Mathematics can be said to be the oldest and most basic discipline in natural science, and it is also an essential basic tool for learning and studying modern science and technology. Mathematics has been accompanied by human development and evolution since human beings tied ropes to remember things.
We began to learn mathematics in kindergarten and continued to college. As a basic course, mathematics is unavoidable for any student, whether you like it or not. Through basic mathematics learning, we can exercise our thinking ability, which is very helpful to our daily life.
I have always liked mathematics and have been studying and applying mathematics. Fortunately, both undergraduate and graduate students majored in mathematics. During my work, I mainly focused on big data and artificial intelligence. I often use mathematics. I have been dealing with mathematics for almost 30 years. Through learning and practice, I have a deep understanding of the value of mathematics and have been thinking about what mathematics can bring to us? To sum up, mathematics can cultivate five abilities.
It is believed that it is not difficult to understand that the word "number" in mathematics can directly explain that mathematics is a science dealing with numbers, which is also the most primitive and intuitive understanding of mathematics, although modern mathematics has already exceeded the category of numbers.
I don't need to say more about the value of digital computing power. It is necessary to use digital computing in daily life for shopping, calculating wages, buying a house and a car, having dinner with friends, etc. Good digital computing ability, at least you can quickly deal with these matters related to digital computing, save your time and reduce your trouble. In fact, many calculations have been imperceptibly introduced into our consciousness. For example, when crossing the road, we can judge the distance and speed of the vehicle from you, and determine whether it is safe to cross the road. I believe that most people can make good intuitive judgments.
Although we all have mobile phones now, we can use the calculator on mobile phones to complete many complex calculations, but in simple scenarios and special scenarios, we have to deal with and calculate by ourselves. Now many primary and secondary schools can use calculators, which is a bad phenomenon and kills students' ability to master numerical calculation.
Abstract concept is very important. It can be said that abstract thinking is the most important ability that distinguishes human beings from animals. Abstract thinking is accompanied by human development and evolution. The numbers 1, 2, 3... are very abstract in themselves. A knot in the knotted notes represents the occurrence of something, such as hunting a sheep. In modern society, let alone words, words are abstract expressions. Natural and social sciences, such as philosophy, computer, finance, economics, law, etc., contain a large number of abstract concepts.
It can be said that mathematics is the most abstract subject in natural science. Any concept in mathematics is abstract, and even the methods in mathematics are abstract. Many abstract concepts in mathematics come from life, such as numbers, simple geometric shapes, sets, functions, probabilities, limits, integrals, graphs, etc., and abstract methods such as mathematical induction, counterevidence, etc. also come from life. More abstractions in mathematics originate from the superposition of basic concepts and abstract methods from abstract concepts. Mathematics is a science that originates from life but transcends life.
Abstract things are often difficult to understand. It takes a long time for 2-3 year old children to really understand 1, 2 and 3. Because of the abstract nature of mathematical concepts, many people do not like mathematics very much, and it is difficult to learn mathematics well.
Learning mathematics from an early age has trained our abstract thinking ability and made it easier for us to understand abstract concepts, which is of great benefit for us to learn new knowledge and understand abstract concepts in modern life and social interaction.
Mathematics is a science of logical reasoning. Numeric calculation, formula deduction, proof that many of us may hate
Mathematical induction is a process and method of logical reasoning. The axiomatic system in higher mathematics, based on the initial axioms, deduces all correct formulas, theorems and deductions, which is the best embodiment of logical reasoning. The modern probability theory is that the Russian mathematician Kolmogorov based on three axioms (suppose the sample space of random experiment E is Ω. If according to some method, each event A of E is assigned a real number P (A), and meets the following axioms: (1) non negativity: P (A) ≥ 0; (2) Normality: P (Ω)=1; (3) Countable (completely) additivity: for two incompatible countable events A1, A2,......, An,......, there are
The real number P (A) is called the probability of event A.) It is a very practical subject. Mathematical logic, a branch of mathematics, is itself a subject of logical reasoning.
There are a lot of logical thinking and methods in mathematics. Through the training and learning of mathematics, we can greatly improve our logical reasoning ability and ultimately help us to better analyze and solve problems.
The value of logical reasoning is very great. Major discoveries in natural science, such as heliocentric theory, electromagnetic wave discovery, and the theory of relativity, are all based on mathematical formula reasoning. In real life, detectives and solving cases need to rely on the power of logical reasoning. The suspense detective story that many people like is the development and embodiment of logical thinking in literature.
The help of logical reasoning ability is indispensable to the understanding of human nature, the analysis of competitors, the troubleshooting of problems and failures, the summary and reflection of the past, and the selection of various possibilities (such as multiple contacts and offers). Even if we lose something in our daily life and think about where we might lose it, we also need to go through a process of logical reasoning, which is ubiquitous and helps us all the time.
Mathematics comes from life. Many concepts in mathematics can find the corresponding in life. For example, the concept of mapping can find the corresponding in life very well. Everyone has a name. From person to name is a mapping, but many people have duplicate names. In order to distinguish people one by one, each person has an ID card number, and each person has a unique ID card number, Any two people are different, so that each person can establish a one-to-one relationship with their ID card number, which is called one-to-one mapping. Geometric shapes, not to mention, are directly derived from the shapes of objects in life. This correspondence between life and mathematical concepts can help us learn and understand mathematics better and exercise our ability of analogy and association.
Through the study of mathematical knowledge, we can learn a lot of such knowledge points and methods of analogy and association. When these thoughts are solidified into our cognition, they will help us to work and live better.
Take computer programming language for example, the method in the program is similar to the function in mathematics, the input is the independent variable, and the output is the function value. For functional programming languages, input and output can be other functions, which can be directly compared with the concept of functional in functional analysis. Object oriented programming language is an analogy of algebraic structure in algebra. Elements in algebraic structure are equivalent to variables of class, and operations in algebraic structure are equivalent to functions of class. With these mathematical knowledge, it is very helpful for us to better understand and master programming.
For example, when testing new drugs in the drug research and development stage, we often first do experiments on lower mammals or primates, which is to directly use the similarities in drug reactions between humans and these animals (which can be regarded as the equivalent of the algebraic space mentioned above), so as to ensure that drugs are ultimately safe for humans.
The space imagination ability in mathematics starts from geometry. The plane geometry we learned in junior high school and the solid geometry we learned in senior high school (I believe everyone is familiar with various ingenious auxiliary lines in geometry) let us better understand the three-dimensional space of our life.
In higher mathematics, we have expanded the space to a higher dimension or even an infinite dimension space, and the vector in linear algebra can be seen as a point in a high-dimensional space (dimension is the number of components of a vector). The vast majority of function spaces in functional analysis are infinite dimensional spaces, such as polynomial function spaces composed of polynomials.
Beyond the concept of 3D, it is difficult for us to find the corresponding in the three-dimensional space of life, so it is difficult for human beings to understand intuitively. High dimensional space will produce many complex problems and phenomena, which are very difficult for us to deal with. People who have learned machine learning know that the "dimension disaster" is a common and difficult phenomenon in high-dimensional space.
High dimensional space needs to be understood and recognized with the help of people's imagination. A large number of high dimensional spaces have been studied in mathematics. Through learning and practicing mathematics, we can better exercise our spatial imagination.
The most direct embodiment of the value of space imagination in reality is the design industry. Whether it is architectural design, decoration design, road and bridge design, tunnel design, aerospace aircraft design, automobile and ship design, medical equipment design, etc., we need to have a better understanding and grasp of space.
In art and aesthetics, it is also necessary to understand the positional relationship of space. Photography, video shooting, painting, sculpture, etc. all need good spatial perception.
You may say that the above is far away from ordinary people and can't be used at all. In fact, good spatial perception is very helpful for us to appreciate and experience beautiful things. We can admire profound works of art and marvel at beautiful buildings. A good perception of the three-dimensional space of our life can also help us avoid many troubles in our daily life.
Space imagination is a very important kind of imagination. Learning and cultivating space imagination can help improve our imagination, and imagination is the source of all human inventions.
