出版社: 清华大学出版社
副标题: 研究生必备数学知识
出版年: 20048
页数: 347
定价: 49.00元
丛书: 天元基金影印系列丛书
ISBN: 9787302090854
内容简介 · · · · · ·
Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge ,but few have such a backgroud .This book will help stedents see the broad outline of mathematics and to fill in the gaps in their knowlegde.
The author explains the basic points and a few key results of the most important undergradute t...
Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge ,but few have such a backgroud .This book will help stedents see the broad outline of mathematics and to fill in the gaps in their knowlegde.
The author explains the basic points and a few key results of the most important undergradute topics in mathematics ,emphasizing the intutions behind the subject.The topics include linear algebra,vector calculus,differential geometry,real analysis ,pointset topology,differential equations,probability theory,complex analysis,abstract algebra,and more.An annotated biliography offers a guide to further reading and more rigorous foundations.
This book will be an essential resource for advanced undergraduate and beginning graduate students in mathematics,the physical sciences,engineering,computer science,statistics,and economics,and for anyone else who needs to quickly learn some serious mathemaics.
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Mobing (转行ing)
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split in... (2回应)20131007 18:26
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split into physics, chemistry, biologyand geology. But the very opposite has happened. Since World War II, it has become increasingly clear that mathematics is one unified discipline. What were separate areas now feed off of each other. Learning and creating mathematicsis indeed a worthwhile way to spend one'slife .. Math is Hard. Unfortunately,people are just not that good at mathematics. While intensely enjoyable, it also requires hard work and selfdiscipline. I know of no serious mathematician who finds math easy. In fact, most,after a few beers, will confess as to how stupid and slow they are. This is one of the personal hurdles(障碍) that a beginning graduate student must face,namely how to deal with the profundity(深度，深奥) of mathematics in stark comparison to our own shallow understandings of mathematics. This is in part why the attrition rate(退学率) in graduate school is so high. At the best schools, with the most successful retention rates(保留率), usually only about half of the people who start eventually get their PhDs. Even schools that are in the top twenty have at times had eighty percent of their incoming graduate students not finish. This is in spite of the fact that most beginning graduate students are, in comparison to the general population, amazingly good at mathematics.Most have found that math is one area in which they could shine. Suddenly,in graduate school, they are surrounded by people who are just as good(and who seemeven better). To make matters worse, mathematics is a meritocracy(英才教育).The faculty will not go out of their way to make beginning students feel good(this is not the faculty's job; their job is to discover new mathematics).The fact is that there are easier (though, for a mathematician, less satisfying) ways to makea living. There is truth in the statement that you must be driven to become a mathematician. Mathematics is exciting, though. The frustrations should more than be compensated for by the thrills of learning and eventually creating (or discovering) new mathematics. That is, after all, the main goal for attending graduate school, to become a research mathematician. As with all creative endeavors(创造性事业), there will be emotional highs and lows. Only jobs that are routine and boring will not have these peaks and valleys. Part of the difficulty of graduate school is learning how to deal with the low times.  Goal of Book. The goal of this book is to give people at least a rough idea of the many topics that beginning graduate students at the best graduate schools are assumed to know. Since there is unfortunately far more that is needed to be known for graduate school and for research than it is possible to learn in a mere four years of college, few beginning students know all of these topics, but hopefully all will know at least some. Different people will know different topics. This strongly suggests the advantage of working with others. There is another goal. Many nonmathematicians suddenly find that they need to know some serious math. The prospect of struggling with a text will legitimately seem for them to be daunting(使人气馁的). Each chapter of this book will provide for these folks a place where they can get a rough idea and outline of the topic they are interested in. As for general hints for helping sort out some mathematical field, certainly one should always, when faced with a new definition, try to find a simple example and a simple nonexample. A nonexample, by the way, is an example that almost, but not quite, satisfies the definition. But beyond finding these examples, one should examine the reason why the basic definitions were given. This leads to a split into two streams of thought(思想流) for how to do mathematics. One can start with reasonable, if not naive, definitions and then prove theorems about these definitions. Frequently the statements of the theorems are complicated, with many different cases and conditions, and the proofs are quite convoluted(费解的), full of special tricks. The other, more midtwentieth century approach, is to spend quite a bit of time on the basic definitions, with the goal of having the resulting theorems be clearly stated and having straightforward proofs. Under this philosophy, any time there is a trick in a proof, it means more work needs to be done on the definitions. It also means that the definitions themselves take work to understand,even at the level of figuring out why anyone would care. But now the theorems can be cleanly stated and proved. In this approach the role of examples becomes key. Usually there are basic examples whose properties are already known. These examples will shape the abstract definitions and theorems. The definitions in fact are made in order for the resulting theorems to give, for the examples, the answers we expect. Only then can the theorems be applied to new examples and cases whose properties are unknown. For example, the correct notion of a derivative and thus of the slope of a tangent line is somewhat complicated. But whatever definition is chosen, the slope of a horizontal line (and hence the derivative of a constant function) must be zero. If the definition of a derivative does not yield that a horizontal line has zero slope, it is the definition that must be viewed as wrong, not the intuition behind the example. For another example, consider the definition of the curvature曲率 of a plane curve, which is in Chapter Seven. The formulas are somewhat ungainly.不雅 But whatever the definitions, they must yield that a straight line has zero curvature, that at every point of a circle the curvature is the same and that the curvature of a circle with small radius must be greater than the curvature of a circle with a larger radius (reflecting the fact that it is easier to balance on the earth than on a basketball). If a definition of curvature does not do this, we would reject the definitions, not the examples. Thus it pays to know the key examples. When trying to undo the technical maze迷惑 of a new subject, knowing these examples will not only help explain why the theorems and definitions are what they are but will even help in predicting what the theorems must be. Of course this is vague含糊的 and ignores the fact that first proofs are almost always ugly and full of tricks, with the true insight usually hidden. But in learning the basic material, look for the key idea, the key theorem and then see how these shape the definitions. Caveats for Critics.(对吹毛求疵人的警告) This book is far from a rigorous treatment of any topic. There is a deliberate looseness in style and rigor. I am trying to get the point across and to write in the way that most mathematicians talk to each other. The level of rigor in this book would be totally inappropriate in a research paper. Consider that there are three tasks for any intellectual discipline: 1. Coming up with new ideas. 2. Verifying new ideas. 3. Communicating new ideas. How people come up with new ideas in mathematics (or in any other field) is overall a mystery. There are at best a few heuristics启发 in mathematics, such as asking if something is unique or if it is canonical. It is in verifying new ideas that mathematicians are supreme. Our standard is that there must be a rigorous proof. Nothing else will do. This is why the mathematical literature is so trustworthy (not that mistakes don't creep in, but they are usually not major errors). In fact, I would go as far as to say that if any discipline has as its standard of verification rigorous proof, than that discipline must be a part of mathematics. Certainly the main goal for a math major in the first few years of college is to learn what a rigorous proof is. Unfortunately,we do a poor job of communicating mathematics. Every year there are millions of people who take math courses. A large number of people who you meet on the street or on the airplane have taken college level mathematics. How many enjoyed it? How many saw no real point to it? While this book is not addressed to that random airplane person, it is addressed to beginning graduate students, people who already enjoy mathematics but who all too frequently get blown out精疲力竭 of the mathematical water by mathematics presented in an unmotivated, but rigorous, manner. There is no problem with being nonrigorous, as long as you know and clearly label when you are being nonrigorous. Comments on the Bibliography.There are many topics in this book. While I would love to be able to say that I thoroughly完全地 know the literature on each of these topics, that would be a lie. 哈哈The bibliography has been cobbled被修补的 together from recommendations from colleagues, from books that I have taught from and books that I have used. I am confident that there are excellent texts that I do not know about. If you have a favorite, please let me know at tgarrity@williams.edu. While this book was being written,Paulo Ney DeSouza and JorgeNuno Silva wrote Berkeley Problems in Mathematics[26], which is an excellent collectionof problems that have appeared over the years on qualifying exams (usually taken in the first or second year of graduate school) in the math department at Berkeley. In many ways, their book is the complement of this one, as their work is the place to go to when you want to test your computational skills while this book concentrates on underlying intuitions. For example, say you want to learn about complex analysis. You should first read chapter nine of this book to get an overview of the basics about complex analysis. Then choose a good complex analysis book and work most of its exercises. Then use the problems in DeSouza and Silva as a final test of your knowledge. Finally,the book Mathematics, Form and Function by Mac Lane[82], is excellent. It provides an overview of much of mathematics. I am listing it here because there was no other place where it could be naturally referenced. Second and third year graduate students should seriously consider reading this book.
2回应 20131007 18:26

Mobing (转行ing)
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split in... (2回应)20131007 18:26
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split into physics, chemistry, biologyand geology. But the very opposite has happened. Since World War II, it has become increasingly clear that mathematics is one unified discipline. What were separate areas now feed off of each other. Learning and creating mathematicsis indeed a worthwhile way to spend one'slife .. Math is Hard. Unfortunately,people are just not that good at mathematics. While intensely enjoyable, it also requires hard work and selfdiscipline. I know of no serious mathematician who finds math easy. In fact, most,after a few beers, will confess as to how stupid and slow they are. This is one of the personal hurdles(障碍) that a beginning graduate student must face,namely how to deal with the profundity(深度，深奥) of mathematics in stark comparison to our own shallow understandings of mathematics. This is in part why the attrition rate(退学率) in graduate school is so high. At the best schools, with the most successful retention rates(保留率), usually only about half of the people who start eventually get their PhDs. Even schools that are in the top twenty have at times had eighty percent of their incoming graduate students not finish. This is in spite of the fact that most beginning graduate students are, in comparison to the general population, amazingly good at mathematics.Most have found that math is one area in which they could shine. Suddenly,in graduate school, they are surrounded by people who are just as good(and who seemeven better). To make matters worse, mathematics is a meritocracy(英才教育).The faculty will not go out of their way to make beginning students feel good(this is not the faculty's job; their job is to discover new mathematics).The fact is that there are easier (though, for a mathematician, less satisfying) ways to makea living. There is truth in the statement that you must be driven to become a mathematician. Mathematics is exciting, though. The frustrations should more than be compensated for by the thrills of learning and eventually creating (or discovering) new mathematics. That is, after all, the main goal for attending graduate school, to become a research mathematician. As with all creative endeavors(创造性事业), there will be emotional highs and lows. Only jobs that are routine and boring will not have these peaks and valleys. Part of the difficulty of graduate school is learning how to deal with the low times.  Goal of Book. The goal of this book is to give people at least a rough idea of the many topics that beginning graduate students at the best graduate schools are assumed to know. Since there is unfortunately far more that is needed to be known for graduate school and for research than it is possible to learn in a mere four years of college, few beginning students know all of these topics, but hopefully all will know at least some. Different people will know different topics. This strongly suggests the advantage of working with others. There is another goal. Many nonmathematicians suddenly find that they need to know some serious math. The prospect of struggling with a text will legitimately seem for them to be daunting(使人气馁的). Each chapter of this book will provide for these folks a place where they can get a rough idea and outline of the topic they are interested in. As for general hints for helping sort out some mathematical field, certainly one should always, when faced with a new definition, try to find a simple example and a simple nonexample. A nonexample, by the way, is an example that almost, but not quite, satisfies the definition. But beyond finding these examples, one should examine the reason why the basic definitions were given. This leads to a split into two streams of thought(思想流) for how to do mathematics. One can start with reasonable, if not naive, definitions and then prove theorems about these definitions. Frequently the statements of the theorems are complicated, with many different cases and conditions, and the proofs are quite convoluted(费解的), full of special tricks. The other, more midtwentieth century approach, is to spend quite a bit of time on the basic definitions, with the goal of having the resulting theorems be clearly stated and having straightforward proofs. Under this philosophy, any time there is a trick in a proof, it means more work needs to be done on the definitions. It also means that the definitions themselves take work to understand,even at the level of figuring out why anyone would care. But now the theorems can be cleanly stated and proved. In this approach the role of examples becomes key. Usually there are basic examples whose properties are already known. These examples will shape the abstract definitions and theorems. The definitions in fact are made in order for the resulting theorems to give, for the examples, the answers we expect. Only then can the theorems be applied to new examples and cases whose properties are unknown. For example, the correct notion of a derivative and thus of the slope of a tangent line is somewhat complicated. But whatever definition is chosen, the slope of a horizontal line (and hence the derivative of a constant function) must be zero. If the definition of a derivative does not yield that a horizontal line has zero slope, it is the definition that must be viewed as wrong, not the intuition behind the example. For another example, consider the definition of the curvature曲率 of a plane curve, which is in Chapter Seven. The formulas are somewhat ungainly.不雅 But whatever the definitions, they must yield that a straight line has zero curvature, that at every point of a circle the curvature is the same and that the curvature of a circle with small radius must be greater than the curvature of a circle with a larger radius (reflecting the fact that it is easier to balance on the earth than on a basketball). If a definition of curvature does not do this, we would reject the definitions, not the examples. Thus it pays to know the key examples. When trying to undo the technical maze迷惑 of a new subject, knowing these examples will not only help explain why the theorems and definitions are what they are but will even help in predicting what the theorems must be. Of course this is vague含糊的 and ignores the fact that first proofs are almost always ugly and full of tricks, with the true insight usually hidden. But in learning the basic material, look for the key idea, the key theorem and then see how these shape the definitions. Caveats for Critics.(对吹毛求疵人的警告) This book is far from a rigorous treatment of any topic. There is a deliberate looseness in style and rigor. I am trying to get the point across and to write in the way that most mathematicians talk to each other. The level of rigor in this book would be totally inappropriate in a research paper. Consider that there are three tasks for any intellectual discipline: 1. Coming up with new ideas. 2. Verifying new ideas. 3. Communicating new ideas. How people come up with new ideas in mathematics (or in any other field) is overall a mystery. There are at best a few heuristics启发 in mathematics, such as asking if something is unique or if it is canonical. It is in verifying new ideas that mathematicians are supreme. Our standard is that there must be a rigorous proof. Nothing else will do. This is why the mathematical literature is so trustworthy (not that mistakes don't creep in, but they are usually not major errors). In fact, I would go as far as to say that if any discipline has as its standard of verification rigorous proof, than that discipline must be a part of mathematics. Certainly the main goal for a math major in the first few years of college is to learn what a rigorous proof is. Unfortunately,we do a poor job of communicating mathematics. Every year there are millions of people who take math courses. A large number of people who you meet on the street or on the airplane have taken college level mathematics. How many enjoyed it? How many saw no real point to it? While this book is not addressed to that random airplane person, it is addressed to beginning graduate students, people who already enjoy mathematics but who all too frequently get blown out精疲力竭 of the mathematical water by mathematics presented in an unmotivated, but rigorous, manner. There is no problem with being nonrigorous, as long as you know and clearly label when you are being nonrigorous. Comments on the Bibliography.There are many topics in this book. While I would love to be able to say that I thoroughly完全地 know the literature on each of these topics, that would be a lie. 哈哈The bibliography has been cobbled被修补的 together from recommendations from colleagues, from books that I have taught from and books that I have used. I am confident that there are excellent texts that I do not know about. If you have a favorite, please let me know at tgarrity@williams.edu. While this book was being written,Paulo Ney DeSouza and JorgeNuno Silva wrote Berkeley Problems in Mathematics[26], which is an excellent collectionof problems that have appeared over the years on qualifying exams (usually taken in the first or second year of graduate school) in the math department at Berkeley. In many ways, their book is the complement of this one, as their work is the place to go to when you want to test your computational skills while this book concentrates on underlying intuitions. For example, say you want to learn about complex analysis. You should first read chapter nine of this book to get an overview of the basics about complex analysis. Then choose a good complex analysis book and work most of its exercises. Then use the problems in DeSouza and Silva as a final test of your knowledge. Finally,the book Mathematics, Form and Function by Mac Lane[82], is excellent. It provides an overview of much of mathematics. I am listing it here because there was no other place where it could be naturally referenced. Second and third year graduate students should seriously consider reading this book.
2回应 20131007 18:26

Mobing (转行ing)
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split in... (2回应)20131007 18:26
Preface Math is Exciting.We are living in the greatest age of mathematicsever seen. In the 1930s, there were some people who feared that the rising abstractions of the early twentieth century would either lead to mathematicians working on sterile(贫瘠的), silly intellectual exercises or to mathematics splitting into sharply distinct subdisciplines, similar to the way natural philosophy split into physics, chemistry, biologyand geology. But the very opposite has happened. Since World War II, it has become increasingly clear that mathematics is one unified discipline. What were separate areas now feed off of each other. Learning and creating mathematicsis indeed a worthwhile way to spend one'slife .. Math is Hard. Unfortunately,people are just not that good at mathematics. While intensely enjoyable, it also requires hard work and selfdiscipline. I know of no serious mathematician who finds math easy. In fact, most,after a few beers, will confess as to how stupid and slow they are. This is one of the personal hurdles(障碍) that a beginning graduate student must face,namely how to deal with the profundity(深度，深奥) of mathematics in stark comparison to our own shallow understandings of mathematics. This is in part why the attrition rate(退学率) in graduate school is so high. At the best schools, with the most successful retention rates(保留率), usually only about half of the people who start eventually get their PhDs. Even schools that are in the top twenty have at times had eighty percent of their incoming graduate students not finish. This is in spite of the fact that most beginning graduate students are, in comparison to the general population, amazingly good at mathematics.Most have found that math is one area in which they could shine. Suddenly,in graduate school, they are surrounded by people who are just as good(and who seemeven better). To make matters worse, mathematics is a meritocracy(英才教育).The faculty will not go out of their way to make beginning students feel good(this is not the faculty's job; their job is to discover new mathematics).The fact is that there are easier (though, for a mathematician, less satisfying) ways to makea living. There is truth in the statement that you must be driven to become a mathematician. Mathematics is exciting, though. The frustrations should more than be compensated for by the thrills of learning and eventually creating (or discovering) new mathematics. That is, after all, the main goal for attending graduate school, to become a research mathematician. As with all creative endeavors(创造性事业), there will be emotional highs and lows. Only jobs that are routine and boring will not have these peaks and valleys. Part of the difficulty of graduate school is learning how to deal with the low times.  Goal of Book. The goal of this book is to give people at least a rough idea of the many topics that beginning graduate students at the best graduate schools are assumed to know. Since there is unfortunately far more that is needed to be known for graduate school and for research than it is possible to learn in a mere four years of college, few beginning students know all of these topics, but hopefully all will know at least some. Different people will know different topics. This strongly suggests the advantage of working with others. There is another goal. Many nonmathematicians suddenly find that they need to know some serious math. The prospect of struggling with a text will legitimately seem for them to be daunting(使人气馁的). Each chapter of this book will provide for these folks a place where they can get a rough idea and outline of the topic they are interested in. As for general hints for helping sort out some mathematical field, certainly one should always, when faced with a new definition, try to find a simple example and a simple nonexample. A nonexample, by the way, is an example that almost, but not quite, satisfies the definition. But beyond finding these examples, one should examine the reason why the basic definitions were given. This leads to a split into two streams of thought(思想流) for how to do mathematics. One can start with reasonable, if not naive, definitions and then prove theorems about these definitions. Frequently the statements of the theorems are complicated, with many different cases and conditions, and the proofs are quite convoluted(费解的), full of special tricks. The other, more midtwentieth century approach, is to spend quite a bit of time on the basic definitions, with the goal of having the resulting theorems be clearly stated and having straightforward proofs. Under this philosophy, any time there is a trick in a proof, it means more work needs to be done on the definitions. It also means that the definitions themselves take work to understand,even at the level of figuring out why anyone would care. But now the theorems can be cleanly stated and proved. In this approach the role of examples becomes key. Usually there are basic examples whose properties are already known. These examples will shape the abstract definitions and theorems. The definitions in fact are made in order for the resulting theorems to give, for the examples, the answers we expect. Only then can the theorems be applied to new examples and cases whose properties are unknown. For example, the correct notion of a derivative and thus of the slope of a tangent line is somewhat complicated. But whatever definition is chosen, the slope of a horizontal line (and hence the derivative of a constant function) must be zero. If the definition of a derivative does not yield that a horizontal line has zero slope, it is the definition that must be viewed as wrong, not the intuition behind the example. For another example, consider the definition of the curvature曲率 of a plane curve, which is in Chapter Seven. The formulas are somewhat ungainly.不雅 But whatever the definitions, they must yield that a straight line has zero curvature, that at every point of a circle the curvature is the same and that the curvature of a circle with small radius must be greater than the curvature of a circle with a larger radius (reflecting the fact that it is easier to balance on the earth than on a basketball). If a definition of curvature does not do this, we would reject the definitions, not the examples. Thus it pays to know the key examples. When trying to undo the technical maze迷惑 of a new subject, knowing these examples will not only help explain why the theorems and definitions are what they are but will even help in predicting what the theorems must be. Of course this is vague含糊的 and ignores the fact that first proofs are almost always ugly and full of tricks, with the true insight usually hidden. But in learning the basic material, look for the key idea, the key theorem and then see how these shape the definitions. Caveats for Critics.(对吹毛求疵人的警告) This book is far from a rigorous treatment of any topic. There is a deliberate looseness in style and rigor. I am trying to get the point across and to write in the way that most mathematicians talk to each other. The level of rigor in this book would be totally inappropriate in a research paper. Consider that there are three tasks for any intellectual discipline: 1. Coming up with new ideas. 2. Verifying new ideas. 3. Communicating new ideas. How people come up with new ideas in mathematics (or in any other field) is overall a mystery. There are at best a few heuristics启发 in mathematics, such as asking if something is unique or if it is canonical. It is in verifying new ideas that mathematicians are supreme. Our standard is that there must be a rigorous proof. Nothing else will do. This is why the mathematical literature is so trustworthy (not that mistakes don't creep in, but they are usually not major errors). In fact, I would go as far as to say that if any discipline has as its standard of verification rigorous proof, than that discipline must be a part of mathematics. Certainly the main goal for a math major in the first few years of college is to learn what a rigorous proof is. Unfortunately,we do a poor job of communicating mathematics. Every year there are millions of people who take math courses. A large number of people who you meet on the street or on the airplane have taken college level mathematics. How many enjoyed it? How many saw no real point to it? While this book is not addressed to that random airplane person, it is addressed to beginning graduate students, people who already enjoy mathematics but who all too frequently get blown out精疲力竭 of the mathematical water by mathematics presented in an unmotivated, but rigorous, manner. There is no problem with being nonrigorous, as long as you know and clearly label when you are being nonrigorous. Comments on the Bibliography.There are many topics in this book. While I would love to be able to say that I thoroughly完全地 know the literature on each of these topics, that would be a lie. 哈哈The bibliography has been cobbled被修补的 together from recommendations from colleagues, from books that I have taught from and books that I have used. I am confident that there are excellent texts that I do not know about. If you have a favorite, please let me know at tgarrity@williams.edu. While this book was being written,Paulo Ney DeSouza and JorgeNuno Silva wrote Berkeley Problems in Mathematics[26], which is an excellent collectionof problems that have appeared over the years on qualifying exams (usually taken in the first or second year of graduate school) in the math department at Berkeley. In many ways, their book is the complement of this one, as their work is the place to go to when you want to test your computational skills while this book concentrates on underlying intuitions. For example, say you want to learn about complex analysis. You should first read chapter nine of this book to get an overview of the basics about complex analysis. Then choose a good complex analysis book and work most of its exercises. Then use the problems in DeSouza and Silva as a final test of your knowledge. Finally,the book Mathematics, Form and Function by Mac Lane[82], is excellent. It provides an overview of much of mathematics. I am listing it here because there was no other place where it could be naturally referenced. Second and third year graduate students should seriously consider reading this book.
2回应 20131007 18:26
在哪儿买这本书 · · · · · ·
在哪儿借这本书 · · · · · ·
这本书的其他版本 · · · · · · ( 全部3 )
 Cambridge University Press版 20011112 / 29人读过
 机械工业出版社版 201731 / 7人读过 / 有售
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3 有用 阅微草堂 20130309
很多原创的思想隐藏在初次证明里面。线性代数的关键在于不同的可逆条件的等价性，解方程等价于算子的核元素。复分析的关键是不同的解析函数的定义的等价性。计算复杂性问题本质是可构造性和存在性证明的区别。粒子的运动和曲线（波）的运动是过程和对象之间的类比；Lewy's Example本质是解存在依赖于几何条件
1 有用 GoodMorning 20121221
好书。三百余页的书覆盖了如此广泛的数学，而且深入浅出实属不易。尽管每一专题都是brief overview，但即使是学过此专题，书中对于intuition的强调仍然让人受益匪浅。
1 有用 [已注销] 20140106
1，2章全部+部分散篇 号称休闲读物
0 有用 Grasie 20160515
不像教材，像教辅。
0 有用 Viiiiiii 20121210
好吧，其实我不打算读
0 有用 Grasie 20160515
不像教材，像教辅。
0 有用 黄色小星星 20131008
据说很经典 下次再看
0 有用 Fetalian 20131206
感觉内容太少
0 有用 Viiiiiii 20121210
好吧，其实我不打算读
1 有用 [已注销] 20140106
1，2章全部+部分散篇 号称休闲读物