Introduction to computing science (II)

1) (in the debate on the basic problems of mathematics and the relationship between mathematics and logic, there are three schools) logical schools: logic prevails over mathematics. Mathematics can be obtained completely from pure logic without the introduction of the original word term and the assumption of the plus. The idea of this school is embodied in Russell's masterpiece mathematical principles.

2) the formalism school holds that mathematics itself is a pile of formal systems, each of which establishes its own logic system and its own mathematics. By developing these deduction systems through formal (logical) reasoning, we can establish a specific mathematical branch. In addition, the various mathematical branches established in this way will be more rigorous, there will be no paradox. (I like this one. If I have not understood this correctly, I think this idea is really seamless. It is like creating a new world to put the logic system inside the formal system)

3)The intuition school is closely related to computing science.
For the inverse proof method widely used in mathematical proof, the intuition school is only limited to proving the negative proposition, that is, the inverse law in mathematical logic, which is weaker than the inverse proof method. (Why ?)
Starting from the most intuitive concept, the constructive definition of the concept and the construction method of the mathematical theorem proof, the developed mathematics forms the so-called constructive mathematics.

4) "... History of mathematics... Mathematical Philosophy... Ancient and Modern mathematical ideas ..."

5) in history, the most famous outcome of research on the enforceability and structuring of computing isTuring Machine. If there is no discussion of the basic mathematical problems at the end of the 19th century and the beginning of the 20th centuryIntuitionThe contribution of logic to mathematics may be postponed.

6)Mathematical Logic and Abstract AlgebraAs the two most important mathematical foundations of Computational Science, their research ideas and methods have been widely used in many in-depth fields of computational science.
Today, no science in the world is as closely linked with mathematics as computing science, because mathematical logic and abstract algebra are the most widely used in computational science, they not only solve a large number of computational science problems, but also reflect and integrate them into the mainstream of modern mathematical research.

7)It is necessary for students to continue to master new knowledge smoothly in the future study and re-education of engineers after graduation, the teaching of mathematical logic, abstract algebra, set theory, graph theory, and theoretical computer science must be strengthened. Because,The content of Theoretical Computer Science contains many of the most basic methods of the subject. They can unify the knowledge of the subject in a deep layer.

8)Physical and chemical methodsIt is to use logical reasoning rules (that is, reasoning rules that reflect scientific reasoning, starting from the minimum number of primitive concepts (basic concepts) that do not need to be defined. Note that such logical reasoning rules often have syntax-based and semantic-based reasoning rules, and use deductive reasoning to conduct scientific research on a subject.

9)Unfortunately, Godel has pointed out that a complete formal mathematical system does not exist. (?)