Mathematics in a broad sense is an abstract science that studies quantity, structure, space and change. It is mainly divided into pure mathematics and applied mathematics, among which pure mathematics is also called basic mathematics, which mainly studies the internal relations of mathematical laws abstracted from the objective world, and it can also be said that it is the study of mathematics itself, not application-oriented knowledge; Applied mathematics focuses on explaining natural phenomena and solving practical problems, and is a bridge between pure mathematics and science and technology. Please see below 86 my analysis! Professional department

Common research directions of basic mathematics include:

Algebra algebra

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Topology topology

Geometric geometry

number theory

Logical logic

Differential equation theory

partial differential equation

Common branches of applied mathematics include:

Operational Research and Optimization Theory Operational Research/Optimization

Differential equations and dynamic systems

Stochastic systems and control theory/stochastic control theory

Actuarial/financial mathematics/financial mathematics

mathematical physics

Mathematical biology of biological mathematics

Scientific calculation scientific calculation

Probability theory and statistical probability and statistics

The above are the common branches of mathematics major in American universities, but not every school has these branches. Most schools have only a few branches, so when choosing a school, you should find your own matching branch direction.

Curriculum design of American mathematics specialty

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Typical masters in mathematics are divided into Master of Science (MS) and Master of Arts (MA). Doctor's degree is mainly doctor of philosophy. Mathematics, as a discipline in science, mainly recruits doctoral students, especially in the field of basic mathematics. Some schools don't even set up independent master's programs, such as Harvard University and Princeton University.

Master students need to take 30-36 credits (about 8- 10 courses), and they can choose to graduate in the form of papers or non-papers, and the study time is 1.5-2 years; The doctoral stage requires 72 credits. In addition to courses, students also need to take part in course examinations, oral examinations, thesis defense and other stages, which last for 4-7 years.

In the application process of American schools, knowing the courses offered by American colleges and universities in advance will help us to choose a school that is more suitable for us. There are some common parts in postgraduate courses, such as linear algebra, number theory, topology, differential geometry, multivariate analysis, functional analysis, harmonic analysis, ordinary differential equations, partial differential equations, numerical methods, numerical analysis, scientific calculation, fluid dynamics, probability theory and so on. , and some distinctive parts.