出版社: Cambridge University Press
副标题: But Need to Know for Graduate School
出版年: 20011112
页数: 376
定价: USD 44.99
装帧: Paperback
ISBN: 9780521797078
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 background. This 2002 book will help students to see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important und...
Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge. But few have such a background. This 2002 book will help students to see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential geometry, real analysis, pointset topology, probability, complex analysis, abstract algebra, and more. An annotated bibliography then offers a guide to further reading and to 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 who need to quickly learn some serious mathematics.
喜欢读"All the Mathematics You Missed"的人也喜欢的电子书 · · · · · ·
喜欢读"All the Mathematics You Missed"的人也喜欢 · · · · · ·
> 更多短评 8 条
All the Mathematics You Missed的书评 · · · · · · (全部 1 条)
雅各比行列式和矩阵的秩
这篇书评可能有关键情节透露
> 更多书评1篇
读书笔记 · · · · · ·
我来写笔记
It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity... Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring t...
20150710 16:21
It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity...Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring theory.Besides, I don't think listing all the definition and theorem then proving them one by one is a good idea to learn mathematics, except that you want a pure proof exercise (but I think it is a wast of time).回应 20150710 16:21 
You need to know: 1. Structure of /公式内容已省略/. 2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative /公式内容已省略/. Actually, to define derivative, linear mapping /公式内容已省略/ is a better idea than a number /公式内..
20150705 20:28
You need to know:1. Structure of ($R^n$).2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative ($\frac{dy}{dx}$). Actually, to define derivative, linear mapping ($\frac{dy}{dx}:R^n \to R^m$) is a better idea than a number ($f'(x)$).3. Inverse function theorem and implicit function theorem.Books:Spivak's Calculus on Manifold is great. I prefer Zurich's masterpiece.回应 20150705 20:28 
PS: \epsilon = /公式内容已省略/ and \delta = /公式内容已省略/. Some basic knowledge of one variable calculus. Actually it is boring. Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of f...
20150705 20:21
PS: \epsilon = ($\epsilon$) and \delta = ($\delta$).Some basic knowledge of one variable calculus. Actually it is boring.Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of function series in a function space with uniform metric).Many people speak highly of Michael Spivak's Calculus. And I recommend V. A. Zurich's Mathematical Analysis.回应 20150705 20:21 
I have learned some linear algebra, so the first chapter is not very interesting. For freshmen, I suggest you to pay special attention to the following points: 0. Definition of vector space. 1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix). 2. Definition and basic ...
20150705 20:13
I have learned some linear algebra, so the first chapter is not very interesting.For freshmen, I suggest you to pay special attention to the following points:0. Definition of vector space.1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix).2. Definition and basic properties of eigenvalues and eigenvectors.3.* Dual space. Many textbook neglect this important topic, which appears frequently in analysis(differential form), geometry(covector) and etc..FYI, I recommend Sheldon, Axler, Linear Algebra Done Right 3ed.回应 20150705 20:13

I have learned some linear algebra, so the first chapter is not very interesting. For freshmen, I suggest you to pay special attention to the following points: 0. Definition of vector space. 1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix). 2. Definition and basic ...
20150705 20:13
I have learned some linear algebra, so the first chapter is not very interesting.For freshmen, I suggest you to pay special attention to the following points:0. Definition of vector space.1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix).2. Definition and basic properties of eigenvalues and eigenvectors.3.* Dual space. Many textbook neglect this important topic, which appears frequently in analysis(differential form), geometry(covector) and etc..FYI, I recommend Sheldon, Axler, Linear Algebra Done Right 3ed.回应 20150705 20:13 
PS: \epsilon = /公式内容已省略/ and \delta = /公式内容已省略/. Some basic knowledge of one variable calculus. Actually it is boring. Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of f...
20150705 20:21
PS: \epsilon = ($\epsilon$) and \delta = ($\delta$).Some basic knowledge of one variable calculus. Actually it is boring.Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of function series in a function space with uniform metric).Many people speak highly of Michael Spivak's Calculus. And I recommend V. A. Zurich's Mathematical Analysis.回应 20150705 20:21 
You need to know: 1. Structure of /公式内容已省略/. 2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative /公式内容已省略/. Actually, to define derivative, linear mapping /公式内容已省略/ is a better idea than a number /公式内..
20150705 20:28
You need to know:1. Structure of ($R^n$).2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative ($\frac{dy}{dx}$). Actually, to define derivative, linear mapping ($\frac{dy}{dx}:R^n \to R^m$) is a better idea than a number ($f'(x)$).3. Inverse function theorem and implicit function theorem.Books:Spivak's Calculus on Manifold is great. I prefer Zurich's masterpiece.回应 20150705 20:28 
It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity... Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring t...
20150710 16:21
It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity...Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring theory.Besides, I don't think listing all the definition and theorem then proving them one by one is a good idea to learn mathematics, except that you want a pure proof exercise (but I think it is a wast of time).回应 20150710 16:21

It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity... Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring t...
20150710 16:21
It covers some basic knowledge of point set topology, including definition of topology space, open and closed set, induced topology, Hausdorff space, base, second countable space, compactness, connectedness, continuity...Almost all the results are ordinary, except the last section: Zariski topology of commutative rings. I recommend to skip it if not having a basic knowledge of commutative ring theory.Besides, I don't think listing all the definition and theorem then proving them one by one is a good idea to learn mathematics, except that you want a pure proof exercise (but I think it is a wast of time).回应 20150710 16:21 
You need to know: 1. Structure of /公式内容已省略/. 2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative /公式内容已省略/. Actually, to define derivative, linear mapping /公式内容已省略/ is a better idea than a number /公式内..
20150705 20:28
You need to know:1. Structure of ($R^n$).2. Differential of a function is a linear mapping, so Jacobi matrix replaces the role of derivative ($\frac{dy}{dx}$). Actually, to define derivative, linear mapping ($\frac{dy}{dx}:R^n \to R^m$) is a better idea than a number ($f'(x)$).3. Inverse function theorem and implicit function theorem.Books:Spivak's Calculus on Manifold is great. I prefer Zurich's masterpiece.回应 20150705 20:28 
PS: \epsilon = /公式内容已省略/ and \delta = /公式内容已省略/. Some basic knowledge of one variable calculus. Actually it is boring. Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of f...
20150705 20:21
PS: \epsilon = ($\epsilon$) and \delta = ($\delta$).Some basic knowledge of one variable calculus. Actually it is boring.Limit, continuity, differentiation, integration, point wise and uniform convergence of function series. Uniform convergence can be understand better after studying metric space (it is just limit of function series in a function space with uniform metric).Many people speak highly of Michael Spivak's Calculus. And I recommend V. A. Zurich's Mathematical Analysis.回应 20150705 20:21 
I have learned some linear algebra, so the first chapter is not very interesting. For freshmen, I suggest you to pay special attention to the following points: 0. Definition of vector space. 1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix). 2. Definition and basic ...
20150705 20:13
I have learned some linear algebra, so the first chapter is not very interesting.For freshmen, I suggest you to pay special attention to the following points:0. Definition of vector space.1. The relation between linear mapping and matrix (Matrix is just a representation of linear mapping and different matrices representation of one linear mapping is similar matrix).2. Definition and basic properties of eigenvalues and eigenvectors.3.* Dual space. Many textbook neglect this important topic, which appears frequently in analysis(differential form), geometry(covector) and etc..FYI, I recommend Sheldon, Axler, Linear Algebra Done Right 3ed.回应 20150705 20:13
在哪儿买这本书 · · · · · ·

亚马逊
508.00 元
买满 ￥88.00 立减 ￥10.00
 > 查看1家网店价格 (508.00 元起)
这本书的其他版本 · · · · · · ( 全部2 )
 清华大学出版社版 20048 / 31人读过 / 有售
以下豆列推荐 · · · · · · ( 全部 )
 学习DL/算法/医学图像分析/的路程 (风细细™)
 外文数学书籍储藏室（A） (Kogorou)
 我的書架數學物理類~ (eulen)
 All the Mathematics You Missed 17 (BBDD)
 论文准备 Methodology (Mogician Hans)
谁读这本书?
二手市场
 > 点这儿转让 有277人想读,手里有一本闲着?
订阅关于All the Mathematics You Missed的评论:
feed: rss 2.0
4 有用 安雪仁次 20140429
终于翻完了这本小巨著，深觉会的部分讲得好浅，不会的部分看这个也不能入门QAQ
0 有用 qwertyuiop 20160308
科普书。
0 有用 philohistoria 20121129
Excellent work...
0 有用 ren 20101228
正在分辨不清雅可比矩阵与黑赛矩阵，或者一致连续与逐点连续，或者散度与旋度，或者测度与度量的时候，遇到了这本书。
0 有用 Harrison 20160824
查漏补缺...可怕的PhD life已经来了
0 有用 头上有角 20150818
理工科读phd前暑假必读书籍之一
0 有用 qwertyuiop 20160308
科普书。
0 有用 TZX 20140707
万门大学童哲推荐的。
4 有用 安雪仁次 20140429
终于翻完了这本小巨著，深觉会的部分讲得好浅，不会的部分看这个也不能入门QAQ