College mathematics specialized course
1, mathematical analysis
This course is a mathematical summary course for everyone from elementary school to university, and it is also a course from 1 to real numbers. I say this because the content of this course may be familiar to everyone. We have been learning to count since kindergarten, and the process of counting seems very simple. But in fact, it contains some very important concepts in this course and is also a necessary means to prove many theorems later. In kindergarten, the number we count is a natural number, but in primary school, we may be able to count to an integer. But many people should not know that rational numbers can also be counted. It may be a little counterintuitive to accept this concept at first, which we will mention later. Our intuition may sometimes not conform to the standardized way of thinking. Since the Pythagorean school discovered the root number 2, mathematics has come to the category of real numbers, which is the end of high school. Mathematical analysis, as the foundation of real analysis course for graduate students, studies various properties of real numbers. Among the properties of real numbers, the most important may be the completeness axiom of real numbers. Simply put, part of this axiom is that if I know that the amount of sand on a beach is limited and there must be sand, then there is an upper bound for the amount of sand on this beach. With real numbers, we can continue to discuss the series on real numbers. 1, 2, 3, … is a series, but the series is not just that simple, it is actually a mapping from real numbers to natural numbers. Probabilistically, it doesn't look like a similar mapping relationship between mapping and random variables.
2. Abstract algebra
Abstract algebra belongs to the department of mathematics, which tests people's abstract thinking. A brief introduction, I believe everyone should be familiar with the collection. The whole modern mathematics is a subject based on set theory. Then, a simple set looks very clear. When the number of elements in a collection is very large, does the collection look less tidy? At the same time, the set encounters disorder, and the two elements have nothing to do with each other, which seems a bit chaotic. At this time, if we add a structure to this set, can we make it more regular? This structure is called binary operation, that is, two elements can interact to produce new elements, so that each element in the set has a certain relationship with other elements, thus connecting them to form an orderly whole. This binary operation can be intuitively addition and multiplication. It can also be any kind of operation. With this operation, plus this set meets some conditions under this operation, we have produced a new species called a group.
3. Stochastic process
Stochastic process is closely related to our life and is a course based on probability theory. Obviously, this process has a beginning, but it is not necessarily the end. This contains a limited state space. For a simple example, do people sometimes have to wait when they go to the barber shop? If through a large number of statistical calculations, it is found that the number of people who appear in this barber shop per unit time obeys Poisson distribution, then the number of people who appear in the barber shop at different times is actually a Poisson process.
These three courses have their own characteristics, and they are also very popular courses for mathematics majors in every school. There are courses in analysis, algebra and operational research. Mathematics is inseparable from numbers, but numbers are only superficial, and the rigorous logic behind numbers is the real value of ordinary people learning mathematics. The development of mathematics is often very advanced, and many things may be used for a hundred years. Therefore, we don't have to prove profound theorems, but we must know how to appreciate the beauty of logical thinking.
Expanding reading: the employment prospect and direction of mathematics major
1, Basic Mathematics: Suitable for research or teaching.
Basic mathematics is also called pure mathematics, that is, according to the inherent needs of mathematics or possible future applications, studying the inherent laws of mathematical structure itself has no direct connection with seeking common ground while reserving differences and solving practical problems in other disciplines, but only studies the quantitative relationship and spatial form of things in pure form.
Basic mathematics is the core of mathematical science. It is not only the basis of other branches of applied mathematics, but also provides essential language, tools and methods for natural science, technical science and social science. Differential geometry, mathematical physics and partial differential equations all belong to the category of basic mathematics. The well-known story of Chen Jingrun proving Goldbach's conjecture "1+2" happened in this field.
Employment prospects:
This major requires students to have a solid theoretical foundation in mathematics and train graduate students in mathematics, applied mathematics and related disciplines for colleges and universities and scientific research. A few years ago, compared with other majors in mathematics, the employment was relatively narrow, but in recent years, various disciplines related to mathematics have developed rapidly, and the number of scientific research and teaching talents needed in this area has also increased greatly. In particular, most teaching talents in mathematics-related disciplines need a solid mathematical foundation, so the demand also increases.
2. Computational Mathematics: It involves many interdisciplinary subjects.
Computational mathematics is a new discipline that has developed rapidly with the appearance of computers, involving computational physics, computational chemistry, computational mechanics, computational materials science, environmental science, earth science, finance and insurance and many other interdisciplinary subjects. It uses modern mathematical theories and methods to solve various scientific and engineering problems, analyze and improve the reliability, effectiveness and accuracy of calculation, and study the development technology of various numerical software. It not only highlights the solution of some core theoretical and technical problems in the fields of information, electronics and computers, but also notes that new mathematical theories are abstracted from these high and new technologies; On the basis of maintaining the advantages of the main research directions of applied mathematics and computational mathematics, we should attach importance to and strengthen the research on the mathematical basis of information science, data analysis and statistical calculation, scientific calculation, modern optimization, numerical simulation of electronic systems and mathematical modeling of biological systems.
Professional background: Candidates are required to have basic mathematics, applied mathematics, information technology, computer science, data processing and system analysis, engineering, digital images and other knowledge.
Research interests: numerical methods of engineering problems, numerical methods of evolution equations and dynamic systems, numerical approximation and digital image processing, computer graphics and computer software, mathematical problems in optics and electromagnetism, etc.
Employment prospects:
Standing on the shoulders of mathematics, students in this direction have great advantages in both exams and going abroad. If graduate students are engaged in program development, their salary is generally higher, but their work intensity is relatively high.
In addition, graduates of this major can also engage in teaching in major universities, which can not only carry out further research, but also contribute to the cultivation of professional talents.
3. Probability statistics: the demand of government departments has increased greatly.
As a branch of mathematics, probability is a science and technology that studies random events, involving applications such as engineering, biology, chemistry, genetics, game theory and economics, covering almost all scientific and technological fields, and can be said to be the cornerstone of various predictions. Statistics is a science of collecting, sorting, analyzing and interpreting statistical data. It mainly uses probability theory to establish mathematical model, collect data of observation system, make quantitative analysis and summary, and then make inference and prediction, so as to provide basis and reference for relevant decision-making.
Probability theory and mathematical statistics are rapidly developing disciplines in this century. They study the essence and inherent regularity of various random phenomena in natural science, social science and other disciplines, as well as the scientific comprehensive processing and statistical inference methods of various data. With the continuous improvement of the scale, complexity and accuracy of various systems in human society and the extensive use of computers, probability statistics will become more and more important.
Employment prospects:
Mainly engaged in the development, application and management of statistical investigation, statistical information management and quantitative analysis in enterprises and institutions and economic and government management departments, or engaged in research and teaching in scientific research and education departments. Employment opportunities are very extensive, and the demand of some financial departments and units for statistics professionals has even exceeded that of some popular economics majors. Especially in recent years, the decision-making of government departments has put more emphasis on science, and the strength of statistical departments has increased. Therefore, when the government recruits civil servants every year, the demand for statistics graduates also increases greatly.
4. Applied mathematics: the broadest development space.
Applied mathematics includes two parts, one is related to application, and the other is the application of mathematics, that is, using mathematics as a tool to explore and solve problems in science, engineering and sociology. Applied mathematics is mainly used in two fields. One is a computer. With the rapid development of computer, a large number of software engineers who understand mathematics are needed to develop the corresponding database. The second is economics, many of which need very professional mathematics to analyze. Many related courses of applied mathematics are designed on the basis of economic examples.
The biggest difference between applied mathematics and pure mathematics is the combination with reality: trying to solve the mathematical problems raised by natural phenomena and social development, and applying the results to nature and society.
Employment prospects:
Whether it is scientific research data analysis, software development, three-dimensional animation production, or financial insurance, international economy and trade, business administration, chemical and pharmaceutical, communication engineering, architectural design, etc. , can not be separated from the relevant professional knowledge of mathematics. The employment destination of graduates of this major is mostly concentrated in major group companies, scientific research and design units and financial institutions related to the information industry, and they also have great advantages in going abroad or pursuing further studies. According to relevant sources, if this science applies mathematics, it will have great advantages in choosing the development direction when applying for a master's degree, especially in finance and economy, which is more advantageous than the graduates of this major and can also make by going up one flight of stairs.
5. Mathematics education
Employment prospects:
The demand is large and the treatment is stable.
Employment Analysis: China has the greatest demand for math teachers. Math teachers are in great demand. Broadening the channels for teachers and recruiting teachers for the society has become an important measure for the reform of the education and personnel system. This undoubtedly provides a great development space for the employment of graduates majoring in mathematics education.