Book Description
This book provides the first clear, comprehensive, and accessible account of complex adaptive social systems, by two of the field's leading authorities. Such systems--whether political parties, stock markets, or ant colonies--present some of the most intriguing theoretical and practical challenges confronting the social sciences. Engagingly written, and balancing technical detail with intuitive explanations, Complex Adaptive Systems focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It provides a detailed introduction to concepts such as emergence, self-organized criticality, automata, networks, diversity, adaptation, and feedback. It also demonstrates how complex adaptive systems can be explored using methods ranging from mathematics to computational models of adaptive agents.
John Miller and Scott Page show how to combine ideas from economics, political science, biology, physics, and computer science to illuminate topics in organization, adaptation, decentralization, and robustness. They also demonstrate how the usual extremes used in modeling can be fruitfully transcended.
Customer Reviews:
Annie Wu -- Book #1.......2007-08-10
I am a purchasing agent who buys books for my faculty, and as far as I know, this faculty member is very impressed with this particular book.
The Emergence of Convergence .......2007-08-04
At the time of writing this review, this book isn't searchable through Amazon, that's too bad because if you're reading the reviews wondering if it's worth buying, just browsing through any page from the intro or appendix B would clearly resolve any remnant hesitation. This book is a must have for anyone even remotely interested in complex adaptive systems. Scott Page and John Miller dress the landscape and state of the art of computational social science, the issues are motivated from the ground up and the existing approaches to resolve them explicitly detailed, yet using clear and jargon free language. For example, descriptions of the many concepts repeatedly used in the scientific method (of CAS et al) such as ergodicity or optimization theory are refreshing and insightful, simply stuff you don't get from textbooks, but rather that one would learn over years of experience doing.
In summary, the authors are handing us an expert summary of literature and developments of a complex field in a concise, fun and delightful read, it would be a shame to miss it.
Book Description
Political Game Theory is a self-contained introduction to game theory and its applications to political science. The book presents choice theory, social choice theory, static and dynamic games of complete information, static and dynamic games of incomplete information, repeated games, bargaining theory, mechanism design and a mathematical appendix covering, logic, real analysis, calculus and probability theory. The methods employed have many applications in various disciplines including comparative politics, international relations and American politics. Political Game Theory is tailored to students without extensive backgrounds in mathematics, and traditional economics, however there are also many special sections that present technical material that will appeal to more advanced students. A large number of exercises are also provided to practice the skills and techniques discussed.
Book Description
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Customer Reviews:
Perhaps the best written written elementary book of logic.......2006-07-11
I bought the book just because my teacher of elementary philosophy in the university respected Tarski as a master of formal logic. It took me 26 years to get this book in my hands. What makes Tarski unique is, that he was a great logician and a great teacher, too.
I belive that there still are no better guide for a student who wants to understand logic, not just try to remember basic rules of it. The beauty of logic has never been exposed in a better way.
The fifth star was spared to a new, annotated edition of this classic among the field of logic. I hope I can find one some day.
TIMELESS CORE HOLDING IN ANY LOGIC LIBRARY.......2004-03-14
This timeless classic by one of the five greatest logicians of all time should be owned by anyone who cares about logic - especially at this illogically low price. The Greek philosopher Aristotle (384-322 BCE), the English mathematician George Boole (1815-1864), the German mathematician Gottlob Frege (1848-1925), the Austrian-American mathematician Kurt Gödel and the Polish mathematician Alfred Tarski (1901-1983) are considered to be the five greatest logicians of history. Today it is difficult to appreciate the astounding permanence of what is accomplished in the works of Aristotle, Boole, and Frege without seeing their ideas surviving in the work of a modern master. Of the two modern master logicians Tarski is by far the most suitable for this purpose since he was by far the one most interested in the articulation of the conceptual basis of logic, he was by far the one most interested in history and philosophy of logic, and he was the only one to write an introductory book attempting to explain his perspective in accessible terms. This book, together with Aristotle's Prior Analytics and Boole's Laws of Thought, should form the core of any logic library. All three are still in print and available in inexpensive paperback editions. Hackett publishes an excellent up-to-date translation of Prior Analytics by Robin Smith and Prometheus recently reprinted Laws of Thought with an introduction by John Corcoran.- Frango Nabrasa.
I will always keep it as a reference.......2002-07-14
This is one of the classic introductory mathematics books. When I was learning logic, I relied on it heavily, although it was not the text for the course. Over my years as a teacher, I have consulted it often and when I was working on a recent book on logic, there were very few days when I did not open it in search of an idea or clarification.
All of the basics of logic are covered in one of the most readable texts I have ever opened. Exercises are given at the end of each chapter, although no solutions are included. This is one of those books that will always be on my key shelves of reference works and it will no doubt receive a great deal of use.
Book Description
This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.
Customer Reviews:
This book is adequate but needs improvement.......2004-10-19
I have an older edition of this book. It is well-written and has a good selection of homework problems, but it lacks clarity and does not emphasize practice. Most proof books are good for learning the basics of proofs but aren't sufficient to do proofs in a specific area of math. My website focuses on how to practice doing proofs, fsc729.ifreepages.com.
John G.
Do not buy this book!.......2003-10-22
I had one of my math courses at Macalester College use this book in addition to the main textbook. It is one of the most boring readings in math ever. If you want a beginning book that would teach you how to do problem-oriented math, you had better consider George Polya's How to Solve It or consult a math teacher near you;-) In order to further underscore my poit, I will just say that it was not only I but the whole class that disgruntled against the book and we hated it so much that the professor does not use it anymore.
Big Improvement in Second Edition.......2002-02-15
Contrary to the review by the person from Louisiana I feel the second edition is better than the first. The typesetting is greatly improved, and there are a few new tools for your toolbag in the second edition.
As to the criticism that the second edition only has solutions for the odd numbered problems, the reviewer failed to mention that there are twice as many problems in the new edition and that all the problems from the first edition were carried into the second (along with their solutions). I found it more satisfying working through the second edition knowing that the problems were correctly solved - not because the answer matches the back of the book - but because the arguments are compelling and demonstrably correct.
I heartily recommend this book to anyone who feels mystified at the process of writing proofs.
Great Introduction to proofs.......2001-09-21
When I order this book it was not at all clear if I would like it, because of it low grades contain and examples. I was very surprised when I received it, because the book is written very clearly. The author make a great job when he explains the technics of proof. The exercises and the examples are definitely too easy for an undergraduate or graduate but you must take a look at it just for the explanation that the author gives for the technics of proof. The examples and exercises are mostly for high school students. The price of the book make it very affordable. It worth the price. I would recommend this book to anyone who want to introduce himself into the basic of proofs.
YOUR FIRST BOOK IN MATHEMATICS.......2001-06-04
YOU REALLY NEED THIS BOOK IF YOU ARE TRYING TO STUDY ABSTRACT MATHEMATICS BY YOURSELF OR WITH A TEACHER. LIKE ELECTRONIC ENGINEERING THAT LIKE TO DO MATHEMATICS THIS BOOK REALLY HELP ME TO UNDERSTAND HOW TO READ PROOFS AND MADE MY OWNS.
Book Description
Seminal work by great modern philosopher and mathematician focuses on certain issues of mathematical logic that Russell believed invalidated much traditional and contemporary philosophy. Topics include number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into the realm where mathematics and philosophy meet.
Customer Reviews:
A Joyful, Friendly Introduction to Bertrand Russell.......2007-09-07
Okay, I have to be honest- I was a little intrepid picking up this book, and it had nothing to do with Russell's math. I had this really dogmatic atheist friend who used to endlessly quote "Why I am not a Christian," and it put me off of Bertrand Russell.
This book is a joy. It's easy to read, interesting to think about, and inexpensive. Three virtues of math books that are hard to find in combination!
A Philosophy Reading Classic.......2005-09-11
A great book by a great philosopher. Of course, much of the material was for its time advanced and revolutionary now it is more of a classic introductory text given a basic preparation in critical reading and basic mathematics to sufficiently appreciate the nuance of his thought.
Good introduction To Mathematical Logic.......2005-07-08
Bertand Russell's "Introduction to Mathematical Philosophy" provides the reader with a great understanding of mathematical philosophy in a very simple and straightforward manner. Though this is an introductory work it may not be casual reading to all who endeavor to read it. Beginning with definition of numbers and sets it expands to provide definitions of simple and complex and builds to provide a good understanding of the logic behind mathematics. While much of what is spoken about may seem very elementary the logic behind certainly is not. While the book is not nearly as expansive ad "Principia Mathematica" it is a good distillation of the bigger work and provides a great introduction to anyone wishing to explore that work. I recommend this book to anyone interested in formal logic and believe that it should be in the required reading for any formal logic introductory class. Further anyone interested in reading Goedel's work's which expand on Russell's work needs at least to read this work prior to Goedel. I find this book to be very succinct and readable and ultimately very worthy of the effort it takes to read.
-- Ted Murena
Substantial effort required. Careful reading necessary........2003-10-02
Bertrand Russell and Alfred North Whitehead created the monumental work Principia Mathematica (1910-1913), the ambitious and comprehensive effort to provide a detailed reduction of the whole of mathematics to logic. In 1919 Russell was jailed for antiwar protests and while in prison he wrote Introduction to Mathematical Philosophy, a seminal work in the field for more than 70 years.
I have devoted substantial time and effort to this 200 page book. Unless you are a student of logic, this book may not be for you. I suggest alternatives below.
I stayed the course and worked my way through each chapter, sometimes backing up, and often repeating several chapters before advancing again. Bertrand Russell is admired for his eloquence and style. Nonetheless, I can assure you that a methodical reading will require much effort.
I was forewarned. At one point a friend and colleague, a previous professor of mathematics at Texas A&M, expressed surprise that I was tackling this particular book. He considered Russell's work to be dated and not particularly easy going. I continued plodding along.
Russell begins with familiar ground, Peano's effort to derive the entire theory of natural numbers from five premises and three undefined terms (primitives). Russell demonstrates why Peano's approach fails to serve as an adequate basis for arithmetic.
In chapter 2 Russell introduces the work of Frege, who first succeeded in logicising arithmetic. We are led to a definition of number: the number of a class is the class of all those classes that are similar to it, or more simply, a number is anything which is the number of some class.
The third chapter introduces properties termed hereditary, posterity, and inductive. After some effort, we define the natural numbers as those to which proofs by mathematical induction can be applied. We also learn that mathematical induction is not valid for infinite numbers.
Russell now addresses the serial character of natural numbers, a characteristic involving finding or construction of an asymmetrical transitive connected relation.
In Chapters 5 and 6 Russell distinguished between cardinal numbers (the earlier definition of number) and relation numbers (also called ordinal numbers). I had difficulty with the interplay between the relations aliorelative, transitive, asymmetrical, square, and connected. For example, an asymmetrical relation is the same thing as a relation whose square is an aliorelative.
In chapter 7 I was initially surprised by Russell's assertion that the common belief that the complex numbers include the real numbers, the real numbers include the rational numbers, and the rational numbers include the natural numbers is erroneous and must be discarded.
The next thee chapters - infinite cardinal numbers, infinite series and ordinals, and limits and continuity - were more difficult. Eight more chapters follow.
Introduction to Mathematical Philosophy is philosophy, logic, and mathematics. It investigates the logical foundations of mathematics. It requires very careful reading.
I can suggest alternatives. Howard Eves in his delightful Foundations and Fundamental Concepts of Mathematics offers an excellent chapter titled Logic and Philosophy that compares three approaches - Logicism (Russell and Whitehead), Intuitionism (Brouwer and Heyting), and Formalism (Hilbert's Grundlagen der Geometrie). He also provides in an appendix a short overview of Godel's theorems (1931) which demonstrated that no complete or consistent axiomatic development of mathematics is attainable.
I also highly recommend Godel's Proof, a short book by Ernest Nagel and James R. Newman. Godel's Proof demonstrates that Russell and Whitehead's Principia Mathematica must necessarily be incomplete and inconsistent.
As all Russell's writings, a masterwork........2002-07-09
A magnificent, fantastic and very readable introduction to the highly abstract world of formal logic and the foundations of mathematics. Lord Russell is not only one of the greatest logicians of all time, but he is also an astonishing writer, blessed with an elegant, heavenly precise concision of style and sharpness of argumentation.
Book Description
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Customer Reviews:
More math books should be written like this one........2006-07-15
I full concur with Greenberg's review. Assimilating Potter's book is also much easier if one has had a prior introduction to mathematical logic and axiomatic set theory.
Potter sets out an axiomatic set theory he calls ZU, whose axioms are: there is a ground level of sets, every level has a successor level, Infinity, and Reflection (a schema). These axioms are a perspicuous embodiment of the iterative conception of sets and the related hierarchical ontology. Potter then shows that these axioms achieve, in a fairly relaxed way, all we would want these axioms to achieve. This theory should be given an important place at the high table of foundational mathematics.
Set theory is inherently philosophical because its true subject matter is patterns in the human mind and human sensory experience (in this respect, I concur with Lakoff and Nunez). Potter is a bracing philosophical read, but be aware that there is a good deal more to the philosophy of set theory and foundational math than he lets on. His ample bibliography nicely shows the way to more reading in this vein.
Some intellectual history. In the 1960s, the mighty Dana Scott began working on a new axiomatization of set theory, grounded in type theory and the iterative conception. This work culminated in a talk he gave at a 1971 conference, whose proceedings were published in 1974. Scott was also supposed to be working on a monograph on set theory with Montague, who died in 1971, and Tarski, who died in 1983. The monograph will never appear, and Scott never fleshed out the intriguing proposals he published in 1974. Potter's book is the belated bloom of Scott set theory.
Greenberg is right about Mendelson's intro to NBG; it is a good introduction to the mechanics of axiomatic set theory, independently of Potter's book. Potter is also not as well disposed to Quinian set theory as I am.
I am puzzled by Potter's claim that Skolem arithmetic (just multiplication over the naturals) is finitely axiomatizable. Cegielski (1981) firmly asserts otherwise.
Unique blending of mathematics and philosophy.......2004-11-24
I believe one has to have some familiarity with logic and set theory in order to fully appreciate this wonderful book. Granting that, reading it was the first time I have ever read a mathematics book that I could hardly put down, it was so fascinating.
When I was an undergraduate, a course in naive set theory (similar in content to Halmos' classic) persuaded me to become a mathematician. But when I asked my instructor to precisely define what a 'property' of a set was, a notion that was used in the Axiom of Separation, he evaded the question as too philosophical. Much later, when I studied mathematical logic, I found a precise definition.
Michael Potter does not seem to evade any philosophical questions about set theory. The answers he proposes are given from various points of view so the reader can clearly see the differences and possibly choose the one most congenial: platonism (internal, uncritical, limiting case), constructivism, formalism (pure, postulational). I couldn't pin down exactly what is Potter's point of view except that he is not a strict formalist or a strict constructivist or an uncritical platonist.
His development of the purely mathematical part of set theory is very elegant, especially his axiomatization of the levels of the set theoretical hierarchy. Unlike most strictly mathematical texts, Potter explains why, at each major stage, he is doing what he is doing. In three appendices he also contrasts his approach with the traditional ones. I felt he did not give enough credit to the simplicity and elegance of NBG theory, so well presented in Mendelson's classic text; he is averse to introducing classes as well as sets.
His treatment is replete with fascinating history. He does not hesitate to discuss advanced results which he cannot prove in a treatment at this level, and he provides ample references if the reader is interested in pursuing them.
I am still puzzled by the nature of second order logic, which he says "decides" the continuum hypothesis, which is an undecidable statement in first order logic. I wish he had explained that more.
This is a book that I intend to re-read and to discuss with colleagues who are expert in the field. Very highly recommended.
Book Description
Designed to make logic interesting and accessible—without sacrificing content or rigor—this classic introduction to contemporary propositional logic explains the symbolization of English sentences and develops formal-proof, truth-table, and truth-tree techniques for evaluating arguments. An accompanying computer tutorial program, PropLogic, is available on CD-ROM in two versions: one version can be installed and run off a hard drive; one (identical) “portable” version can be run off the CD-ROM itself (allowing students/instructors flexibility on when/where they use the program). An appendix in the text describes program details. Tutors readers on formula construction, symbolization, formal proofs, full and brief truth tables, and truth trees. Also provides additional practice exercises. Content organized around natural-deduction formal-proof procedures, truth tables, and truth trees. Gradual presentation of logical statement connectives. Shows students how to symbolize sentences containing the connective and how to use proof rules involving that connective before introducing additional connectives. Examples of actual arguments similar to those readers encounter, and to which they can readily relate. Draws examples and exercises from newspapers, magazines, television, books, textbooks, term papers, posters, comic strips, television programs, films, records, and conversations. Increases students' awareness of the arguments they read and hear every day. Extensive exercise sets throughout provide solutions to about one-quarter of the exercises (in an appendix). Provides ample opportunities for assignments and practice.
Customer Reviews:
The most user-friendly book for Propositional Logic.......2004-10-10
This is a easy to use text for learning the basics of Propositional Logic. The rule set is simple and symmetrical, easy to use. The CD gives important feedback to the student and contains the answers to almost every exercise in the book plus additional practice exercises. I would recommend this textbook to any professor wishing to teach Propositional Logic.
Book Description
Mathematical Olympiad competitions started in Hungary at the end of the nineteenth century, and are now held internationally. They bring together able secondary school pupils who attempt to solve problems which develop their mathematical skills. Olympiad problems are unpredictable and have no obvious starting point, and although they require only the skills learnt in ordinary school problems they can seem much harder. The Mathematical Olympiad Handbook introduces readers to these challenging problems and aims to convince them that Olympiads are not just for a select minority. The book contains problems from the first 32 British Mathematical Olympiad (BMO) papers 1965-96 and gives hints and outline solutions to each problem from 1975 onwards. An overview is given of the basic mathematical skills needed, and a list of books for further reading is provided. Working through the exercises provides a valuable source of extension and enrichment for all pupils and adults interested in mathematics.
Customer Reviews:
The Mathematical Olympiad Handbook: An introduction to problem solving based on the first 32 British Mathematical Olympiads 1965.......2007-01-12
A very good problem book for training mathematical olympiad.
Very usefull book........2001-08-29
I teach students, a mathematical olympic team, and this book will help them to get the training they need in order to have more medalls and achievements in their carreers. It has everything they need to do their exams and practice.
Excellent introduction to problem solving.......2001-06-03
The last time I competed in a mathematical competition was in elementary school. So when I recently picked up and tried to solve some old Olympiad and Putnam questions I was dumbfounded, to say the least. Then I discovered "The Mathematical Olympiad Handbook." This book is an excellent intro to problem solving. It is an immense help in dealing with the frustration of problems that will not yield. No solutions are given-- only outlines to the solutions(which you should only read part of if you get stuck, as the outlines will easily lead to a solution). This structure was an excellent choice as it gives novice problem solvers a chance to solve problems on their own with a little help if they need it. Highly recommend!
[people new to problem solving should also check out "The Art and Craft of Problem Solving" by Paul Zeitz]
A must-buy for problem-solvers........1999-01-06
This book has proven: The olympiad problems are not so hard as they appears. For every problem, there is a valuable solution outline ,teaching us how to attack it in a natural way. Furthermore, here is a good list of reference books.
Book Description
This is the first book to systematically survey new areas of substructural logics. This book is geared to introduce the topic to advanced students. An Introduction to Substructural Logics covers the area of logic that is crucial to developments in computing, philosophy and linguistics.
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