Amazon.com: Customer Reviews: The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip
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on October 4, 2000
Devlin's "The Math Gene" is a wonderful book, well worth reading if you've an interest in how we think, and absolutely essential if your interest extends further to why we can do mathematics.
This is an intriguing question. After all, it's a fairly new part of human behavior - having been around maybe 10,000 years - that we all can do, at least a bit, and the rest of the animal kingdom can't, at least as far as we know.
Devlin's the first mathematician I know of who's looked deeply into this subject using recent research in the area; he's done a great job fitting the available data to a theory that starts to answer the question, how it is we can do mathematics?
First, though, you have to understand what mathematics really is. Devlin's definition is the "science of patterns" and he explains clearly and convincingly why it's the right one.
His premise, roughly, is that however we acquired language, and he stays mostly on the sidelines of the heated debates about that, mathematical ability came along for the ride. His reasoning is that "off-line reasoning" is an essentially equivalent to language, as you can't have one without the other, and that this plus some other abilities, such as a number sense and spatial reasoning, give us the ability to do mathematics.
He then explains why so many of us find the subject difficult. A simplified version is that we use language mainly to talk about interpersonal relationships. In a word, gossip. Note he's not claiming this to have been the purpose for it's development, just that it's what we mostly do with it now. And we're very good at gossiping. In fact, it's so easy we consider it to be a form of relaxation. To Devlin, you need to have the same kind of relationship with mathematical objects in order to be able to work with them.
The book's greatest strength, to my mind, is its gathering of results in cognitive psychology into a coherently developed thesis regarding the origins of mathematical ability. It's a worthy contribution to the discussion, even if the theory proposed is completely wrong, as it may well be. Devlin's open and clear about it being highly speculative.
I do have quibbles, but they're just that. Its major weakness, if the book can be said to have any, is that it doesn't make much by the way of predictions based on his theory, which would make it far more convincing. But this is a terrific starting point for other work.
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on December 31, 2000
"The Math Gene" presents a theory of how mathematical ability and language are related, and how they might have evolved. Devlin starts by separating "number sense" from mathematical ability. Many animals as well as humans can estimate the quantity of something; rats can be taught to press a lever about sixteen times to get a reward. The "about" is significant though; it's an estimate, not an exact count, as far as the rats are concerned. So if number sense and mathematical ability are not the same, what else is needed for mathematics? Devlin lists eight other attributes, including algorithmic ability, a sense of cause and effect, and relational reasoning ability.
Then there's a fairly long discussion of mathematics from the inside--are mathematician's brains different? What is it mathematicians do?--including a moderately detailed description of the basics of mathematical groups. I think Devlin does this to provide non-mathematicians with a sense of what mathematics is about, to make the rest of the book more plausible. This section is well-written and fluent, but I found myself getting a little impatient for the meat of his argument, which comes in the last half of the book. I suspect any reader with a good mathematics background would react the same way.
The next piece of the argument is to demonstrate that language is unlikely to have developed solely as a result of evolutionary pressure towards communication. This is a subtle point I haven't seen made before, but Devlin (who acknowledges his debts to other workers in this area) makes the case quite convincing. In summary: apart from extremely simple messages like "Danger!" and "Mammoth here" you can't communicate what you don't have a mental representation of. The evolution of communication can't have driven representation; it must have always lagged a half-step behind. So mental representation must have evolved first. I am not doing this argument justice here, but Devlin buttresses it well.
The inference is that language is simply a natural but lucky result of our ability to represent the world in our minds. Devlin's key point, however, is that since mathematics is essentially the ability to construct and work with increasingly abstract representations, the same mental changes that gave rise to language have also given rise to mathematics. His conclusion is that we all have the ability to do mathematics: there is no "math gene" except in the same way there is a "language gene": it's universal.
As a side note, not critical to his main argument, he points out that the most likely reason for the growth of representational ability in human brains was to foster understanding of other humans in the group; to encourage a sense of group-ness. For a creature that was more effective in group actions (e.g. hunting) there would have been a strong evolutionary advantage to having an emotional investment in the success of the group. Hence much of the early use of this ability would have been to represent others in the group; when language was added, it would have enabled people to talk about each other. In Devlin's words, "Having arisen as a side-effect of off-line thinking, language was immediately hijacked to facilitate gossip." (Off-line thinking is used to mean representational thinking that doesn't result in or from actions in the immediate environment.)
Two particular items in the book are worth mentioning. One is a followup to some famous experiments done by child psychologist Piaget in the 1930's. Piaget thought he'd demonstrated that children don't acquire a fully-developed number sense till around six years old. More recent work has demonstrated that children are much smarter than Piaget realized: there was a subtle and fascinating methodological flaw in Piaget's experiment. The second item is a little test of logical reasoning, presented with four cards on a table. Even mathematicians, who will probably get the test right, may be surprised at the coda to the test, which forms one of the few methods of direct verification of Devlin's claim that everyone can do mathematics.
The case is well-argued, but one problem with theories like these is that there *are* so few ways of finding out if they're true. "The Math Gene" is reminiscent of Julian Jaynes' "The Origin of Consciousness in the Breakdown of the Bicameral Mind" in this way; a fascinating argument that we may never be able to test. However, it's thought-provoking and plausible, and left me, at least, convinced of its likely truth.
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on January 16, 2013
I am a cognitive scientist who studies how children acquire number concepts and numerical language. Based on the last 30 years of research on the acquisition of numerical thought, I think there are good reasons to believe that math and language are intimately related. Having enjoyed parts of Devlin's "The Language of Mathematics", I had high hopes when I picked up this book. The first few chapters were promising. For example, I completely agree with Devlin that, contrary to what is implicitly assumed in the field, the Number Sense has little to do with mathematical thought. Being a complete math neophyte, I also enjoyed his chapter on the nature of mathematical thinking. Unfortunately, for the rest, I was quite disappointed to find many interesting theses, but little in the way of articulate reasons for believing that they may be correct. Rather, I found much to disagree with.

The main theses of this book are:

1) Mathematical thought is a type of linguistic thought.
2) The math gene is the genetic endowment for Universal Grammar.
3) Universal Grammar specifies the "fundamental language tree" - i.e., the basic X-bar tree consisting of an XP, which consists of a SPEC and an X-bar, which consists of an X which optionally combines with another XP.
4) During the first hundred of thousands, if not millions of years of evolution of the genus "homo", brain size grew rapidly. Given the cost of growing a bigger brain, it had to be very useful. Growing the brain was useful because it allowed homo to recognize more types (bananas, monkeys, palm trees, etc...)
5) Then, sometime around 200,000 thousand years ago full-blown language appears. How? With the emergence of "off-line thinking": the brain can self-trigger patterns of activity that used to have to be caused by external stimuli.
6) off-line thinking requires more than types; it requires representations of structural relations between them (e.g., cause-effect).
7) types + structural relations = syntax
8) being able to talk about relations between people is the same as being able to talk about mathematical relations

There are several problems with these theses. First, the author rarely considers alternatives. Take for example the argument that goes: a) the increase in brain size had to be useful to make up for its cost; b) being able to recognize types is useful; c) therefore, the brain grew because brain growth allowed homo to recognize more types.

This could be. The problem is that there are many other alternatives. It could be that brain growth allowed homo to have a larger working memory, or to store more mental images of individual objects and events, or to inhibit immediate desires in the interest of delayed gratification, etc...To show that the brain grew to represent more types, Devlin would have to consider some alternatives and show that the alternatives are wrong. However, far too little of that happens. Moreover, there are other sources of evidence that could support Devlin's thesis. For example, if evolution endowed us with the capacity to recognize multiple types, then type recognition should be innate - it should be available to young human babies. Much infant research suggests that indeed human infants do distinguish basic types - e.g., animate-inanimate. However, this is a far cry from the whole inventory of types Devlin seems to have in mind. More importantly, Devlin doesn't present other types of evidence that could support or disconfirm his hypothesis.

Unfortunately, this is typical of most other arguments in the book. Devlin presents arguments that are consistent with his theses, but rarely considers alternatives. Moreover, the evidence he considers is usually deplorably thin.

The other strain of problems comes from loose and usually erroneous analyses of mental representations. For example, Devlin characterizes syntax as the fundamental language tree, a characterization that finds much support in linguistic theory. But then later on syntax is said to be the same as representations of relations between types (or of the structure of the world). The fundamental language tree does not represent any contentful relations between objects or types. Syntax is pure form, not meaning. So the relation between the fundamental language tree and representations of the structure of the world escapes me. More generally, I don't see why Devlin dedicated a whole chapter to the fundamental language tree (which by itself is quite good) because he never goes back to that idea. Be that as it may, there is another problem with the thesis. Syntax is not a representation of structural relations of the physical or of the social kind. For example, consider these sentences: "Joe convinced Bob," "Joe kissed Bob," "Joe purchased a log" and "Joe burned a log". These sentences have the same syntactic structure: NP VP NP. However, they are about completely different types of relations. The first is about mental causation, the second is about contact, the third is about transfer, and the fourth is about physical causation. Clearly then, syntactic structure is not the same as representation of relations between objects and people.

This problem recurs in many the arguments of the second half of the book. For example, if off-line thinking evolved the way Devlin says it evolved (i.e., it is an internally generated simulation of on-line thinking), then the capacity to think about the past or the future does not necessarily follow from off-line thinking. On its own, a simulation of on-line thinking (thinking about what is here now), is no more a representation of the past or future than on-line thinking itself. To think about the past or the future, one needs to represent the structure of time. If no such structure is available in on-line thinking, then it cannot appear in a simulation of on-line thinking. The general problem is that, other than being able to run without an external cause, the simulation cannot have properties that are not in what is being simulated.

The latter point also holds for the book's final thesis - i.e., that our capacity for math grew out of our capacity to gossip - to talk about relations between people. Devlin's argument for this seems to be that all relations are equal. So if i can talk about relations between people then, necessarily, I can also talk about relations between geometric transformations or between numbers. But this is not so, at least, not patently. Love, argue with, hide from, embarrass, and flirt with are all social relations. Each of them has a particular content, as seen by the fact that each of them entails particular things (e.g., if A embarrassed B, then it is plausible that B's ego dropped temporarily but if A flirted with B, it is likely that A's ego enjoyed a temporary boost). Likewise, mathematical relations like SUCCESSOR, IDENTICAL, or SIMILAR have their particular content. How the content of any of these relations can be derived from social relations is quite unclear. To argue for his thesis that gossip is the origin of math, Devlin owes us an explanation of how one gets from the content of social relations such as embarass and flirt with, to relations like successor and identical. However, no such explanation is to be found. Therefore, as far as I can tell, there are no reasons to believe Devlin's final thesis. Rather, there are some pretty good ones to doubt it - i.e., that you cannot get representations of mathematical relations out of representations of social relations.

What Devlin really needs is evidence for abstract symbols that only capture the most basic logical properties of relations (say whether they are symmetrical or transitive). Here syntactic categories and the fundamental language tree could be part of the answer. But unfortunately Devlin does not make this connection.
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on December 20, 2005
The author presents a carefully crafted theory of how language developed in humans, and links our innate mathematical abilities to this skill with language. Although his position is that everybody has some level of mathematical skill beyond number sense, he never really addresses in detail why some people have an aptitude for math and others don't, other than to mention the mathematician's ability to cope with abstraction.

This is the second book by Devlin I've read, and I'm impressed by his boldness in escorting the reader through difficult mental terrain. If you find the topic of language development interesting, and you're willing to exert some mental effort to keep up with his arguments, you'll find this book a thought-provoking read. However if you want to know why high-school algebra gave you such trouble, you'll have to look elsewhere for the answer.
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on September 5, 2002
The Math Gene is a wonderful insight into mathematics and how humans may have evolved the ability for mathematical thought. Dr Devlin gives a powerful argument for his theory in three parts. He begins with an explanation of the nature of mathematics, and dispells many misconceptions about math held by people outside of the mathematics community. He then spends the bulk of his text describing the nature and evolution of language and communication in humans and their differences with animals in that respect. He explains what pressures in the environment would be necessary to cause an evolutionary change in language and thought in a way that is understandable by a layperson and plausable to someone with a strong scientific background. He ends his book with a comparison of the mind's mathematical and language processes, why language (particularly gossip) must have preceded mathematical thought, and why mathematical thought is a direct product of any consciousness capable of language.
I thoroughly enjoyed this book, and have recommended it to friends and colleages alike. I would also recommend another one of Devlin's books, The Language of Mathematics, for a glimpse into the diverse and beautiful world of math any person could understand and appreciate.
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Let's face it. Most people have trouble with math, and are delighted when they don't have to figure out any more when two trains are going to collide or pass each other. Personally, I always liked problems, so I found math interesting. My friends always thought that was one of my more peculiar characteristics.
Dean Keith Devlin deplores the fact that the way math (that which we learn after arithmetic is mastered) is taught obscures access to the most interesting parts of the subject. I agree with him on that. In this book, he tries to take away some of the fog for the reader by showing you thought processes that mathematicians use in some simple situations and problems that most people can grasp. These examples are nicely designed to build on one another, so you get a cumulative learning experience from them of how a mathematician may think. The "nested" design of the examples was impressive to me as an author.
This book is for those who think of themselves as nonmathematical and want to understand more about why they experience a weak skill set in that way. Mathematicians will probably find the book much too elementary to be interesting, except as a model of how to explain mathematics to the lay person. Those who study mind development will find the book full of logical proofs, but modest insight.
The author also tries to build a plausible scenario for how mathematical ability developed in primitive humans. I applaud his ambition. His speculations are interesting, but certainly did not persuade me. I think his problem was that he did not look far enough into the scientific research on how we learn.
Everyone has problems with something where we have no experience. As David Ingvar pointed out, we simply draw a blank until we can create experience in that area or connect to an existing experience. To help people learn, give them experience in the new thing that is structured to be connected to some familiar thing. This point is made indirectly by an example Dean Devlin provides: Children who have trouble doing simple arithmetic can make change perfectly well. The best educational techniques create simulations that encourage this approach focused in relevant experiences. Unfortunately, those who teach math are mostly immune to using this method. Higher math is taught in the way that makes it most difficult to understand -- as abstractions unconnected to other math or ordinary situations and people. You will often "feel" an underlying unity in math, but I never had a teacher who addressed it. The closest I came was in a calculus class where we wrote software programs to solve problems. Putting a virtually infinite set of rectangles together and adding their areas to approach the answer for the area under the curve was fascinating and useful to me.
The other problem with his arguments about the origins of mathematical ability is that he concentrates on the "formal proof" parts of this thinking which are conscious. Many people report that math for them is more unconscious and intuitive. I am one of those people. I can see the solution in a nonverbal, nonmathematical form. After I know the answer, then I sit down and painstakingly translate it into formal proofs. But that is merely for communication purposes. It doesn't help me at all. I was not surprised that Dean Devlin sees conscious mathematical thinking as being like language -- because that's the exact same purpose it serves. The more important question of how mathematical insight can be developed is not really addressed, as I understood the book. Dean Devlin alludes to those moments of inspiration, but doesn't tie them into his main themes. I suspect that "knowing" the answer in this unconscious way is much like "knowing" where to throw a rock to hit something, an example that Dean Devlin uses.
Reading this book made me realize that there are many disciplines where I do not understand the fundamental thought processes involved. Perhaps that is true of you, too. Since we often rely on other people to help us in these areas, we cannot hope to understand their advice if we do not understand the mental processes for how they arrive at that advice. I suggest that you and I start spending some time over lunch and drinks getting some more understanding of medicine, engineering, pscyhology, and teaching in this same way from professionals in those disciplines. I suspect we will be greatly helped by what we learn.
Peer out from the other person's mind from time to time to see more!
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on April 20, 2002
In the book The Math Gene, author Keith Devlin stated that math is just a special use of our language faculty and every one should be able to do math. The basic structure of the book is Prologue, what is math, what is language, and from language to math( the point). We can see this clearly from the last sentence of the prologue," Once you know what mathematics is really about, and once you see how our brains create language, you should find it far less surprising that thinking mathematically is just a specialized form of using our language facility."
He spends the first 4 chapters talking about what math is: the science of pattern.
Chapter 2 and 3 is mostly boring to me, maybe people with little math background will appreciate it. Chapter 4 is not bad, especially when he cited the research on animal coating, it is really interesting that the coating of a leopard could be generated by solving math equations. Other examples are also very interesting.

In chapter 5, the author talked about math thinking. It is abstract thinking. Then he used the house metaphor to compare it with daily life. Make it simple to understand for the readers. He also talked about the high concentration you need in doing math problems, this kind of concentration is very hard for ordinary people who are busy worrying about their daily life. And that¡¯s one of major hurdle preventing most people from being good at math. This chapter is quite good.
Again chapter 6 and 7 is a bit uninteresting. It talked about what language is. Then in chapter 8 he talked about how math thinking evolved and the idea of offline thinking, how important it is to human, etc. It is an important chapter, though I don¡¯t find it interesting.
The best part of the book for me, also the whole point of the book comes last in chapter 9. It tells "why numbers are like gossip". I am very interested to read about it.
It first cited a very common fact: that people like to talk about other people, also they are interested in other people¡¯s lives, it¡¯s like a need for them. Then he said the usefulness of this is that it will benefit the group, make its members more close to each other.
Then he said the same thinking involved could be used in math thinking. How relationship between people in real world could also be applied to the relationships between abstract objects in the imaginary world created by human brain. Then he said why most people can not do math even they have this faculty in them. It is because it takes training most people don¡¯t have. Once those people get training, they will also be able to do math. However most people are not motivated.
And he said how mathematicians are able to do it and how wonderful the math world is. Only people that has reached the summit of one of the many math mountains can see the whole picture and the very picture motivate them to go further. While amateurs and outsiders only walk around the valley and never see the whole picture, and that is why they think math is difficult and uninteresting.
Chapter 10 is just citing about some other people¡¯s opinion and his viewpoint on it.
The epilogue of the book " how to sell soap" is also quite funny.
Overall, it is a worth reading book. It is something new for me. Gives me more insight in language, math and gossip. The idea of the author is quite convincing. Some chapters of the book serve as background knowledge and could be skipped if you already have them. Mainly chapter 2, 3, 6, also chapter 10 could be skipped.
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on December 20, 2000
This is a book from a well-known and respected popular science writer and mathematician, Professor Keith Devlin, on a very intriguing question: how and why did people acquire the skill of doing mathematics. Unfortunately, many readers will probably still be looking for more after finishing this one.
Devlin starts with our sense for numbers. Not all numbers are the same: we instantly recognize one or two objects; beyond that number, we have to count them. But counting itself is not yet mathematics. So what is mathematics? Devlin fancies the answer that it is a science of patterns, and spends a whole chapter on what he really means by the extended concept of pattern. In order to describe abstract patterns, mathematics has developed a specialized language. So is it possible to learn anything about mathematics from what the linguists have already learned about the generalized structural grammar, underlying every known language? How did the full language - with grammar - evolve at all from the "momma hungry" protolanguage? And why?
The above arguments pose a grandiose ouverture for Devlin's thesis, which we are finally ready for in the second-but-last chapter: in order to be able to plan and predict, human ancestors have some 300.000 years ago developed what Devlin calls "off-line" thinking. With off-line thinking came grammar and language. Language is, and always was, used predominantly to build the "team spirit" among humans, or, with other words, for gossip. Mathematicians can avoid one unnecessary level of abstractions if they visualize the entities they are working with. So for them, doing mathematics is like gossiping. Well, sort of.
And that is it. The book is actually quite a pleasant read, with lots of interesting stuff. On the other hands, Devlin drags us on and around general linguistics and the evolution of speech and God knows what else before getting to the promised topic. The final thesis comes then rather unculminating. On the plus side, Devlin is fair at citing books and articles he had learned from. I wish I could say the same about some other popular science authors.
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VINE VOICEon May 30, 2010
"THE MATH GENE" poses an interesting thesis and contains a wide range of interesting examples. I was immediately drawn into the book with it's discussion of grammar school arithmetic, interesting math "geniuses" and correlations to language development. Unfortunately however, beyond these introductory chapters the discussion becomes both abstract and difficult to follow. Mid-way, the author delves into the dangerous territory of group theory. Given my background in chemistry, I've had the opportunity to study rudimentary group theory as it relates to molecules and stereochemistry. I won't deny that Dr. Devlin explains the premise of groups in a very eloquent and concise manner (I think even my cat could follow his analogies.) Notwithstanding, the average reader may find themselves wondering, "why the heck did I pick this book up anyway?" after a few dozen pages of group theory. Following group theory, he goes into a bit of a tangent on language development and basic linguistic theory (the "Fundamental Language Tree".) In fact, this discussion begins to wander so far off the beaten path that it concludes in an appendix at the back of the book. Following the linguistic hurdle, Devlin jumps into anthropological and evolutionary evidence for brain development and language acquisition. This is where he finally lost me. At this point I was so lost from the original intent of the discussion that I surrendered and began to skim the remaining chapter in search of his lost thesis. "Why are numbers like gossip?!?" I'm not entirely certain that question was ever answered, however, there are some pretty interesting ideas here which are certainly worth your time. Just adjust your expectations accordingly!
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on April 18, 2002
In the book The Math Gene, author Keith Devlin stated that math is just a special use of our language faculty and every one should be able to do math. The basic structure of the book is Prologue, what is math, what is language, and from language to math( the point). We can see this clearly from the last sentence of the prologue,¡± Once you know what mathematics is really about, and once you see how our brains create language, you should find it far less surprising that thinking mathematically is just a specialized form of using our language facility.¡±
He spends the first 4 chapters talking about what math is: the science of pattern.
Chapter 2 and 3 is mostly boring to me, maybe people with little math background will appreciate it. Chapter 4 is not bad, especially when he cited the research on animal coating, it is really interesting that the coating of a leopard could be generated by solving math equations. Other examples are also very interesting.

In chapter 5, the author talked about math thinking. It is abstract thinking. Then he used the house metaphor to compare it with daily life. Make it simple to understand for the readers. He also talked about the high concentration you need in doing math problems, this kind of concentration is very hard for ordinary people who are busy worrying about their daily life. And that¡¯s one of major hurdle preventing most people from being good at math. This chapter is quite good.
Again chapter 6 and 7 is a bit uninteresting. It talked about what language is. Then in chapter 8 he talked about how math thinking evolved and the idea of offline thinking, how important it is to human, etc. It is an important chapter, though I don¡¯t find it interesting.
The best part of the book for me, also the whole point of the book comes last in chapter 9. It tells ¡°why numbers are like gossip¡±. I am very interested to read about it.
It first cited a very common fact: that people like to talk about other people, also they are interested in other people¡¯s lives, it¡¯s like a need for them. Then he said the usefulness of this is that it will benefit the group, make its members more close to each other.
Then he said the same thinking involved could be used in math thinking. How relationship between people in real world could also be applied to the relationships between abstract objects in the imaginary world created by human brain. Then he said why most people can not do math even they have this faculty in them. It is because it takes training most people don¡¯t have. Once those people get training, they will also be able to do math. However most people are not motivated.
And he said how mathematicians are able to do it and how wonderful the math world is. Only people that has reached the summit of one of the many math mountains can see the whole picture and the very picture motivate them to go further. While amateurs and outsiders only walk around the valley and never see the whole picture, and that is why they think math is difficult and uninteresting.
Chapter 10 is just citing about some other people¡¯s opinion and his viewpoint on it.
The epilogue of the book ¡° how to sell soap¡± is also quite funny.
Overall, it is a worth reading book. It is something new for me. Gives me more insight in language, math and gossip. The idea of the author is quite convincing. Some chapters of the book serve as background knowledge and could be skipped if you already have them. Mainly chapter 2, 3, 6, also chapter 10 could be skipped.
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