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Introduction to advanced mathematics

Elementary mathematics studies constants and advanced mathematics studies variables.

Advanced mathematics (also known as calculus, which is the general name of several courses) is an important basic subject in science and engineering colleges. As a science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstract is the most basic and remarkable feature of mathematics-high abstraction and unity, which can profoundly reveal its essential laws and make it more widely used. Strict logic means that in the induction and arrangement of mathematical theory, whether it is concept and expression, or judgment and reasoning, we must use the rules of logic and follow the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics. Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into the field of social sciences extensively and deeply. Therefore, it is very important for us to learn advanced mathematics well. However, many students are confused about how to learn this course well. If you want to learn advanced mathematics well, you must at least do the following four things:

First, understand the concept. There are many concepts in mathematics. Concepts reflect the essence of things. Only by figuring out how it is defined and what its essence is can we really understand a concept.

Secondly, master the theorem. Theorem is a correct proposition, which is divided into two parts: condition and conclusion. In addition to mastering its conditions and conclusions, we should also understand its scope of application and be targeted.

Third, do some exercises on the basis of understanding the examples. Especially remind learners that the examples in the textbook are very typical, which is helpful to understand concepts and master theorems. Pay attention to the characteristics and solutions of different examples, and do appropriate exercises on the basis of understanding examples. When writing a topic, you should be good at summing up-not only the methods, but also the mistakes. You will gain something after doing this, so you can draw inferences from others.

Fourth, clear the context. We should have an overall grasp of the knowledge we have learned and summarize the knowledge system in time, which will not only deepen our understanding of knowledge, but also help us to further study.

Advanced mathematics includes calculus and solid analytic geometry, series and ordinary differential equations. Calculus is the most systematic and widely used in other courses. The theory of calculus was completed by Newton and Leibniz. (Of course, calculus was applied before them, but it was not systematic enough. ) The basic concepts of calculus and extreme calculus are difficult to understand.

Training objectives of mathematics and applied mathematics;

This major trains 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 and technology, education, economy and other departments, or engage in practical application, development, research and management in production, operation and management departments.

Business training requirements:

Students in this major mainly study the basic theories and methods of mathematics and applied mathematics, receive the basic training of mathematical models, computers and mathematical software, have good scientific literacy, and initially have the basic abilities of scientific research, teaching, solving practical problems and developing software.

Graduates should have the following knowledge and abilities:

1. Have a solid mathematical foundation, received strict scientific thinking training, and initially mastered the thinking method of mathematical science;

2. Have the preliminary ability to apply mathematical knowledge to solve practical problems, especially to establish mathematical models.

3. Skillful use of computers (including common languages, tools and some mathematical software) and the ability to write simple application programs;

4. Understand the national science and technology policies and regulations;

5. Understand some new developments and application prospects of mathematical science;

6. Have strong language expression ability, master the basic methods of information inquiry, document retrieval and using modern information technology to obtain relevant information, and have certain scientific research and teaching ability.

Main subject: Mathematics.

Main courses: 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.

Length of study: four years.

Degree awarded: Bachelor of Science.

Similar majors: information and computing science, statistics.

Mathematics and Applied Mathematics (General Class)

Business development goals:

This major trains students to master the basic theories, knowledge and methods of mathematical science, apply mathematical knowledge and solve some practical mathematical problems with computers. It has teachers, teaching researchers and other educators who teach mathematics in universities and middle schools.

Business training requirements:

Students in this major mainly study the basic theories and methods of mathematics and applied mathematics, receive strict mathematical thinking training, master the basic principles and application means of computers, form good teachers' quality through educational theory courses and teaching practice links, and cultivate their basic abilities in mathematics teaching and mathematical education research, mathematical scientific research and practical application.

Graduates should have the following knowledge and abilities:

1. has a solid mathematical foundation, and initially grasps the basic thinking methods of mathematical science, including the basic abilities of mathematical modeling, mathematical calculation and solving practical problems;

2. Good computer skills, simple programming, mastery of mathematical software and computer multimedia technology, and simple secondary development of teaching software;

3. Have a good professional quality of teachers and the basic ability to engage in mathematics teaching. Familiar with educational laws and regulations, master and initially apply basic theories of pedagogy, psychology and mathematics teaching theory;

4. Understand the development of modern mathematics and its role in social development, some latest developments in mathematical science, some latest research results and teaching methods in the field of mathematics teaching, and understand the general principles and knowledge of similar majors; Learn the courses permeated with arts and sciences, and gain a wide range of humanities and scientific literacy;

5. Strong language skills and class management skills;

6. Master the basic methods of information inquiry, document retrieval and obtaining relevant information by using modern information technology, and have certain scientific research ability.

Main subject: Mathematics.

Main courses: mathematical analysis, geometry, algebra, physics, probability theory and mathematical statistics, differential equations, function theory, discrete mathematics, mathematical history, numerical method and computer technology, mathematical model, mathematical experiment, foundation of education and psychology, mathematical teaching theory, and foundation of humanities and social sciences.

The main practical teaching links include educational practice, probation, educational investigation, social investigation or graduation thesis, etc. , the general arrangement is 15 ~ 20 weeks.

Length of study: four years.

Degree awarded: Bachelor of Science.

Similar majors: information and computing science, statistics.