孙成-高考志愿专家2016-04-23 21:49:31高考报考指南 大学专业解读 阅读(1817) 评论(0)
声明：本文由入驻搜狐公众平台的作者撰写，除搜狐官方账号外，观点仅代表作者本人，不代表搜狐立场。举报
数学是一门最古老的科学，有着悠久的历史。早在公元前3000年左右，古巴比伦、古埃及、中国就相继出现了算术、代数和几何，被应用于天文、税收及建筑等领域。想想看，在牛顿时代就可以算出每秒钟8公里的第一宇宙速度，为星际航行的开端迈出了第一步。爱因斯坦质能方程成就了核子物理，也为人类指出寻找新能源的方向。这些伟大发现的背后都离不开数学原理。
现代生活中数学更是无处不在，从指纹识别到CT技术，从数据处理到信息安全，从大气科学到火箭飞行器的设计，从地质勘探到施工建筑，形形色色的技术革命的背后，数学都扮演着不可缺少的角色。那么数学到底是怎样一个学科，包含了哪些专业，未来就业出路如何呢?
一、专业解析
什么是数学
什么是数学?很多科学家从不同的角度给过不同的定义。米斯拉说：“数学是人类的思考中最高的成就。”爱因斯坦说：“纯粹数学，就其本质而言，是逻辑思想的诗篇。”伽利略说：“自然界这部伟大的书是用数学语言写成的。”
数学是自然科学之基础。从概念上讲，数学是研究数量、结构、变化以及空间模型等概念的一门学科。
数学有广阔的应用空间。著名数学家华罗庚说：“凡是出现‘量’的科学部门中就少不了要用数学。研究量的关系、量的变化、量的变化的关系，量的关系的变化等等现象都是少不了数学的，所以数学之为用贯穿到一切科学部门深处，而且成为它们的得力的助手和工具。”
数学也有纯粹理论的一面。现代数学已经发展出了众多的分支，而且不断深入。在纯数学很多领域，数学家的工作不为大众所了解，很可能也看不到什么应用前景，但是，数学的美激励着一代代数学家不断去探索未知。
大学里数学学什么?
数学类专业属于理学，按照教育部《普通高等学校本科专业目录》(2012年)的划分，数学类专业主要包括数学与应用数学、信息与计算科学、数理基础科学(特设)等。
数学与应用数学包括基础数学和应用数学两方面。基础数学研究的是数学本学科的基本理论与发展规律，如著名的哥德巴赫猜想等问题就是基础数学的研究对象;应用数学就是由大量的实际问题引发的数学理论，解决现实生活或其他学科与科学技术中碰到的问题;信息与计算科学包括计算数学与信息处理中的数学两个方面，主要培养学生运用数学的思维和方法解决信息技术领域中的实际问题。另外，统计学是应用数学的一个分支，很多高校的数学学院除了有数学系、信息科学系外，还设有统计、精算、金融数学等科系。
数学系毕业生小李说：“大学之前的数学可以称为初等数学，大学是进入高等阶段的学习。高等数学不是初等数学的一种简单提升，而是以微积分和高等代数为基础的一个体系，大致可以衍生出五个专业方向，即：基础数学、应用数学、概率统计、科学与工程计算、信息科学等方向，只是不同的学校名称可能不一样。”
数学与应用数学专业的课程比较偏重基础数学理论，核心课程有分析基础、高等代数、几何学、常微分方程、实变函数、概率论、科学计算、抽象代数、微分几何、复变函数、泛函分析等。同一专业各校开设的课程或许也有不同，考生可根据兴趣爱好和不同专业查阅高校课程设置。
二、专业与就业
很长一段时间以来，人们认为数学这样的基础学科难学、就业不易，是专业中的冷门。然而事实上，基础学科和应用学科之间存在着你中有我、我中有你，相互交叉、相互渗透的联系。以数学为代表的基础科学，就像是一个强大的引擎，它的运转带动相关科学研究和具体技术的巨大发展。
近几年，数学等理学基础类专业，无论是在校生规模还是就业率都呈上升趋势，男女比例也不再是男生一统天下的局面，甚至出现了女生更多的现象。阳光高考平台统计数据显示，数学与应用数学专业2013年毕业生规模在46000-48000人，就业率在80%-85%之间，男女比例为1∶1.3。
1. 就业面较广
社会对数学人才的需求也是多方面、多层次的。无论是进行理论研究、科研数据分析、软件开发还是从事金融保险、国际经济与贸易、工商管理、通讯工程、建筑设计等行业，都离不开相关的数学专业知识。其应用面也极其广泛，具有扎实基础的数学人才既可以做职业数学家，又可以在各类学校做数学老师;还可以成为某种领域(如金融、统计)的数据分析师，也可以从事软件设计、工程计算、网络安全、国防科技等方面的技术工作。
2. “跨专业”方便
数学专业毕业生具有比较扎实的理论基础，只要再学习一些相关知识，他们可以转向很多理工、经济类专业，比如计算机、统计、金融、经济学等。随着现代计算机技术的飞速发展，需要一大批懂数学的工程师做相应的数据库开发，经济领域中也有很多情况需要具有专业数学知识的人才。
本科毕业生除了就业，还可以选择读研或出国深造。事实上，基础类专业毕业生很多都会选择继续深造。浙江大学该专业选择读研究生的学生，有三分之一选择继续从事基础数学研究方向，三分之一选择应用数学方向，另外有三分之一选择经济、金融、精算、计算机等其他方向。北京大学本科毕业生中约30%得到美国或欧洲著名大学的奖学金，出国攻读学位;约50%保送攻读国内硕士或博士学位;国内就业只占20%。清华大学2014年本科毕业生，境外深造人数占 58%，本科读研人数占37%，就业比例占5%。
数学专业毕业生在专业知识、逻辑性思维和创新能力上都有较大的优势，一般来说，跨专业考研或跨专业就业都不困难。
3.上升快、收入高
据统计，毕业后收入较高、工作相关度高、提升较快的专业主要集中在计算机、金融、信息安全、软件工程等相关行业领域。而数学专业毕业生大多从事相关行业的技术岗位，如精算师、银行、证券业工作、程序员、数据分析师等。
“21世纪依赖高技术劳动力，”康奈尔大学应用数学教授史蒂芬?斯托加茨说，“如果你想进入高科技行业、医疗或者金融行业，你必须对数学得心应手。若放弃数学，你根本不会有这些机会。”OECD成员国对成年人知识技能的调查显示，缺少数学技能严重限制了人们获得更好的报酬和更好的工作。在新兴市场国家，精通数学的人，收入平均比其他人高出40%。
三、报考指南
开设院校多 选择余地大
目前，全国本科阶段开设数学类专业的院校有108所，开设数学与应用数学的专业院校有523所，大多集中在一批、二批院校中，考生可选择的余地较大。
成绩拔尖的同学可以考虑历史悠久、实力雄厚的名牌高校。如北京大学、清华大学、北京师范大学、南开大学、吉林大学、复旦大学、南京大学、浙江大学、中国科学技术大学、山东大学、四川大学等，这些院校都拥有数学一级学科国家重点学科，名师云集，专业齐全。像首都师范大学、华东师范大学、厦门大学、武汉大学、中山大学、大连理工大学、湘潭大学、中南大学等一些院校的数学专业二级学科也都拥有国家重点学科，专业实力很强。
师范院校是基础专业开设较比较集中的院校，在500余所开设数学与应用数学专业的院校中，师范院校就占了135所。除了北京师范大学、华东师范大学外，陕西师范大学、华中师范大学、东北师范大学等也实力强劲。这类院校中的数学专业大多是师范类专业，当然也有非师范专业。
另外，二本院校中可选择的范围也很广，很多高校数学专业都各具特色。由于开设院校多，该专业在各个高校的培养特色和课程设置上也有不同侧重。有的侧重基础数学、金融数学，有的侧重理论与应用，有的侧重信息与计算科学。考生在选报时，可根据自己的兴趣爱好和分数情况等综合考虑。
了解专业方向和招生大类
值得注意的是，在招生时，一些高校是按数学与应用数学专业招生，如北京师范大学的数学与应用数学专业包括基础数学、应用数学、数学教育、信息处理与计算科学等方向;中央财经大学的数学与应用数学专业、金融数学方向等。还有很多高校是按“数学类”招生的，比如北京大学、复旦大学、南开大学等。不同院校的专业类中包含的专业不同，以北大为例，数学科学学院设有五个系：数学系、概率统计系、科学与工程计算系、信息科学系和金融数学系。北大招生时按数学大学科招生，入学两年后学生可自由选择进入五个系之一学习。
考生在报考时，可提前了解一下报考院校专业大类中包含哪些专业。一般来说，各个专业在大一大二所开设的基础课程基本相同，大二下学期才进入各自的专业学习。另外，有很多院校的理科实验班学生毕业以后也可以选择数学专业为将来的发展方向。
学好数学，爱好很关键
一般来说数学能力强的人，基本体现在两种能力上，一是逻辑思维能力，二是抽象思维能力。爱因斯坦也说过：“纯粹数学，就其本质而言，是逻辑思想的诗篇。”所以，考生在报考数学专业时，最好要了解自己的专长和兴趣，例如是否擅长逻辑思维、是否有较好的图形、图像想象力及代数运算能力，是否喜欢用数学概念来了解和解释世界。
不同于其他学科，纯数学是一个偏重理论研究的基础学科。兴趣爱好、良好的基础和天赋是发展的关键。如果希望自己将来能从事数学基础理论的研究并有所建树，首先要对数学有浓厚的兴趣和探究、钻研精神，其次最好有一定的数学天赋。
（文章来源：阳光高考，若涉及侵权，请联系管理员进行删除）
聚铭师教育“聚天下名师 助四海学子”
微信咨询：17701057000 全国高考志愿QQ群：527315338 电话：010-57354567http://learning.sohu.com/20160423/n445775912.shtml
Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\title{\bf Announcement 179: Division by zero is clear as z/0=0 and it is fundamental in mathematics\\
}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
\date{\today}
\maketitle
{\bf Abstract: } In this announcement, we shall introduce the zero division $z/0=0$. The result is a definite one and it is fundamental in mathematics.
\bigskip
\section{Introduction}
%\label{sect1}
By a natural extension of the fractions
\begin{equation}
\frac{b}{a}
\end{equation}
for any complex numbers $a$ and $b$, we, recently, found the surprising result, for any complex number $b$
\begin{equation}
\frac{b}{0}=0,
\end{equation}
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices, and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers. The result is a very special case for general fractional functions in \cite{cs}.
The division by zero has a long and mysterious story over the world (see, for example, google site with division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei, Takahasi (\cite{taka}) (see also \cite{kmsy}) established a simple and decisive interpretation (1.2) by analyzing some full extensions of fractions and by showing the complete characterization for the property (1.2). His result will show that our mathematics says that the result (1.2) should be accepted as a natural one:
\bigskip
{\bf Proposition. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ such that
$$
F (b, a)F (c, d)= F (bc, ad)
$$
for all
$$
a, b, c, d \in {\bf C }
$$
and
$$
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
$$
Then, we obtain, for any $b \in {\bf C } $
$$
F (b, 0) = 0.
$$
}
\medskip
\section{What are the fractions $ b/a$?}
For many mathematicians, the division $b/a$ will be considered as the inverse of product;
that is, the fraction
\begin{equation}
\frac{b}{a}
\end{equation}
is defined as the solution of the equation
\begin{equation}
a\cdot x= b.
\end{equation}
The idea and the equation (2.2) show that the division by zero is impossible, with a strong conclusion. Meanwhile, the problem has been a long and old question:
As a typical example of the division by zero, we shall recall the fundamental law by Newton:
\begin{equation}
F = G \frac{m_1 m_2}{r^2}
\end{equation}
for two masses $m_1, m_2$ with a distance $r$ and for a constant $G$. Of course,
\begin{equation}
\lim_{r \to +0} F =\infty,
\end{equation}
however, in our fraction
\begin{equation}
F = G \frac{m_1 m_2}{0} = 0.
\end{equation}
\medskip
Now, we shall introduce an another approach. The division $b/a$ may be defined {\bf independently of the product}. Indeed, in Japan, the division $b/a$ ; $b$ {\bf raru} $a$ ({\bf jozan}) is defined as how many $a$ exists in $b$, this idea comes from subtraction $a$ repeatedly. (Meanwhile, product comes from addition).
In Japanese language for "division", there exists such a concept independently of product.
H. Michiwaki and his 6 years old girl said for the result $ 100/0=0$ that the result is clear, from the meaning of the fractions independently the concept of product and they said:
$100/0=0$ does not mean that $100= 0 \times 0$. Meanwhile, many mathematicians had a confusion for the result.
Her understanding is reasonable and may be acceptable:
$100/2=50 \quad$ will mean that we divide 100 by 2, then each will have 50.
$100/10=10 \quad$ will mean that we divide 100 by10, then each will have 10.
$100/0=0 \quad$ will mean that we do not divide 100, and then nobody will have at all and so 0.
Furthermore, she said then the rest is 100; that is, mathematically;
$$
100 = 0\cdot 0 + 100.
$$
Now, all the mathematicians may accept the division by zero $100/0=0$ with natural feelings as a trivial one?
\medskip
For simplicity, we shall consider the numbers on non-negative real numbers. We wish to define the division (or fraction) $b/a$ following the usual procedure for its calculation, however, we have to take care for the division by zero:
The first principle, for example, for $100/2 $ we shall consider it as follows:
$$
100-2-2-2-,...,-2.
$$
How may times can we subtract $2$? At this case, it is 50 times and so, the fraction is $50$.
The second case, for example, for $3/2$ we shall consider it as follows:
$$
3 - 2 = 1
$$
and the rest (remainder) is $1$, and for the rest $1$, we multiple $10$,
then we consider similarly as follows:
$$
10-2-2-2-2-2=0.
$$
Therefore $10/2=5$ and so we define as follows:
$$
\frac{3}{2} =1 + 0.5 = 1.5.
$$
By these procedures, for $a \ne 0$ we can define the fraction $b/a$, usually. Here we do not need the concept of product. Except the zero division, all the results for fractions are valid and accepted.
Now, we shall consider the zero division, for example, $100/0$. Since
$$
100 - 0 = 100,
$$
that is, by the subtraction $100 - 0$, 100 does not decrease, so we can not say we subtract any from $100$. Therefore, the subtract number should be understood as zero; that is,
$$
\frac{100}{0} = 0.
$$
We can understand this: the division by $0$ means that it does not divide $100$ and so, the result is $0$.
Similarly, we can see that
$$
\frac{0}{0} =0.
$$
As a conclusion, we should define the zero divison as, for any $b$
$$
\frac{b}{0} =0.
$$
See \cite{kmsy} for the details.
\medskip
\section{In complex analysis}
We thus should consider, for any complex number $b$, as (1.2);
that is, for the mapping
\begin{equation}
w = \frac{1}{z},
\end{equation}
the image of $z=0$ is $w=0$. This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere.
However, we shall recall the elementary function
\begin{equation}
W(z) = \exp \frac{1}{z}
\end{equation}
$$
= 1 + \frac{1}{1! z} + \frac{1}{2! z^2} + \frac{1}{3! z^3} + \cdot \cdot \cdot .
$$
The function has an essential singularity around the origin. When we consider (1.2), meanwhile, surprisingly enough, we have:
\begin{equation}
W(0) = 1.
\end{equation}
{\bf The point at infinity is not a number} and so we will not be able to consider the function (3.2) at the zero point $z = 0$, meanwhile, we can consider the value $1$ as in (3.3) at the zero point $z = 0$. How do we consider these situations?
In the famous standard textbook on Complex Analysis, L. V. Ahlfors (\cite{ahlfors}) introduced the point at infinity as a number and the Riemann sphere model as well known, however, our interpretation will be suitable as a number. We will not be able to accept the point at infinity as a number.
As a typical result, we can derive the surprising result: {\it At an isolated singular point of an analytic function, it takes a definite value }{\bf with a natural meaning.} As the important applications for this result, the extension formula of functions with analytic parameters may be obtained and singular integrals may be interpretated with the division by zero, naturally (\cite{msty}).
\bigskip
\section{Conclusion}
The division by zero $b/0=0$ is possible and the result is naturally determined, uniquely.
The result does not contradict with the present mathematics - however, in complex analysis, we need only to change a little presentation for the pole; not essentially, because we did not consider the division by zero, essentially.
The common understanding that the division by zero is impossible should be changed with many text books and mathematical science books. The definition of the fractions may be introduced by {\it the method of Michiwaki} in the elementary school, even.
Should we teach the beautiful fact, widely?:
For the elementary graph of the fundamental function
$$
y = f(x) = \frac{1}{x},
$$
$$
f(0) = 0.
$$
The result is applicable widely and will give a new understanding for the universe ({\bf Announcement 166}).
\medskip
If the division by zero $b/0=0$ is not introduced, then it seems that mathematics is incomplete in a sense, and by the intoduction of the division by zero, mathematics will become complete in a sense and perfectly beautiful.
\bigskip
section{Remarks}
For the procedure of the developing of the division by zero and for some general ideas on the division by zero, we presented the following announcements in Japanese:
\medskip
{\bf Announcement 148} (2014.2.12): $100/0=0, 0/0=0$ -- by a natural extension of fractions -- A wish of the God
\medskip
{\bf Announcement 154} (2014.4.22): A new world: division by zero, a curious world, a new idea
\medskip
{\bf Announcement 157} (2014.5.8): We wish to know the idea of the God for the division by zero; why the infinity and zero point are coincident?
\medskip
{\bf Announcement 161} (2014.5.30): Learning from the division by zero, sprits of mathematics and of looking for the truth
\medskip
{\bf Announcement 163} (2014.6.17): The division by zero, an extremely pleasant mathematics - shall we look for the pleasant division by zero: a proposal for a fun club looking for the division by zero.
\medskip
{\bf Announcement 166} (2014.6.29): New general ideas for the universe from the viewpoint of the division by zero
\medskip
{\bf Announcement 171} (2014.7.30): The meanings of product and division -- The division by zero is trivial from the own sense of the division independently of the concept of product
\medskip
{\bf Announcement 176} (2014.8.9): Should be changed the education of the division by zero
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{ahlfors}
L. V. Ahlfors, Complex Analysis, McGraw-Hill Book Company, 1966.
\bibitem{cs}
L. P. Castro and S.Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{kmsy}
S. Koshiba, H. Michiwaki, S. Saitoh and M. Yamane,
An interpretation of the division by zero z/0=0 without the concept of product
(note).
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. Vol. 27, No 2 (2014), pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{msty}
H. Michiwaki, S. Saitoh, M. Takagi and M. Yamada,
A new concept for the point at infinity and the division by zero z/0=0
(note).
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. Vol.4 No.2 (2014), 87-95. http://www.scirp.org/journal/ALAMT/
\bibitem{taka}
S.-E. Takahasi,
{On the identities $100/0=0$ and $ 0/0=0$}
(note).
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operators on the real and complex fields. (submitted)
\end{thebibliography}
\end{document}
アインシュタインも解決できなかった「ゼロで割る」問題
http://matome.naver.jp/odai/2135710882669605901
Title page of Leonhard Euler, Vollständige Anleitung zur Algebra, Vol. 1 (edition of 1771, first published in 1770), and p. 34 from Article 83, where Euler explains why a number divided by zero gives infinity.
https://notevenpast.org/dividing-nothing/
私は数学を信じない。 アルバート・アインシュタイン / I don't believe in mathematics. Albert Einstein→ゼロ除算ができなかったからではないでしょうか。
1423793753.460.341866474681。
Einstein's Only Mistake: Division by Zero
http://refully.blogspot.jp/2012/05/einsteins-only-mistake-division-by-zero.html
0 件のコメント:
コメントを投稿