What's the difference between applied mathematics, basic mathematics and computational mathematics?

Applied mathematics, basic mathematics and computational mathematics have different concepts, characteristics and main courses.

1, with different concepts:

(1) Applied Mathematics majors train senior professionals who master the basic theories and methods of mathematical science, have the ability to use mathematical knowledge and solve practical problems with computers, have received preliminary training in scientific research, and can engage in research and teaching in science, technology, education and economy departments or engage in practical application, development, research and management in production, operation and management departments;

(2) Basic mathematics, also called pure mathematics, specializes in studying the inherent laws of mathematics itself. The knowledge of algebra, geometry, calculus and probability introduced in primary and secondary school textbooks belongs to pure mathematics. A remarkable feature of pure mathematics is to temporarily put aside the specific content and study the quantitative relationship and spatial form of things in pure form.

(3) Computational mathematics is a science specialty formed by the cross-infiltration of mathematics, physics, computer science, operational research and control science.

2. Different characteristics:

(1) Applied mathematics requires a solid mathematical foundation, strict scientific thinking training, and a preliminary grasp of mathematical scientific thinking methods; Have the preliminary ability to apply mathematical knowledge to solve practical problems, especially to establish mathematical models, and have some understanding; Proficient in using computers (including common languages, tools and some mathematical software) and the ability to write simple applications; Understand national science and technology and other related policies and regulations.

(2) Basic Mathematics Basic mathematics is the foundation of foundation. Its research field is broad and theoretical. Specific branches include: projective differential geometry, Riemannian geometry, global differential geometry, harmonic analysis and its application, wavelet analysis, partial differential equations, applied differential equations, algebra and so on.

(3) Computational problems can be said to be common in all fields of modern society, such as industry, agriculture, transportation, medical care, culture and education, etc. All walks of life have a lot of data to calculate. Through data analysis, we can grasp the law of the development of things. A subject that studies the solutions to computational problems and related mathematical theoretical problems is called computational mathematics. Computational mathematics belongs to the category of applied mathematics, which mainly studies how to effectively solve related mathematical and logical problems with computers.

3. The main courses are different:

(1) Main courses of applied mathematics: analysis, algebra, geometry, probability theory, physics, mathematical model, mathematical experiment, computer foundation, numerical method, mathematical history, etc. , and the basic courses selected according to the application direction.

Main practical teaching links: including computer practice, production practice, scientific research training or graduation thesis, etc. , usually arranged in 10 ~ 20 weeks.

(2) Basic mathematics mainly refers to geometry, algebra (including number theory), topology, analysis, equations and some branches of mathematics developed on this basis.

(3) Computational mathematics includes arithmetic, elementary algebra, advanced algebra, number theory, Euclidean geometry, non-Euclidean geometry, analytic geometry, differential geometry, algebraic geometry, projective geometry, topology, fractal geometry, calculus, real variable function theory, probability and mathematical statistics, complex variable function theory, functional analysis, partial differential equations, ordinary differential equations, mathematical logic, fuzzy mathematics and so on.

References:

Baidu encyclopedia-computational mathematics

Baidu encyclopedia-basic mathematics

Baidu encyclopedia-applied mathematics