this book out."-Keay Davidson in the San Francisco Examiner.

"Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." -Christian Science Monitor.

"Merely knowing about the existence of some of these golden rules may spark new, interesting-maybe revolutionary-ideas in your mind." -Robert Matthews in New Scientist (United Kingdom).

"This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." -Ben Bova in the Hartford Courant

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." -Rudy Rucker, author of The Fourth Dimension.

"With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." -John Allen Paulos, author of A Mathematician Reads the Newspaper.
Previous slide of product details
  1. ISBN-10
    0471193372
  2. ISBN-13
    978-0471193371
  3. Edition
    First Edition
  4. Publisher
    Wiley
  5. Publication date
    September 22, 1997
  6. Language
    English
  7. Dimensions
    6.12 x 0.67 x 9.31 inches
  8. Print length
    256 pages
  9. See all details
Next slide of product details
Amazon First Reads | Editors' picks at exclusive prices

Customers who bought this item also bought

Page 1 of 1 Start overPage 1 of 1
Previous page
  1. Casti Five More Golden Rules
Next page

Editorial Reviews

From the Back Cover

Praise for Five Golden Rules

"Casti is one of the great science writers of the 1990s. . . . If you'd like to have fun while giving your brain a first-class workout, then check this book out."-Keay Davidson in the San Francisco Examiner.

"Five Golden Rules is caviar for the inquiring reader. . . . There is joy here in watching the unfolding of these intricate and beautiful techniques. Casti's gift is to be able to let the nonmathematical reader share in his understanding of the beauty of a good theory." -Christian Science Monitor.

"Merely knowing about the existence of some of these golden rules may spark new, interesting-maybe revolutionary-ideas in your mind." -Robert Matthews in New Scientist (United Kingdom).

"This book has meat! It is solid fare, food for thought. Five Golden Rules makes math less forbidding and much more interesting." -Ben Bova in the Hartford Courant

"With this groundbreaking work, John Casti shows himself to be a great mathematics writer. Five Golden Rules is a feast of rare new delights all made perfectly comprehensible." -Rudy Rucker, author of The Fourth Dimension.

"With the lucid informality for which he has become known, John Casti has written an engaging and articulate examination of five great mathematical theorems and their myriad applications." -John Allen Paulos, author of A Mathematician Reads the Newspaper.

About the Author

JOHN L. CASTI is a resident member of the Santa Fe Institute and a professor at the Technical University of Vienna. He is the author of four other trade books, Would-Be Worlds (Wiley), Paradigms Lost, Searching for Certainty, and Complexification, as well as the two-volume Reality Rules, a text on mathematical modeling (also published by Wiley).

Product details

  • Publisher ‏ : ‎ Wiley; First Edition (September 22, 1997)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 256 pages
  • ISBN-10 ‏ : ‎ 0471193372
  • ISBN-13 ‏ : ‎ 978-0471193371
  • Item Weight ‏ : ‎ 11 ounces
  • Dimensions ‏ : ‎ 6.12 x 0.67 x 9.31 inches
  • Customer Reviews:
    4.1 4.1 out of 5 stars 22 ratings

About the authors

Follow authors to get new release updates, plus improved recommendations.
Previous page
  1. John L. Casti

    John L. Casti

    Brief content visible, double tap to read full content.
    Full content visible, double tap to read brief content.

    One of the pioneers of complexity science and systems theory, John L. Casti, Ph.D., is Senior Research Scholar at the International Institute for Applied Systems Analysis, where he heads an initiative on Extreme Events in Human Society. He worked for many years at the Sante Fe Institute and The RAND Corporation, as well as serving on the faculties of Princeton, the University of Arizona, and New York University. A former editor of the journal Complexity, Casti has published nearly 20 volumes of academic and popular science and received his Ph.D. in mathematics from the University of Southern California. He lives in Vienna, Austria.

    See more on the author's page
  2. John L. Casti

    John L. Casti

    Brief content visible, double tap to read full content.
    Full content visible, double tap to read brief content.

    John Casti is an internationally-recognized complexity scientist and best-selling popular science author, mathematician, and entrepreneur. He has written more than 120 scientific articles, seven technical monographs and textbooks on mathematical modeling, and sixteen books on popular science.

    His book, Alternate Realities, was awarded the Association of American Publishers prize. Prey for Me is his first work of fiction.

    See more on the author's page
Next page

Customer reviews

4.1 out of 5 stars
4.1 out of 5
We don’t use a simple average to calculate the overall star rating and percentage breakdown by star. Our system gives more weight to certain factors—including how recent the review is and if the reviewer bought it on Amazon. Learn more
22 global ratings

Top reviews from the United States

Kyle Maxwell
5.0 out of 5 stars Understandable but not dumbed down
Reviewed in the United States on March 1, 2001
Verified Purchase
Casti's text focuses on five key mathematical theories from the 20th century; this is actually somewhat misleading, since 4 of them are actually proved theorems. It's an interesting survey of applied mathematics; a number of sub-disciplines are covered here.
He does an excellent job of bringing the math down to a reasonable level without dumbing it down. Most of the book can be understood with simple logic and algebra; truly understanding a few of the theorems (not just appreciating them) does take a little calculus. Knowing some more advanced math (like topology) helps, but a reasonably mathematically-inclined person with less formal education will be able to follow it just fine. I'd like to see more popular math books at this level; this is somewhere between the level of Paulos' series of books ("Innumeracy" et al) and an undergrad maths textbook.
It's interesting to see a side of mathematics not often covered in high school maths courses. I really recommend this book to anyone with more than a passing interest in mathematics; it may even rejuvenate your interest to a more active level.
16 people found this helpful
Helpful
 Report
D. H. Maxwell
5.0 out of 5 stars golden rules is golden
Reviewed in the United States on August 19, 2005
Verified Purchase
this book has a lot to offer. i have gone through it several times and even discussed the ideas with family.
Helpful
 Report
A.Luther
3.0 out of 5 stars Some Mathematical Knowledge Is Helpful
Reviewed in the United States on December 17, 2018
Casti covers five significant theories of mathematics coming from the fields of Game Theory, Topology, Singularity Theory, Computational Theory and Optimization Theory. Casti illustrates the theories very succinctly, introducing each theory by using examples of how we might use the theorem to solve problems in the practical world. If you don't know about the Brouwer Fixed-Point Theorem in Topology, Morse's Theorem (or Catastrophe Theory) in Singularity Theory or the so-called "Halting Problem" in the theory of Computation, this book is a nice introduction. I single out these three areas (as opposed to the other two areas) because I find them to be the most fascinating. For example, the Fixed-Point Theorem tells us that if we take a continuous map, such as a straight, flat piece of paper and screw it up (twist, stretch and crumple) into a mangled ball, without tearing it, there will always be some point (X) on this screwed up piece of paper that is positioned at the exact same point as it was originally, when the piece of paper was straight and flat. An equivalent theorem in algebraic topology is the Borsuk-Ulum theorem which maps a pair of antipodal points on a sphere of N-dimensions to a single point in Euclidean N-space. These abstract findings from topology have real world implications. The Borsuk-Ulum theorem result demonstrates that there is at least one set of opposite (antipodal) points on a sphere with the same set of values for a particular variable. Surprisingly, this can show us empirical facts about the world. For example. the theorem results in the realisation that the Earth (a sphere) must have a least one pair of antipodal points on its surface that possess the exact same temperature. Less empirical, but more philosophically, the Fixed-Point Theorem also tells us that if time travel were possible, there would be at least one pathway in which one could travel backward in time so that this backwards-in-time travel was self-consistent with our more familiar, future directed time travel, thus preventing temporal paradoxes from ensuing. The section of Morse's Theorem touches on Catastrophe Theory, a beautiful theory from algebraic geometry which models how sudden folds, bends or cusps in physical structured can be modelled algebraically by non-linear equations. More abstractly, these "Catastrophe" types can be also be used to model more abstract phenomena such as changes in psychological variables. Casti gives a brief example of using Catastrophe Theory to model how laughter works as a psychological function of both meaning and interpretation. Casti also covers the Halting Problem as developed in the Turing-Church thesis and elaborated on by mathematician Gregory Chaitin. The Halting Problem says that there are no formal computational systems (computers), that when given a set of inputs, will halt after successfully carrying out its program and also know in advance if its condition for halting can be satisfied. Casti briefly touches on the Halting Problem and arguments made by some philosophers and physicists that the Halting Problem and its mathematical- logical equivalent - Godel's Theorem - stand as proof that computers can't do what the human mind can do. This is a complex (and interesting) subject, and Casti provides us with further readings if you want to explore these issues deeper. Let me add one final speculative idea that flashed to my mind as I was reading this book and thinking of the different topics outlined. Imagine a computing machine that was topologically equivalent to a system that satisfied the Fixed-Point Theorem with regards to time travel? Such a machine would appear to use its output (that occurs when the machine has halted) as its input. So the machine only begins running its program when the program halts! Such a Godelian Paradox makes no sense in terms of everyday classical computing with Turing Machines or your digital computer, but what if the human mind (or brain) was indeed such a paradoxical device? If we had such a machine we could not tell what was its input function and what was its output function. Maybe this is the very problem that faces modern science and its attempt to understand the human mind as a kind of software running on the human brain? The idea that human minds or consciousness are exactly this kind of paradoxical self-referential system is consistent with the idea put forward by Douglas Hosfstadter that consciousness is a kind of "Strange Loop."
3 people found this helpful
Helpful
 Report
randy patton
4.0 out of 5 stars Unique source for exposition on mathematics
Reviewed in the United States on March 12, 2013
Verified Purchase
Casti really knows his stuff and is able to convey the underpinnings and applications of 5 interesting and fundamental topics. Not for the casual reader but for someone with a love of mathematical concepts and not just glorified bookkeeping. Though apparently well reviewed and edited by colleagues, Casti's explanations and examples occasionally lack clarity and can cause confusion.
Helpful
 Report
Michael R. Chernick
5.0 out of 5 stars contemporary mathematics but may be too technical for the lay person
Reviewed in the United States on January 24, 2008
Casti writes about 20th Century mathematics for general audiences. As he states, he uses five mathematical theorems that were proven in the 20th Century and shows how they relate to general theory and application. He gives a reasonable set of criteria to show the reader how these five theorems emerge out of the millions of theorems that mathematicians have proven in the mathematical literature of the 20th Century.
He also explains why all the theorems were developed in the first half of the century. Basically, it takes time for the impact and value of a theorem to take effect. While there may be many theorems developed in the later half of the century that will eventually prove to be more valuable than some of the five golden rules, we may not know this clearly for some time.

There seems to be a preference for theorems related to operations research. For example the Brouwer fixed point theorem from topology has applications to game theory. Von Neumann's minimax theorem was developed for game theory and its application to military strategy and economic problems. This one also falls into the realm of operations research. Finally Dantzig's simplex method provides an algorithm to solve linear programming problems and some extensions. This is also clearly in the realm of optimization problems in operations research.

Turing's halting theorem is also presented. This deals with important questions about the limitation of computing machines as it relates to mimicking human intelligence.

Many of the ideas are difficult to present in lay terms and there is a lot of development to try to make the theory understandable to the reader. But it is difficult to do these subjects justice. Casti's emphasis is clearly in applied mathematics and he excels at showing the impact of the results on our society.
28 people found this helpful
Helpful
 Report

Top reviews from other countries

Mr. David C. R. Hancock
5.0 out of 5 stars very good. I especially enjoyed the section dealing with Rene ...
Reviewed in the United Kingdom on April 6, 2018
Verified Purchase
Very, very good. I especially enjoyed the section dealing with Rene Thom's work on morphology.
Report
Marie-Christine Beaudoin
5.0 out of 5 stars Five Stars
Reviewed in Canada on December 21, 2016
Verified Purchase
Item arrived within 2 days and as described.
Report
Jayant Yadav
5.0 out of 5 stars Spotless
Reviewed in the United Kingdom on November 28, 2015
Verified Purchase
Received a hardbound perfect copy in quick time
Report
I. Viehoff
2.0 out of 5 stars Fails in its mission to make difficult concepts accessible
Reviewed in the United Kingdom on August 3, 2001
Verified Purchase
To make difficult concepts accessible, inevitably you have to be economical with the truth. You have to remain aware of what your audience does and doesn't know, and what lies you have told. Maths teachers do this at every level, so there are some people who are well practised at it.
I had to reach for graduate-level textbooks to work out what Casti was trying to tell me. It ought to be the other way around.
This book is written at a level for the scientifically/mathematically literate reader. So he cannot be allowed to get away with the sloppiness I will now demonstrate.
Casti discusses the concept of convexity in relation to topological spaces, without telling us that convexity is an algebraic or geometric property, not a topological property. Moreover the non-topological nature of convexity is plain to the reader who has understood what went before, since straight lines are not an admissible concept in "rubber sheet" topology. The reader with a little mathematical education (many of the target audience) will further realise that convexity is a property of sets within a larger space, not of a space itself, so to refer to a "convex topological space" is a contradiction in terms.
To illustrate convexity (surely unnecessary for the target readership), he draws some convex and non-convex sets. But some of the non-convex sets plainly possess the Brouwer property that is asserted only for convex sets. There is no explanation of this contradiction. He then asserts that the Brouwer property is held by the surface of a sphere, a set which is non-convex and cannot even be topologically deformed to a convex set.
If the reader was to gain any insight into the Brouwer property, then surely it is to obtain an intuitive understanding of why Brouwer's theorem is true for the surface of a sphere but false for a ring. I would love to understand this. Casti does not even try.
The problems illustrated here are present, to a greater or lesser extent, throughout the rest of the book.
15 people found this helpful
 Report