数学系集合论的书在国外考上了数学系硕士,方向是应用集合论,导师给了本KENNETH KUNEN的SET THEORY,但

已经有了几个解答，1，2，3，我不作了。4，我用另一个方法证明，实际上给了一个定理，可以直接用的。5.好像楼上的结果都有毛病，我来试试。
4.。用｛a1,a2,a3｝表示｛B1,B2,B3｝的表示矩阵为A：
（1 1 0）
A＝（0 1 1）
（1 0 1）
∵A的行列式|A|＝2≠0.
∴｛a1,a2,a3｝与｛B1,B2,B3｝可以互相线性表示。假如｛B1,B2,B3｝线性相关。则它的最大线性无关组的容量＜3，可以表示｛a1,a2,a3｝。
从定理“少表多，多相关”得到，｛a1,a2,a3｝线性相关，矛盾。
∴｛B1,B2,B3｝线性无关。
（定理：容量相同的两组向量，一组可用另一组线性表示，如果表示矩阵的行列式不为零，则这两组向量的秩相等。）
5.。|λI-A|=（λ-1）²（λ+2）.特征值λ=1（二重），λ=-2。
λ＝1：3x1+6x2＝0.
有特征向量（2.-1，0），（0，0，1）。
关于λ＝1的全部特征向量是：
C1（2.-1，0）＋C2（0,0,1）.（C1,C2不全为零）。
λ＝-2：-6x1-6x2＝0.
3x1+6x2-3x3＝0.
有特征向量（1,-1,-1）.
关于λ＝-2的全部特征向量是：C（1,-1,-1）.（C≠0）
（这里再请注意：A有三个线性无关的特征向量，以之为列作可逆矩阵P.有
P逆AP＝对角阵｛1，1，-2｝。这正是特征方法的精髓：对角化。）

解题思路：根据题意，先把5名实习教师分成三组，一组1人，另两组都是2人，计算其分组的方法种数，进而将三个组分到3个班，即进行全排列，计算可得答案．

将5名实习教师分配到高一年级的3个班实习，每班至少1名，最多2名，
则将5名教师分成三组，一组1人，另两组都是2人，有

C15•
C24

A22=15种方法，
再将3组分到3个班，共有15•A₃³=90种不同的分配方案，
故选B．

点评：
本题考点： 计数原理的应用．

考点点评： 本题考查排列、组合的综合运用，注意此类题目一般顺序为先组合、再排列

不会有无数个线性无关的解
这是因为 向量的个数大于维数时线性相关.
如果从可以由其一个解向量组线性表示的角度看
齐次线性方程组与非齐次线性方程组的区别在于:
1.齐次线性方程组的任一解都可由其基础解系线性表示,反之,基础解系的任一个线性组合仍是齐次线性方程组的解
2.对非齐次线性方程组,上述的反之是不成立的.
所以,我所见到的教材中,非齐次线性方程组并没有基础解系的概念

1.根据数列极限收敛定义,希望能够找到 Xn的极限值,前提是当n足够大,n>N.所以证明唯一性的时候,我们有了两个 N1 和N2,当n>max(N1,N2),也就是n>N1,并且 n>N2..(保证两个前提条件满足) 那么数列Xn 都满足那两个极限条件,
abs(Xn-a)

如0.3252525……
=0.3+0.0252525……
=3/10+25/990
0.365079
=0.3……+0.065079……循环（任意拆成两个.因为题要两个分数和的形式.）
=3/9+65079/999990

2的6次方
六位数中的每一位都有两种可能所以是2×2×2×2×2×2

事件C表示被选学生是三年男生

刷习题集呗,定理什么的能理解最好,至少也得会用,关键是自学中不懂的要尽量搞懂它,毕竟没老师问,不过可以上知道啊,相信广大的网友力量是无穷的!

复矩阵中对应元素为共轭关系
这是大一开始几周就上的课,都忘得差不多了,高等代数上的内容,可以找本书看一下

你以后报的就是新G了~
以后1个月考一次所以不再有什么时候报名什么时候考的问题了~
好好准备就行~

iesz表示论：每个正线性泛函对应一个正borel测度.
任意找个有界正线性泛函、就可以找到你想要的测度了.

每个方面都可以但国外还是更注重基础数学

解析几何最重要的思想是：如何将几何图形量化,代数的语言是精确的,还自有一套运算体系,所以如果能把图形转化为代数研究将更能提高图形的应用,

一个量杯，一灯泡
将适当的水放进量杯中，记下水的体积V1，再将灯泡浸入水中，记下水涨后的体积V2，V2-V1就是灯泡的体积，也就是灯泡容积

大工的数学系现在已经叫数学科学学院了.基础数学师资强,应用数学好出论文好毕业,看你怎么取舍了.

应该直接看数学分析,他和高等数学对于数学的训练侧重是不一样的,数分侧重证明,即数学研究思维的培养,而高数一般侧重于计算,即数学在其他一些非数学领域中的实际应用.大多需要计算.
所以要读数学专业的话,一定是直接看数学分析没错.不用弄高数,学完数分,高数就是小case了.

act as Vice Director in the Students Union office of Math. Department

很难说谁是剑桥大学数学系的创始者,只能说Robert Recorde、Wallis、 Barrow、Newton及后来的数学家们逐渐创建并发展了现代意义上的数学,并形成了剑桥大学数学系.
---------------------------------------------------------------------
The History of Mathematics in Cambridge
Mathematics has been studied at Cambridge for a long time. The first figure of note is Robert Recorde (born about 1550) who is credited with the invention of the equality sign "=". He wrote several textbooks in the form of dialogues, but his last book ends with the author being arrested for debt.
Those with less antiquarian interests start their history a century or so later with Wallis, Barrow and Newton. (All three luminaries had interesting non-mathematical careers. Wallis broke codes for the parliamentary side in the civil war. Barrow was noted for his strength and courage, and once when travelling in the East saved his ship by his own prowess from capture by pirates. Newton took a very public part in the university's quarrel with King James II.)
The spectacular success of Newton's work had the fortunate effect of establishing the prestige of mathematics in Britain and Cambridge and the unfortunate effect of blinding British mathematicians to progress in mathematics elsewhere. The parochial century that followed was not a very glorious period for Cambridge or British mathematics. However, it witnessed a slow but important change described in the next paragraph.
Over the years, the syllabus of the Medieval university had lost its relevance and the disputation by which it was examined became a mere formality. Sometime around 1725, a voluntary examination was instituted to help order the better students. At first, the examination was oral and consisted of questions on mathematics and some philosophy. Later, the candidates wrote their answers but the questions were dictated and finally, in around 1790, the questions were printed. Thus was born the Cambridge Mathematical Tripos, the grandparent of every university examination in the world.
The examinations were held in January in the Senate House — a building which happens to be a very beautiful one, with a marble floor and a highly ornamental ceiling; and as it is on the model of a Grecian temple, and as temples had no chimneys, and as a stove or fire of any kind might disfigure the building, we are obliged to take the weather as it happens to be. Sometimes the ink froze in the inkwells.
Since the Mathematical Tripos was the only way in which students could show intellectual prowess, it was taken by many who went on to achieve distinction in other areas. A suitable example, given our present address, is provided by Thomas Clarkson who helped lead the fight against the slave trade. Even when examinations in other subjects became available, the Mathematical Tripos continued to produce people like Keynes and Bertrand Russell who gained eminence in very different fields.
In the 1820s, a group of young mathematicians including Babbage (of the Analytical Engine) modernised the Tripos to take account of the work of continental mathematicians and the glory days of the examination began.
The details changed but, as described by Galton, the examination lasted five and a half hours a day for eight days. Those in the top class were (and still are) called Wranglers in an echo of the old system of disputation. The candidates were listed in order of marks with the top candidate being 'Senior Wrangler' the next 'Second Wrangler' and so on. In one list that Galton was allowed to consult, the Senior Wrangler got more than 7,500 marks, the lowest Wrangler got about 1,500 marks and the lowest candidate to get honours (obtaining 'the wooden spoon') got 300 marks. Although the owner of the wooden spoon had 100 people above him, he in turn outclassed 300 'poll men' who failed or, more usually, did not attempt to obtain honours. (Galton was a poll man.)
The Tripos became something of a national event with substantial betting on the outcome. When, in 1890, Miss Fawcett was placed 'above the Senior Wrangler' (i.e. beat all her male competitors) this, according to the Dictionary of National Biography, 'materially advanced the cause of higher education for women and naturally gave her mother the greatest satisfaction'.
It may be doubted that a system in which the best students spent three years training to solve problems against the clock represented the ideal way to teach mathematics. However, this system was the nursery for the great flowering of British physics in the 19th century. Its products included Maxwell (2nd Wrangler), Kelvin (2nd Wrangler), Stokes (Senior Wrangler) and Rayleigh (Senior Wrangler). On the pure side it produced Sylvester (2nd Wrangler) and Cayley (Senior Wrangler). Pearson, the father of modern statistics, was a 3rd Wrangler.
The 19th century Cambridge system concentrated on undergraduate teaching. Although good research was admired, it was not viewed as a professional duty and the university was not expected to provide support for it. A different view developed in France and then, still more strongly, in the great German universities. Over the course of the 20th century, Cambridge mathematics moved to align itself first with the German model of a research driven university and then with the successor model presented by the major (post 1950) US universities.
Landmarks in this process include the publication of Hardy's A Course of Pure Mathematics (still, as a glance at Amazon will show, a best seller after nearly a century) and the abolition of the order of merit in the Mathematical Tripos in 1909. Present day exams are hard but not ferocious.
Under the old system, the best placed Wranglers could take a further exam in some of the higher branches of mathematics for a Smith's prize. When Kelvin found an interesting result in three dimensional calculus, he communicated it to Stokes who set it as a question in the Smith's prize exam. It is now known as Stokes' theorem. The Smith's prize exam evolved into the present Part III, a one year postgraduate qualification taken by about 200 students from all over the world. From 1885, Smith's prizes (now supplemented by Rayleigh and Knight prizes) were given for an essay in mathematics instead. Today, this usually presents the student's own work after 4 terms of research. Past winners include Turing, Coxeter, Ingham, Hodge and Hoyle.
Although a Faculty like that of the 1930's which included Dirac, G. I. Taylor, Sir Harold Jeffreys, Phillip Hall, Hardy, Littlewood and Mary Cartwright could hardly be faulted on the grounds of research, the supporting structure seems strange to modern eyes. The Faculty met from time to time to decide who should lecture on what, but there was no communal building and everyone worked in their own college.
In about 1960, the Faculty was finally organised into departments. These were housed in a very lightly converted old printing house and offices formerly owned by CUP and then awaiting demolition to make way for a new road. After 40 years, it became clear that, not only was the road never going to be built, but the growth of the Faculty had rendered the premises grossly overcrowded.
In an extraordinarily short time, enough money was raised to move both departments to splendid new buildings in the Centre for Mathematical Sciences (CMS) off Clarkson and Wilberforce Roads. (Wilberforce was another Cambridge anti-slavery campaigner.) Of the £61.4 million required for the whole building project, a total of £30.8 million, or 50%, came from private sources. Another £14 million came from public funds, and the rest from within Cambridge.
Over the last hundred years, the Faculty has grown slowly but steadily and has become more and more international in its staff and students. We hope and expect that these trends will continue. As a result of these and other factors, some of which were discussed above, Cambridge has come to resemble other great mathematical centres much more than it used to. We think, however, that it retains its commitment to teaching at the undergraduate and graduate level together with a certain mild eccentricity.
A search in the Mactutor archives for articles including the word 'Cambridge' will give a good idea of the mathematicians associated with Cambridge but does not include several important physicists. A search for articles including the word 'Wrangler' will give a good idea of the mathematicians who were undergraduates at Cambridge. The Oxford Dictionary of National Biography web site can only be accessed by subscription but, if you can access it, a search for biographies including the word 'Wrangler' will reveal the place this distinction occupied in British life. (A search under 'Optime' gives some of those who attained honours at a lower standard.)

上百度

Reference
[1] Chen Chuanzhang, the Department of mathematics of Fudan University, higher education press
[2] of the Tongji University, "higher mathematics" Fifth Edition
[3]2001 Gu Meiling, the theory and method of university mathematics. Guizhou Education Press,.1995
[4] high Xianglin, development ideas of university mathematics. '' mathematical bulletin 2002 tenth
[5) Zhang Dianzhou, Song Naiqing. Introduction to Mathematics Education (M). Beijing: Higher Education Press, 2006
(6) Tu Rong Bao, Wang Guangming, Ning Lianhua. A new mathematical teaching theory [M]. Shanghai: East China Normal University press, 2008
[7] Ouyang optical medium. Mathematical analysis (Part 1) [M]. Beijing: Higher Education Press, 2007
[8] Liu Yulian et al. Lecture Notes in mathematics analysis (2) [M]. Beijing: Higher Education Press, 2003

这种问题要用二分法近似求把8/π^2*(1+p/k)与e^p*e^t设为p的两个函数,这两个函数的图像有几个交点取决于k、t的正负.在交点附近用二分法逐渐逼近求解.

0是自然数吗?在教学数的整除这一章节中往往会碰到这样的问题,大家争论不休.我们说自然数是指：用来可以数数的数,那么0也可以数,表示没有物体.从这一点来说0应该是自然数.但最终我不敢确定.最近,看到这样的一段解释,现摘录如下：
我们接到一些小学数学教师、家长和学生的来信、来电,询问0是否是自然数的问题.现予以解答如下：
从历史上看,国内外数学界对于0是不是自然数历来有两种观点：一种认为0是自然数,另一种认为0不是自然数.建国以来,我国的中小学教材一直规定自然数不包括0.
目前,国外的数学界大部分都规定0是自然数.为了国际交流的方便,1993年颁布的《中华人民共和国国家标准》（GB3100~3102-93）《量和单位》（11-2.9）第311页,规定自然数包括0.所以在近几年进行的中小学数学教材修订中,我们的教材研究编写人员根据上述国家标准进行了修改.即一个物体也没有,用0表示.0也是自然数.
但是,在小学阶段的“整除”部分,仍然不考虑自然数0,因而在约数、倍数等概念中都不包括0.另外,一般情况下我们不说数0是几位数,所以最小的一位数是1.
看到这里又想到,偶数的概念,能被2整除的数叫做偶数,那么0是吗?肯定是.但是偶数的话必须得是自然数,这怎么跟学生解释了呢?要我们小学老师说,0不是自然数,到初中或高中又要说是,那不是让学生们看笑话吗?真的很难理解.我觉得不能自圆其说,最好的方法应该是把准确的答案告诉学生.让学生们从小有一个科学的说法.
呵呵,不过现在小学教的是"0是自然数"

数学分析已经掌握了就基本差不多了.对于分析学来说,后续的话,主要就复变函数论,实变函数论,泛函分析,拓扑,还有偏微分方程.
对于代数而言,主要就是抽象代数,线性代数,近世代数等等.
物理的话,确实是如此,就是把一些问题进行微元,从而用微积分来解决更一般性的问题.

“许多”和“都”的概念不一样
如果这么说就对了:
数学系的学生都学了不少文科课程,王颖是数学系的学生,所以她也学了不少文科课程.
哲学系的教师都写过哲学方面的论文,老张是哲学系的一名教师,所以他也写过许多哲学方面的论文.

图书馆是一栋白色的高楼.
图书馆有8层.
数学系大楼有50米高.
The building of the math department is 50 meters high.
数学系大楼看起来像一艘帆船.
The building of the math department looks like a sailing boat.
计算机中心共有200台计算机.
The computer center has 200 computers altogether.
学生可以在计算机中心免费上网吗?
Can students surf the internet for free in the computer center ?
我的宿舍是单人间.
My dormitory is a single room.
我宿舍的窗帘是紫色的.
The curtain color of my dorm is purple.
这张学生卡有什么作用呢?
what are the functions of this student card?
你可以用这张学生卡去图书馆借书,在计算机中心上网,还可以去健身中心健身.
With this student card,you can borrow books in the library ,surf the internet in the computer center and keep fit in the fitness center .

这要看你学的是什么专业，数学系一般有数学与应用数学专业、信息与计算科学专业、统计学专业等，不同的专业所学的课程是不一样的。
数学与应用数学专业的主要课程有：分析学、代数学、几何学、概率论、物理学、数学模型/数学实验、计算机基础、数值方法、数学史等。
信息与计算科学专业的主要课程有：数学基础课(分析、代数、几何)、概率统计、数学模型、物理学、计算机基础(计算概论、算法与数据结构、软件系统基础)、信息科学基础、理论计算机科学基础、数值计算方法、计算机图形学、运筹与优化等。
统计学专业的主要课程有：数学基础课(分析、代数、几何)、概率论、数理统计、运筹学、计算机基础、应用随机过程等。

I'm a freshman from class 1 of the Department of Mathematics ,Peking University

就我学过的专业课而言,大致情况是这样的：
大一：数学分析,高等数学,解析几何,高等几何
大二：数学分析,常微分方程,实变函数,复变函数,微分几何,运筹学与控制论
大三：近世代数,拓扑学,泛函分析,概率论与数理统计,初等数论.
数学分析选论,高等代数选论（这两门为考研做准备）
大四：数学分析选论,高等代数选论（这两门为考研做准备）
其中,数学分析开三学期还是四学期是根据学校情况而定的.也有学校学离散方程、数学史等等.

申请滑铁卢大学数学系一般需要平均分至少是83分,数学单科一般至少是86分以上.但是注意这只是“至少”,很多入学学生分数都比这个要高!Good luck.

没有必要 自学
自学 数分学华东师范大学出版社的
除了一些重点大学,一般本一的数学系都用这套教材

你要能全做上了才叫不正常 大家都是这样的 没事多想想水平自然就提高了

Department of Mathematics
Department of Computer Science
Mathematics Department
Computer Science Department

没有。。而且数学系的不学线性代数吧 我们叫 《高等代数》。也没有lz说的三次型四次型。

这几门课就是所谓的老三高和新三高,属于数学系的基础课和专业基础课,即使都学下来,还不能算够数学系本科毕业生的水平.

1+1=2
我修改了问题 所以排在最后了 这个笑话问题还不错 你拿去看看.）刚才打的字不知道怎么搞没了 是我手抄报里的笑话男孩几岁了
"这男孩有几岁了?"售票员问道.竟然有人对他的家庭事务深感兴趣,这真使那乡下人受宠若惊,他得意地回答:"我儿子的年纪是我女儿年纪的5倍,我老婆的岁数是我儿子岁数的5倍,我的年龄为我老婆年龄的2倍,把我们的年龄统统加到一起,正好是祖母的年龄,今天她正要庆祝81岁生日."
试问：那男孩有几岁了?
答案
小男孩的年龄是5岁.

I call***, is mathematics to fasten 072 class a students of classes, I am the character space is bright, cheery girl, take pleasure in help nearby of the classmates, the time in senior high school, I look forward to the life of university very, now, I have already become one member in the tens of thousands university student, I feel very happy.
I love dancing, therefore, at the school hold of the third cultural stanza, lucky of in other classmates waited total 20 people to attend dancing of whole school to compare together just, and acquire an etc. prize.
I have a passion for this university, having already enriched a colorful life here, making amiable of teacher, there is the friend of docile amiability, in order to can live here for 4 years but feel honor, I therefore, I the life for this 4 years, I certainly double effort, delineate perfect picture for my life.

1 要他这个数学系的高材生来接小学二年级的应用题,真是（高射炮打蚊子——大材小用 ）
2 十几年的军旅生涯,让他们结下了深厚的革命情谊,可以说是（ ）
3 真没想到,平日里大大咧咧的他竟然还有如此细心的一面,真是（ ）