Book Description
Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.
Customer Reviews:
Lattice Theory Uber Alles?Begin here.......2005-03-27
A set with, at minimum, one binary operation is a groupoid. If a situation involves an equivalence relation or some sort of symmetry, some sort of groupoid applies. If the set has, at minimum, two binary operations, and one operation distributes over the other, you have a ringoid. Ringoids, which include the real field we all use every day, tell us much about number systems.
Let there be a groupoid. Denote its single binary operation by concatenation. Let that operation commute and associate. So far, we have a commutative semigroup. Now add idempotency, so that AA=A. With that seemingly trivial axiom we turn a corner, farewell the groupoids, and find ourselves among the semilattices.
Now let there be two binary operations, + and *, that commute and associate. Moreover, assume that A*(A+B) = A = A+(A*B). A*A=A=A+A is now an easy theorem. What you now have is a lattice, of which the best known example is Boolean algebra (which requires added axioms). More generally, most logics can be seen as interpretations of bounded lattices. Given any relation of partial or total order, the corresponding algebra is lattice theory. Nevertheless, far fewer mathematicians specialize in lattices than in groupoids and ringoids.
Davey and Priestley has become the classic introduction to lattice theory in our time. Sad to say, it has little competition. It is a bit harder than I would prefer, and the authors do not say enough about the value of lattice theory for nonclassical logic. Their book is a classic nonetheless, and here's hoping that Gian Carlo Rota was right when he said that the 21st century shall be the century of lattices triumphant.
Lattice theory is largely due to the work of the American Garrett Birkhoff, writing in the 1930s. He gets my vote for the
greatest American mathematician of all time.
Excellent introduction and something more.......2000-03-29
This book presents an excellent introduction to the subject, but also goes beyond that, presenting with a fair amount of the detail the theory of Priestley representation. The excercises start at the basic level of checking the understanding of definitions, allowing the reader to build confidence out of the practice. The fact that Priestley herself co-authored it is definitely a plus.
Book Description
From the reviews: "The 2nd (slightly enlarged) edition of the van Lint's book is a short, concise, mathematically rigorous introduction to the subject. Basic notions and ideas are clearly presented from the mathematician's point of view and illustrated on various special classes of codes...This nice book is a must for every mathematician wishing to introduce himself to the algebraic theory of coding." European Mathematical Society Newsletter, 1993 "Despite the existence of so many other books on coding theory, this present volume will continue to hold its place as one of the standard texts...." The Mathematical Gazette, 1993
Customer Reviews:
Excellent book from mathematical standpoint.......2005-02-20
Very good intro textbook. It gives short, detailed preps to various coding areas (linear, cyclic, convolutional). The biggest advantage this book has is that it does not throw at You tonnes of unnecessary info (like many other thick books do). That is, it assumes reader has some basic understanding of algebra and probability theory. Let's say, it gives good theoretical presentation such that the reader gets good theoretical understanding, it is not example-based.
Book Description
This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.
Customer Reviews:
Not bad.......2007-05-18
We used this for a Computer Science class on Graph Theory, and I remember more than one student complaining about the book. Generally speaking, what people found most disconcerting about the text was its level of abstraction, and "lack of motivation" for the theorems provided. In my experience, these complaints are frequently leveled by non-mathematicians at books that are clearly NOT non-mathematical; West's book falls into this category. This is, first and foremost, a book for mathematicians.
As pointed out by other reviewers, the book isn't perfect. There are a lot of errors, although you can obviously deal with these if you read the errata. West also has the habit of sometimes presenting a theorem completely out of the blue, which can cause some confusion. That said, the book does a very good job overall. Graph theory is an exceptionally beautiful subject, but it's easy to obscure that in a theorem/proof/theorem didactic haze. West has an agenda, and therefore the book has a discernible structure, which brings out the beauty of the area. The chapters on coloring and planar graphs are particularly strong, although the most interesting chapter for me was the one on additional topics; the sections on matroids, Ramsey theory, random graphs and spectral graph theory, while far from comprehensive, provide good introductions. Another strong aspect of the book are the exercises; these range from very easy to very difficult, the latter being from major papers in graph theory. The hints section at the end of the book is quite helpful here.
Overall, a very good book. I didn't know anything about graph theory before I started reading it, but I had a professor to help me through the rough spots, so perhaps it's not exactly ideal for self-study. If you've been exposed to the basics before though, it's definitely worth taking a look at.
Good middling book.......2005-10-11
The treatment is logically rigorous and impeccably arranged, yet, ironically, this book suffers from its best feature: it is comprehensive. As a book becomes more encyclopedic, it becomes less useful for pedagogy. Introduction to Graph Theory is somewhere in the middle. It is an adequate reference work and an adequate textbook. Steering a middle course, the book is bound to dissatisfy people with specific needs, but readers needing both a reference and a text will find the book satisfying.
If you buy it for pedagogical purposes, be prepared to consult other works for a more intuitive approach. Introduction to Graph Theory presents few models, relying instead on logically rigorous development. Personally, I'm for both, but that takes up space, meaning less material can be covered.
I'm glad I bought the book, and I will keep it for a future reference.
Graph lovers' book.......2005-05-26
West is enthusiastic about graph theory. I do not recommend this book for independent study, nor would I recommend it for a first-time student of graph theory. It is called "Introduction to Graph Theory", not because it is an appropriate introductory text for new students, but because it covers a broad area of the subject. I recommend it for a student who has read at least one lower-level introductory text and would like to round out their knowledge of graph theory in a more in-depth way.
I have two problems with this book. They both stem from the fact that it reads more like a collection of journal articles than like a cohesive text book. One is that his notation is very specific--he does not always use the most common form of notation, and this means that dipping into the book is difficult. The second problem for me is that West defines many things that I do not feel need defining. Rather than using a short description of a certain type of graph whenever he refers to it, he will give it a label. Again, this makes dipping into his text rather difficult, especially since many of the things he defines are not generally given a definition. Both of these would be perfectly reasonable for a journal article, but seem rather out of place in a large textbook--his definitions particularly clutter up his work. Perhaps West is more used to writing papers than textbooks.
Having said that, West is very knowledgeable and enthusiastic. His exercises are wonderful, marked with a (-) for easy, a (+) for difficult, a (!) for particularly instructive, and a (*) for problems based on optional material. Several of the (!) problems I have worked required me to actually look up the paper that they are based on for the final solution--which is possible due to his excellent citations. His index of works cited is an education in itself, and any student wishing to pursue a specific area in greater depth will find his book an wonderful gateway.
My perspective: I am an undergraduate student doing summer research in graph theory, working under a professor.
Just a pile of theorems without much insight.......2004-12-04
This book is an average book on graph theory. Although the author is an authority in the field, he seems to just have collected a bunch of theorems and put them together "a la" copy-and-paste, without filling up the gaps with useful insights. Intuition is always the key on a book that claims to be introductory, and this book lacks a lot of that. Probably useful as a reference book, but again not as "Introduction to Graph Theory" (and to be used as a "handbook of graph theory" it would need much more material.
Pretty good.......2004-03-03
Level of the book: 3rd-4th year undergrad or 1st-2nd year grad (pretty big range).
Don't let other reviews fool you. This book does an excellent job covering the material at hand, especially given the task West set out to achieve. The book basically stands alone thanks to thorough appendices and a fair amount of examples, plus lots of problems (mostly proofs). Because this material is proof-based, I cannot suggest that this book could stand alone, but that someone else should review problems and such.
When I first was reading this book, I ignored the appendices, and that was my downfall. Once I started using all the tools in this book, things started coming together. Because of the intricate design, I would recommend this book only to people who are serious about a thorough introduction to graph theory. That is, actually proving many of the theorems that play a central role in this introduction. For a simple introduction to concepts, I would recommend Trudeau's book, "Introduction to Graph Theory," which is a good read and introduces a few of the ideas and definitions of graph theory, but does not focus on proofs.
My only major quarrel with this book is that it is completely void of color! This would be EXTREMELY useful in this book because many of the diagrams are complicated and different color labels would make things much clearer (instead of bolding lines and such). The increased price of the book would certainly be worth the clarity from color. There are also some typos throughout the book, but none too major (that have been noticed).
Overall, I would highly recommend this book over any other, but consider waiting until an edition with color comes out.
Customer Reviews:
Do not buy this book........2007-05-20
This book is very poorly written and lacks any kind of order in which to study the chapters. The explanations of theorums and formulas are just not enough. Another thing that I do not like about this is that the section problems want you to work out precise mathematical concepts that were not explained in the relevant section, thus making you have to re-read the section several times over, and even then it is still not enough. I have completed Calculus II and that textbook was nowhere near as difficult to understand than this one. If you want to get a general idea of what Discret Mathematics is or want to do self study, then get this book. But in my opinion, avoid this book at all cost. Pun intended.
More rigorous and lengthy than other discrete texts, too much for my purposes.......2007-01-17
I will once again be teaching discrete mathematics this summer, so I am searching through the mathematical publishing pathways looking for a suitable textbook. Therefore, that is the context within which I examined this book.
It certainly is the largest discrete book that I have encountered; including the appendices and problem solutions, there are over one thousand pages. Grimaldi has tried to include every topic that falls under the discrete mathematics tent. Therefore, this is a book that could be used for a two semester sequence in discrete mathematics.
When examining discrete books for possible adoption I start with the simple premise that logic, set theory and functions and relations must be covered very early. In my ideal world, they are the first three chapters. Set theory and relations are so fundamental a part of other areas that I am surprised when authors don't cover them first. The first chapter in this book covers basic counting principles. While this doesn't break too much from my ideal sequence, I see no overpowering reason why fundamental counting should be before set theory. Given that the rules of counting for sums and products can easily be related to sets, there is a strong justification for putting set theory first.
The coverage is split into four parts, the first of which consists of the seven chapters:
*) Fundamental principles of counting
*) Fundamentals of logic
*) Set theory
*) Properties of integers: mathematical induction
*) Relations and functions
*) Languages: finite state machines
*) Relations: second time around
In my opinion, the order of the topics should be:
*) Fundamentals of logic
*) Set theory
*) Relations and functions
*) Relations: second time around
*) Fundamental principles of counting
*) The principle of inclusion and exclusion (currently chapter 8)
*) Properties of integers: mathematical induction
*) Generating functions (currently chapter 9)
*) Recurrence relations (currently chapter 10)
*) Languages: finite state machines
The current chapters 8 through 10 make up part two of the book.
Part three is graph theory and applications and part four is modern applied algebra. I have no issues with the order here. The chapter headings for the fourth part are:
*) Rings and modular arithmetic
*) Boolean algebra and switching functions
*) Groups, coding theory and Polya's method of enumeration
*) Finite fields and combinatorial design
With this part being nearly two hundred pages in length, the coverage is extensive.
Grimaldi takes a more rigorous approach than many other authors of discrete texts, while I did not examine every single theorem, I did look at a lot of them and all were accompanied by a proof. The exposition is clear, there are many worked examples, a large number of exercises and solutions to the odd-numbered exercises are included. A summary and historical review of the topic follows each section.
If we offered a two course sequence in discrete mathematics, then I would consider adopting this book. Such a situation would allow me to present the material at a higher level of rigor, where this book excels. However, with a one semester course designed to teach computer science majors the mathematical fundamentals they need, this book is both too long and too deep.
ideal for self study.......2006-01-26
Excellent book, carefully chosen examples, ideal for self study. I like it very much. My advice is not to skip any section or solved examples or you might be lost.
Maybe it's just me.......2005-04-20
I find this book lacks explanation at many points, to where I couldn't understand thw way the author presented a problem, a subject, etc... I almost feel like the target audience is to other college professors, and not students of the subject. I also don't like that a lot of the harder problems at the end of the sections are even numbered, so that you don't have a way to see how they are worked. I don't really feel the book warrants just one star, but since most people in my class don't care much for the book, I am confused to all of the great reviews on this web site and felt I needed to show the contrast that my class experienced with it. I think the book requires a good instructor to help you get through it, in contrast to the comments to others who have said it's good for a self learner. I am also enrolled in Calculus 2 and Linear Algebra, and the books I am using for those courses are FAR superior to this one. and I have missed a few class sessions in those two courses and am still running a high B and a mid A in those courses. I wouldn't dream of missing a class in the Discrete Math class because I feel too dependant on the instructor's explanations.
great book on discrete math.......2005-03-21
This is an excellent book for self study. However, there are parts in this book that must be rearranged or deleted. For example, I think Catalan numbers should be deleted. This might be useful for the matrix chaining problem, but that's in the realms of algorithm design (specifically in dynamic programming). Also, I do not understand why Grimaldi sandwiched in a chapter on Finite State Machines between two chapters on Functions and Relations. Maybe he should make a section on languages for FSMs, but I recommend Sipser's Introduction to the Theory of Computation if you want to learn about FSMs.
Book Description
A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.
Customer Reviews:
Fun intro to graph theory.......2006-11-22
I like this book as an intro to graph theory. I already had a little background in graph theory and a graduate degree in mathematics before I got this book, but I think that less experienced readers with an interest in pure math will enjoy this book. It's readable and conversational, and special attention is given to introducing pure mathematics and proof.
Nice Introduction.......2004-12-24
One of the better Dover books I've picked up... but keep in mind it is a (very basic) introduction.
The book gives an introduction to graph theory (take the "introduction to" part of the title very seriously). To give an idea of the depth of this book, I read this book in about 6 hours prior to taking a course in graph theory (an undergraduate and graduate student mixed course), and the material in the book was covered in class in about 4 lectures (there were about 30 lectures in the course). This isn't to say the book isn't good (because it is), but I just have to emphasize it is a basic introduction.
What gives this book 5 stars is that it was written very well and made the material very interesting. I would recommend this book to someone looking to understand the very basics of graph theory, but I would not to someone looking for a thorough introduction to graph theory.
For reference, titles of chapters: 1) Pure Mathematics; 2) Graphs; 3) Planar Graphs; 4) Euler's Formula; 5) Platonic Graphs; 6) Coloring; 7) The Genus of a Graph; 8) Euler Walks and Hamilton Walks.
Concise and very well explained.......2004-05-07
Chapter on planar graphs is superbly done, with very easy to understand proofs and plenty of illustrations. Overall, a great introductory text
Graph theory in (good) words........2000-02-17
This book make you want to know more about graph theory. The concepts are first intuitively explained and then formally stated. The numerous examples are completely treated and then easy to follow. R. Trudeau devoted a large part of the book to the puzzling problems of planar graphs and coloring and explains them in a very pleasant manner. As a result, these problems almost appear as trivial (which of course is not the case).
The main criticism I would make is the following. This book is a corrected and enlarged version of another book. Unfortunately, the updating is not very convincing when the "four color problem" is a conjecture in the body of the book and a theorem in footnotes and afterwords.
A fascinating start into graph theory........1999-07-24
Mr. Trudeau has done a fabulous job of introducing graph theory in a way which is understandable and intellectually provocative. He mentions that some of the problems are easy, and that some have been unsolved. In both cases, they both are fully illustrative of the subject matter. If you want to begin exploring graph theory, this book is for you!
Book Description
Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra and surreal numbers to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and new games, several appearing for the first time in this book. This book makes an excellent guide for undergraduates or for self-study by the enterprising reader, with a generous collection of exercises and problems scattered throughout the book.
Customer Reviews:
understanding many types of games.......2007-03-22
The cover illustration is quite well done. It hints at the range of games considered in the book. Inside, the discourse is highly mathematical. Not a trivial read, but suited to a reader who has already taken a course in discrete maths.
The book explains how to classify games by various criteria. So there could be impartial games and non-impartial games, for example. Another viewpoint is that some games have move order being vital in determining the outcome. Think chess or go.
The authors have also generously supplied many problems in each chapter. Including solutions. But what could be of interest to some readers is the description of the Combinatorial Game Suite. An open source Java program that lets you get at many built in games. While the Java programmer can extend it to incorporate other games written in Java.
Book Description
Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates. Much care has been given to present the material at the most effective level for students taking a first course in graph theory. Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications.
This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Customer Reviews:
An excellent text.......2005-05-13
This textbook was such a great complement to the course I took in Graph Theory. Everything is explained beautifully, from simple things such as definitions of elementary terms to subjects more complex such as the coloring theorems of Vizing and Shannon. Proofs accompany nearly all theorems/conjectures in the book, and they are done in a clear and concise manner. What I also found particularly interesting were the various historical pieces that the authors added to the book. They are not only interesting but they serve as a nice break between sections of purely technical content.
This is a great text to have on hand for an introductory course and I highly recommend it for anyone looking for such a text.
Book Description
This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.
It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and - probably the first of its kind - pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.
Customer Reviews:
Encompassing and Very Clear.......2007-08-23
This book goes step by step on the elementary subjects of Combinatorics, contains many of examples and solved exercises, such that the reader or any autodidact student can experience a meaningful studying experience.
Well structured book.......2005-12-03
The best thing I like about this book, is that it has carefully selected subjects and rich set of exercises with detailed solutions. For the first several chapters, there are even more pages devoted to exercises+answers than the text. I think it is better to learn math by doing exercises than memorizing lots of theorems.
I would have given it 5 stars if there were not so many typos. It is annoying because a lot of times when I puzzled about something, it turns out be a typo. There are several versions of errata online, and none of them is complete. :) You can find them here:
http://www-math.mit.edu/~apost/courses/18.314/
I hope the author will correct all those typos then this would be the very best textbook!
A Stroll Through the Old and New.......2002-10-17
Combinatorics often, but not always, involves finite sets, and the ideas of counting. But the subject of combinatorics has indeed become very large, and it has worked its way into many others parts of mathematics, computer science, science, and engineering. Bona's book, `A Walk Through Combinatorics', is a text designed for an introductory course in combinatorics. It covers the traditional areas of combinatorics like enumeration and graph theory, but also makes a real effort to introduce some more sophisticated ideas in combinatorics like Ramsey Theory and the probabilistic method.
The book is very exciting to read, and the author has a wonderful sense of humor: in Chapter 3 he introduces the idea of a permutation by the example of n people arriving at a dentist's office at the same time. They must decide the order in which they will be served. How many orders are possible?
The problems are a great strength of this text. Each chapter ends with a set of exercises with solutions. These tend to be very interesting and often quite challenging. A set of supplementary exercises follows. These tend to be a little easier, though not always, and make good homework assignments. The supplementary exercises do not have solutions, but a solutions manual is available to instructors.
The book walks through four parts: I. Basic Methods; II. Enumerative Combinatorics; III. Graph Theory; IV. Horizons. I particularly like the fourth part which includes Ramsey Theory, subsequence conditions on permutations, the probabilistic method, and partial orders and lattices. A glimpse of these subjects can whet the walker's appetite for more challenging terrain.
I would have liked to give this book 5 stars, but it suffers from a lack of clarity in some places. For example, the discussion of example 2.2 in Chapter 2 on induction just does not read clearly or make sense as it is written. Though an instructor can figure out what is missing, it would be much harder for a student to do so. And figure 13.1 on the colors of the edge of a triangle in Chapter 13 on Ramsey Theory is mislabeled. Again, this could steer an unwary student off the path of understanding. But these defects are minor compared to the riches contained in this text. The author has chosen his subjects carefully, illustrated them well and provided a wealth of wonderful exercises. And he has given the reader a glimpse of some of the less traditional and newer areas of combinatorics at the end of the book.
Book Description
Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector fields, surfaces, homology of complexes, much more. Some knowledge of differential equations and multivariate calculus required. Many problems and exercises (some solutions) integrated into the text. 1979 edition. Bibliography.
Customer Reviews:
A reader's opinion.......2007-01-04
This is the second time I have bought this book since I offered
the first one to my son. An excellent introduction to the topic!
A good start.......2002-08-16
Historically, combinatorial topology was a precursor to what is now the field of algebraic topology, and this book gives an elementary introduction to the subject, directed towards the beginning student of topology or geometry. Due to its importance in applications, the physicist reader who is intending eventually to specialize in elementary particle physics will gain much in the perusal of this book.
Combinatorial topology can be viewed first as an attempt to study the properties of polyhedra and how they fit together to form more complicated objects. Conversely, one can view it as a way of studying complicated objects by breaking them up into elementary polyhedral pieces. The author takes the former view in this book, and he restricts his attention to the study of objects that are built up from polygons, with the proviso that vertices are joined to vertices and (whole) edges are joined to (whole) edges.
He begins the book with a consideration of the Euler formula, and as one example considers the Euler number of the Platonic solids, resulting in a Diophantine equation. This equation only has five solutions, the Platonic solids. The author then motivates the concept of a homeomorphism (he calls them "topological equivalences") by considering topological transformations in the plane. Using the notion of topological equivalence he defines the notions of cell, path, and Jordan curve. Compactness and connectedness are then defined, along with the general notion of a topological space.
Elementary notions from differential topology are then considered in chapter 2, with the reader encountering for the first time the connections between analysis and topology, via the consideration of the phase portraits of differential equations. Brouwer's fixed point theorem is proved via Sperner's lemma, the latter being a combinatorial result which deals with the labeling of vertices in a triangulation of the cell. Gradient vector fields, the Poincare index theorem, and dual vector fields, which are some elementary notions in Morse theory, are treated here briefly.
An excellent introduction to some elementary notions from algebraic topology is done in chapter 3. The author treats the case of plane homology (mod 2), which is discussed via the use of polygonal chains on a grating in the plane. Beginning students will find the presentation very understandable, and the formalism that is developed is used to give a proof of the Jordan curve theorem. Then in chapter 4, the author proves the classification theorem for surfaces, using a combinatorial definition of a surface.
The author raises the level of complication in chapter 5, wherein he studies the (mod 2) homology of complexes. A complex is defined somewhat loosely as a topological space that is constructed out of vertices, edges, and polygons via topological identification. He proves the invariance theorem for triangulations of surfaces by showing that the homology groups of the triangulation are same as the homology groups of the plane model of the surface. This is an example of the invariance principle, and the author briefly details some of the history of invariance principles, such as the Hauptvermutung, its counterexample due to the mathematician John Milnor, and Heawood's conjecture, the latter of which deals with the minimum number of colors needed to color all maps on a surface with a given Euler characteristic. Integral homology is also introduced by the author, and he shows the origin of torsion in the consideration of the "twist" in a surface.
In the last part of the book, the author returns to the consideration of continuous transformations, tackling first the idea of a universal covering space. Algebraic topology again makes its appearance via the consideration of transformations of triangulated topological spaces, i.e. simplicial transformations. He shows how these transformations induce transformations in the homology groups, thus introducing the reader to some notions from category theory. The elaboration of the invariance theorem for homology leads the author to studying the properties of the group homomorphisms via matrix algebra, and then to a proof of the Lefschetz fixed point theorem. The book ends with a brief discussion of homotopy, topological dynamics, and alternative homology theories.
The beginning student of topology will thus be well prepared to move on to more rigorous and advanced treatments of differential, algebraic, and geometric topology after the reading of this book. There are still many unsolved problems in these areas, and each one of these will require a deep understanding and intuition of the underlying concepts in topology. This book is a good start.
Splendidly intuitive yet rigorous.......2001-05-31
This covers the basics of algebraic topology with simplexes, covering in essence the fundamental ideas behind of the work of Poincare, Brouwer, and Alexander. He proves the Jordan curve theorem, classifies all compact surfaces, and the relationship with vector fields. The homology groups are defined and used.
There are excellent examples, clear writing, and humour. An outstanding introduction.
One nice feature is that he bases his notions of continuity on "nearness" not epsilon-delta.
An excellent read.......2000-06-16
Ignore those that suggest this book is too "elementary". This is a wonderful text that concretizes the more abstract notions of algebraic topology. True, it should not be your only text on algebraic topology, and the proofs are not as rigorous as a pedant might want, but it clearly conveys the geometric underpinnings of topology and deserves a space on any topologist's bookshelf.
Not for resolute students of algebraci/diff. topology........2000-03-03
I believe the two existing reviews are over-ratng. True, the book is accessible to anyone without prior knowledge of topology/algebra, but the treatment is too "elementary". For example, the author doesn't even introduce the word "mod 2 homology". If you are resolutely to study algebraic (or differential) topology, this is NOT the book to "study". Try Bredon or Fomenko-Novikov or May. For the subject covered, look for the book by Stillwell.
Average customer rating:
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Renormalization: An Introduction (Theoretical and Mathematical Physics)
Manfred Salmhofer
Manufacturer: Springer
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Book Description
This book grew out of a one-term course on renormalization at ETH Zürich. It provides a mathematically rigorous, yet simple and clear introduction to that subject. It can be read by students from the third year on and it leads the reader to a level where he or she can start reading the current research literature. The book gives a thorough introduction to field-theoretic techniques such as Feynman graph expansions and renormalization. Special effort has been made to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is done by using an exact renormalization group differential equation. This technique, developed during the last few years and now appearing in a textbook for the first time, provides simple but complete proofs of renormalizability theorems.
Customer Reviews:
A little words.......2000-05-09
It's a door of normalization method. A good introduction!
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- Leonardo's Notebooks
- Let Your Life Speak: Listening for the Voice of Vocation
- Lincoln's Other White House: The Untold Story of the Man and His Presidency
- Linux Enterprise Cluster: Build a Highly Available Cluster with Commodity Hardware and Free Software
- Lorraine 1944 : Patton Vs Manteuffel (Campaign Series, 75)
- Lover Revealed (Black Dagger Brotherhood, Book 4)
Books Index
Books Home
Recommended Books
- History: Fiction or Science
- Dr. Pitcairn's New Complete Guide to Natural Health for Dogs and Cats
- As Hot as It Was You Ought to Thank Me: A Novel
- Avian and Exotic Animal Hematology and Cytology
- Desiring God: Meditations of a Christian Hedonist
- Evolution for Everyone: How Darwin's Theory Can Change the Way We Think About Our Lives
- Field Notes from a Catastrophe: Man, Nature, and Climate Change
- Skin Diseases of Dogs and Cats: A Guide for Pet Owners and Professionals
- Born to Steal: When the Mafia Hit Wall Street
- Physical Stresses in Plants: Genes and Their Products for Tolerance
Combinatorics of Finite Sets (Dover Books on Mathematics)
General Lattice Theory
Conceptual Mathematics: A First Introduction to Categories
Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
Stone Spaces (Cambridge Studies in Advanced Mathematics)
