高等代数,解析几何,什么意思
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发布时间：2022-06-01 17:53
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热心网友
时间：2023-10-10 06:33
楼主的问题，不好回答，回答得一不小心，会被众人喷死，尤其是学数学的人会怒不可遏！
1、高等数学、高等代数，与普通物理学、普通化学、普通天文学、普通水文学
不知道历史上出之何因，出之何人、何团体，从高中升入大学，开始学习大学数学，
大学数学号称高等数学，其实就是微积分calculus。
辛辛苦苦、拚死拚命学了一年半载之后，需要有微积分知识、能力解题才能学的物理，
并不是高等物理，而是普通物理；需要有数学基础、物理基础才能学的化学，也不是
高等化学，而只是普通化学。这个历史性的玩笑一开就是百年之久，至今大家都习以
为常了。教最基础的数学是高等课程，在他们的基础上的课程是普通。
高等代数，其实就是线性代数，就是linear algebra。跟鬼子讨论，linear algebra就是
algebra，跟中国的数学教师谈，一定要夸张到《高等代数》，没有高等二字，他们就
会觉得我们在贬低他们。可是楼主不妨在网上搜叟，看看能不能搜到英文的高等代数
词条？看看我们的数学教师们有多么的狐假虎威。
线性代数，就是从线性方程组的系数出发，引入了矩阵，进而推广到所谓的线性空间，
解决代数结构问题、函数论、、、、问题。下面是维基的英文解说。
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The set of points with coordinates that satisfy a linear equation form a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.
Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.
Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science,computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.
2、解析几何，就算是coordinates geometry，analytic geometry
就是用建立坐标，定量地研究平面几何plane geometry、立体几何solid geometry的问题。
以下是维基的英文解说：
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.
Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) andEuclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. The numerical output, however, might also be a vector or ashape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.
