a***s
发帖数: 616 | 1
the algebra generated by "C", right? I'm not sure.
No. The sigma-algebra generated by "C" is larger than the algebra generated
by
"C". You can say "a" is an algebra containing "C".
algebra? I think "a" is unique since it is the "smallest". But then "C"
generates the same algebra and sigma-algebra, right?
It's the unique sigma-algebra.
same algebra? is this generated algebra still "a"? does "a" and "C" generate
the same sigma-algebra? is this generated sigma-algebra contained by "a"?
The algebra |
|
z****e
发帖数: 2024 | 2 多谢。
赞。
“If "a" is the algebra generated by "C", then the sigma algebra generated by "a" and by "C" are the same.”
一看就是行家。
我理解了，如果用你说的 sigma-algebra contains algebra (both of them 阿are generated by the same "C"), 我就能理解你上面这句话了。因为可以证明
sigma-algebra generated by "C"=sc;
sigma-algebra generated by "a"=sa;
sc, sa 相互 contain. 对吧？
但是我没有理解，为什么 sigma-algebra generated by "C" is larger than the algebra generated by "C"?
按照定义，我怎么觉得 sigma-algebra 是一种带有那个可数集限制条件的，一种特殊的 algebra 呢？
问题1：
我觉得怎么 algebra 比 sigma-al |
|
z****e
发帖数: 2024 | 3 HI guys,
could some one explain the following confusion i have? Thanks.
1. since a sigma-algebra is also an algebra,
if subset collection "C" generates a sigma-algebra "a", then "a" is also the algebra generated by "C", right? I'm not sure.
2. Is this "a" unique? In case it is an algebra. Or in case it is a sigma-algebra? I think "a" is unique since it is the "smallest". But then "C" generates the same algebra and sigma-algebra, right?
3. if "a" is an algebra generated by "C", does "a" and "C" g |
|
a***s
发帖数: 616 | 4 过奖了，别这样讲。
sigma algebra满足algebra的性质，但是algebra不一定有sigma algebra的性质。
比如通常讲的Borel sigma algebra当然是algebra: closed under complement, finit
e union, finite intersection。
但是[0,1)上由[a,b)型区间的finite union构成的collection只是一个algebra而不是s
igma algebra: not closed under countable union/intersection. e.g. intersecti
on over all n from 1 to infinity [0.5,0.5+1/n) gives {0.5} which is not in t
his collection. |
|
d*****l
发帖数: 8441 | 5 http://rhart.org/algebra/
https://jhupbooks.press.jhu.edu/content/chinese-roots-linear-algebra
The Chinese Roots of Linear Algebra
Roger Hart
A monumental accomplishment in the history of non-Western mathematics, The
Chinese Roots of Linear Algebra explains the fundamentally visual way
Chinese mathematicians understood and solved mathematical problems. It
argues convincingly that what the West "discovered" in the sixteenth and
seventeenth centuries had already been known to the Chinese for 1,000... 阅读全帖 |
|
o**a
发帖数: 76 | 6 下学期选课，已经定了Numerical Analysis和Introduction to Stochastic Process
两门。还有一门在Theory of Partial Differential Equations和General Algebra之间
犹豫。
我打算以后做应用数学。PDE是应用数学的基础课。但是我在明年四月份必须过
Algebra和Topology之一的qualify考试，否则只能滚蛋。
方案一：选Algebra的考虑是它是现代数学的基础之一，而且选了它对考qualify有帮助。
我打算选Algebra的同时自学Topology。因为我以前没有学过Algebra或Topology。
如果采用这个方案的话，二年级就努力把Algebra和Topology两门基础给打好了。
同时也是集中精力准备qualify考试。
方案二：选PDE的考虑是它对做应用数学的人很有用。早一点学对将来做研究有利。
但是采用这个方案的话，就只能自学Topology，准备qualify考试。而且将来也许
永远都不懂Algebra了。
大家给点建议？谢谢！ |
|
a***s
发帖数: 616 | 7 Sigma algebra is much more complicate than algebra. So we usually start with
studying algebra and then extend the result to sigma algebra.
In constructing the Lebsgue measure, we want to measure as many sets as poss
ible and also make sure that intervals have measure in the common way, i.e.
[a,b) has measure b-a. (Let's focus on the whole set [0,1) to ,make things s
imple.)
So we start with interval of the form [a,b). Then we can easily extend to fi
nite union of intervals of this form, i.e. [a, |
|
z****e
发帖数: 2024 | 8 太牛逼了。收藏了先。
您是教授吧？
最后，为什么 the sigma-algebra generated by "C", contains the algebra
generated by "C" 呢？
我怎么觉得凡是sigma-algebra就都是algebra，这样的话，不是反过来了吗？
谢谢。 |
|
T*******x
发帖数: 8565 | 9 比如集合的交并运算，满足交换律结合律分配律，但不构成ring。这个叫什么algebra
？我看到有set algebra和boolean algebra，但应该还有通用的名字吧？因为元素不一
定是集合。 |
|
u*****7
发帖数: 746 | 10 你这个Saxon 1 不是Saxon Algebra 1, 1是一年级学的，Algebra 1是7，8年级学的。 |
|
|
i******e
发帖数: 1720 | 12 这个标题有些误导吧。貌似不是"高中之前不要教Algebra"。 我的理解是－不是每一
个学生在上高中前必须修了Algebra。 这是两个不同的概念。 |
|
g*****h
发帖数: 15 | 13 College Algebra by Larson & Hostetler
DVDRip | MKV / AVC 692 Kbps | 720х544 | 29.97 fps | MP3 128 kbps | 8.75 GB
Language: English
Lecture Titles:
Prerequisites
P-1 Review of Real Numbers and Their Properties
P-2 Exponents and Radicals
P-3 Polynomials and Special Products
P-4 Factoring
P-5 Rational Expressions
P-6 Errors and the Algebra of Calculus
P-7 Graphical Representations of Data
Chapter 1 – Equations and Inequalities
1-1 Graphs of Equations
1-2 Linear Equations in in One Variable
1-3 Mode... 阅读全帖 |
|
w**d
发帖数: 2334 | 14 【 以下文字转载自 Mathematics 讨论区 】
发信人: wind (one), 信区: Mathematics
标 题: Textbook for linear algebra?
发信站: BBS 未名空间站 (Sat Sep 29 21:43:44 2007), 转信
Anyone knows some good linear algebra textbook? It is
for senior undergraduate or 1st year graduate. I just briefly
went through the books by G Strang and CW Curtis. Seems both are
not very complete. |
|
v******a
发帖数: 45075 | 15 Herstein, Topics in Algebra
after this, you could read Algebra by Waerden |
|
w**s
发帖数: 8 | 16 【 以下文字转载自 Statistics 讨论区 】
【 原文由 whss 所发表 】
f isσ-algebra的定义里的三个条件,
(1) Ai belongs to f --> Union (Ai) belongs to f, i=0,infinite
(2) A belongs to f --> A非 belongs to f
(3) Ω or Φ belongs to f
关于条件(1),我的理解
因为Ω总是属于f,Ω Union whatever = Ω,这个第一个条件是不是就无意义了?
我觉得我的理解有问题.
还有关于sample space的定义,
sample space of a random experiment is a pair (Ω,f),
where Ω is the set of all possible outcomes of the experiment and
f is the σ-algebra of subsets of Ω.
我的问题是, f是不是就是 the power set of Ω?
Ω的power set is the larges |
|
f******n
发帖数: 176 | 17 如果你以后确定要做应用数学，建议选PDE，再选点analysis的课，打好分析的基础。
学懂Algebra固然好，对思维很有挑战，但也许你根本用不着，即使将来要用，自己看书
好了。
除了Algebra/Topology过一门的选择外，没有别的了吗？比如过real/complex/
functional analysis? |
|
o**a
发帖数: 76 | 18 我暑假刚过complex的prelim，剩下还得过topology/algebra中的一门
现在比较倾向选Algebra，
因为我以前在国内读了研究生，学了PDE
据说现在的PDE课，内容和国内的课程差不多
今天早上听代数老师讲课，确实像系里的同学们说的，讲得非常好
书 |
|
g*****h
发帖数: 15 | 19 College Algebra by Larson & Hostetler
DVDRip | MKV / AVC 692 Kbps | 720х544 | 29.97 fps | MP3 128 kbps | 8.75 GB
Language: English
Lecture Titles:
Prerequisites
P-1 Review of Real Numbers and Their Properties
P-2 Exponents and Radicals
P-3 Polynomials and Special Products
P-4 Factoring
P-5 Rational Expressions
P-6 Errors and the Algebra of Calculus
P-7 Graphical Representations of Data
Chapter 1 – Equations and Inequalities
1-1 Graphs of Equations
1-2 Linear Equations in in One Variable
1-3 Mode... 阅读全帖 |
|
F**S
发帖数: 13 | 20 I am embarrassed to ask such elementary questions but they have bothered me
like a bone in my throat for quite a while. Please be so kind to enlighten
me...
The questions are centered closely about infinite dimensionality:
How exactly to see that a mapping space is infinite dimensional? To be
specific, take the simplest example of the vector space, C(R, R), of
continuous functions from R to R, where R stands for the space of real
numbers. The statement must be obvious since books I have consulte... 阅读全帖 |
|
H****h
发帖数: 1037 | 21 查Serge Lang和Thomas W. Hungerford的Algebra书后的Index，
试着检索词条central algebra和unimodular或相关词汇。 |
|
a***g
发帖数: 2761 | 22 【 以下文字转载自 Mathematics 讨论区 】
发信人: truthmostcom (truthmost), 信区: Mathematics
标 题: 天堂的原始本能是一个一元三次代数方程吗？Is an Algebraic Cubic Equation the Primitive Instinct beyond Electromagnetic and
关键字: 方向导数，解析方法，螺旋星系
发信站: BBS 未名空间站 (Sat Nov 27 12:13:43 2010, 美东)
天堂的原始本能是一个一元三次代数方程吗？
我已经开始为我的新论文的发表战斗！
我先放在一个网站里：
http://vixra.org/abs/1011.0057
实际上，我的新论文提供了我的星系理论的完全的解，这个解是一个由一元三次代数方
程表达的解。
很多人习惯于用显函数表达解，隐函数表达解是一样的效果。
读者想一想，你用一个完全的解，去和整个罪恶的世界斗争，是不是要容易的多？
让我极其后悔的是，这个解在2002年底的时候就差不多已经得到。
实际上，我的星系的想法开始于2000年暑假. 2002年... 阅读全帖 |
|
s*******q
发帖数: 310 | 23 statistics新生master，老师让选applied linear algebra 5316
这个和国内的线性代数一样吗？
只看英文版本的applied linear algebra and matrix analysis Thomas S. Shores写的可以不？
我菜鸟一个，过几天上课了，想找书来先看看。大学学的数学都忘的差不多了，多谢赐
教 |
|
xt
发帖数: 17532 | 24 当然是几何。Algebra是中世纪才出现，你如果读一下
莱布尼茨当年在Eruditorium上面发表的莱布尼茨定理
的文章，你会发现还是用几何方法证明的。 |
|
s******r
发帖数: 5309 | 25 geometry是土地（geo）测量（metry）的意思，字根都是希腊文，古希腊时期达到鼎盛
，所以西文里留下这个希腊词根的词。
Algebra是阿拉伯文，Al相当于阿拉伯文里的冠词。代数在西方是舶来品，所以用阿拉
伯文音。 |
|
s********6
发帖数: 245 | 26 I want a book called: Applied numerical linear algebra, the author is James
W. Demmel, SIAM. If anyone has that book, please contact:
612-206-6945, or email: s********[email protected] |
|
a*****g
发帖数: 19398 | 27 美国高中 Algebra 1 围棋数学题（图）
从第一个落子的人的角度看过去，
如果围棋盘中间（天元）为 Origin，
那么这局棋的前四手都分别落在那个Quadrant ？
【里面涉及到围棋文化、逆向推理、代数等知识点】 |
|
a*****g
发帖数: 19398 | 28 美国高中 Algebra 1 围棋数学题（图）
从第一个落子的人的角度看过去，
如果围棋盘中间（天元）为 Origin，
那么这局棋的前四手都分别落在那个Quadrant ？
【里面涉及到围棋文化、逆向推理、代数等知识点】 |
|
y*****p
发帖数: 733 | 29 这个数学教材如何？K班教Saxon Math Algebra 1 合适吗？ |
|
J*******p
发帖数: 1129 | 30 You are not kidding, are you? Algebra for K?
据我所知，Saxon 不是很好的数学教材。 |
|
a*****g
发帖数: 19398 | 31 美国高中 Algebra 1 围棋数学题（图）
从第一个落子的人的角度看过去，
如果围棋盘中间（天元）为 Origin，
那么这局棋的前四手都分别落在那个Quadrant ？
【里面涉及到围棋文化、逆向推理、代数等知识点】 |
|
w****l
发帖数: 269 | 32 These are all text books required by courses:
Linear Algebra and its applications (4th edition), price $70
Introductory Nuclear Reactor Statics, price $60
Introductory Nuclear Reactor Dynamics, price $60
condition: almost new
contact: 765-491-7284 or w*******[email protected] |
|
s********6
发帖数: 245 | 33 I want a book called: Applied numerical linear algebra, the author is James
W. Demmel, SIAM. If anyone has that book, please contact:
612-206-6945, or email: s********[email protected] |
|
a*****g
发帖数: 1320 | 34 【 以下文字转载自 Parenting 讨论区 】
发信人: ashuang (越忙越年轻), 信区: Parenting
标 题: Algebra problem ask for help
发信站: BBS 未名空间站 (Wed Jul 27 00:11:33 2011, 美东)
WHAT IS THE AREA OF THE FIGURE THAT SHOWS THE SOLUTION OF THE SYSTEM -X+Y>=0
, Y>=-2, AND X<=4 WHEN GRAPHED ON A COORDINATE PLANE?
A) 4 SQUARE UNITS B) 12 SQUARE UNITS C) 18 SQUARE UNITS D) 36 SQUARE
UNITS |
|
a*****g
发帖数: 1320 | 35 【 以下文字转载自 Parenting 讨论区 】
发信人: ashuang (越忙越年轻), 信区: Parenting
标 题: Algebra problem ask for help
发信站: BBS 未名空间站 (Wed Jul 27 00:11:33 2011, 美东)
WHAT IS THE AREA OF THE FIGURE THAT SHOWS THE SOLUTION OF THE SYSTEM -X+Y>=0
, Y>=-2, AND X<=4 WHEN GRAPHED ON A COORDINATE PLANE?
A) 4 SQUARE UNITS B) 12 SQUARE UNITS C) 18 SQUARE UNITS D) 36 SQUARE
UNITS |
|
x***m
发帖数: 1733 | 36 where did you learn algebra? hehe |
|
|
m******s
发帖数: 118 | 38 it's not "Required", however in many schools here in bay area, algebra
starts in 4th grade.
and why does this have anything to do with same sex stuff? |
|
b*****s
发帖数: 1124 | 39 Joking? Which public school start Algebra in 4th grade? |
|
|
f*******5
发帖数: 1815 | 41 algebra starts in 4th grade. 呵呵， 这怎么可能哪？
我邻居小孩上最好的小学之一， API 近1000分， 3 年级， 现在正在教乘法， 绝大
部分小孩都用手指算。 |
|
i******e
发帖数: 1720 | 42 呵呵。当年我家娃很兴奋地报告，we learned geometry. 我一看，就是画个方块叫
square, 画个三角叫triangle. 除非用的一寸厚的教科书封皮上写着“Algebra", 否
则学术意义上都不算。 |
|
m******s
发帖数: 118 | 43 Now you know. hehe
My son is in one of the Cupertino schools.
4th graders start to learn basic algebra, concepts like, evaluating
expressions with variables, solving simple equations with one variable etc.
Heck, once the teacher even gave a problem solving two variables in two
equations.
I think it's all good. |
|
d****a
发帖数: 492 | 44 San Ramon School district still have money to keep the GATE program. 4th
graders start to learn Algebra .
The school budgets in the south bay are so tight and a lot of classes have
but off. so frustrated on that. where the money go?
Thinking about move to San Ramon for better school and life. |
|
v**t
发帖数: 25 | 45 For a Data schema:
Customer(cid, cname, address)
Truck(tid, brand, capacity)
Product (pid, price)
Delivery(did, tid, pid, cid)
How to use relation Algebra to express:
Find ID of all Trucks delivering to all customers.
Could someone help me? Thanks a lot. |
|
c***c
发帖数: 21374 | 46 sql和relation algebra相互转换
free的，呵呵 |
|
mw
发帖数: 525 | 47 【 以下文字转载自 CS 讨论区 】
发信人: mw (mw), 信区: CS
标 题: 大家编程用得algebra lib是什么？
发信站: BBS 未名空间站 (Sat Aug 13 07:18:03 2005)
是都用lapack 吗？
还是有什么更通用的？ |
|
H****h
发帖数: 1037 | 48
没有说Ai中有Ω呀。
也有不是power set的σ-algebra。 |
|
w**s
发帖数: 8 | 49
Ai中有Ω还有Φ,第三条.
是有,power set只是最大的σ-algebra,但是在sample space 的定义里的f,
是不是Ω的power set呢?还是你的意思是说这里f也可以不是power set,
只不过我看到的书上的例题是power set. |
|
B****n
发帖数: 11290 | 50
if Ai is not Ω but in f, union of Ai is still in f
so condition 1 is still meaningful
of course not. Although it's very convenient to use power set as its
sigma algebra, sometimes the power set is too large to be meaningful.
(one of the reasons is not measurable in some cases such as
[0,1]'s power set) |
|
