What is Mathematical Logic? What is Mathematical Logical Thinking?

The past year has been full of ups and downs, joys and sorrows. In what used to be a classroom, all the emotions fluttered and danced, filling the whole semester. Now that's just the past, or worse, because we can't go back.

During this semester, I will do my best to study to achieve my future goals and ideals. I look forward to the future, embrace the future, and look forward to the future. "There is a diligent path in the book mountain, and the bitter sea is endless.

You can. Goal, sprint 630! In the face of goals, first of all, face learning with a good attitude.

Challenge yourself and believe in yourself. Secondly, one point that cannot be ignored in learning is to learn to analyze one's own learning characteristics, and one point that cannot be ignored is to learn to analyze one's own learning characteristics.

My reasoning skills are okay, but I always feel too difficult and boring for some things that can only be learned by rote, which is my shortcoming, and I will overcome it in the first semester of junior high school. Finally, and most importantly, it is necessary to arrange time scientifically, without reasonable arrangement, no matter how good the plan is, it will be in vain. Efficiency is always important in my planning.

First, it is necessary to make reasonable arrangements for study, recreation, and rest time, and to grasp every bit of precious time. Second, set aside a part of your time to exercise, for yourself and for better study.

Logic

Main article: Mathematical logic.

Mathematical logic focuses on placing mathematics on a solid axiomatic framework and studying the results of this framework. For its part, it is the source of Gödel's second incompleteness theorem, which is perhaps the most widely circulated result of logic Modern logic is divided into recursive theory, model theory, and proof theory, and is closely related to theoretical computer science.

The above content reference: Encyclopedia - Mathematics.

Mathematical logic is similar to mathematical logic, also known as symbolic logic and theoretical logic. It is both a branch of mathematics and a branch of logic. It is a discipline that studies logic or formal logic with mathematical methods.

The object of study is the formal system after the symbolization of the two intuitive concepts of proof and computation. Mathematical logic is an indispensable part of basic mathematics. Although the word logic is included in the name, it does not belong to the category of pure logic.

I think mathematical logical thinking definitely refers to reasoning ability. , that is, what conditions are known, and then a certain result can be deduced, this is the ability of logical reasoning.

The relationship between logic and mathematics: mathematics originates from intuition, mathematics originates from logic, and both are equally important.

Intuitionism holds that mathematics originates from intuition.

Logicism holds that mathematics originates from logic.

Formalism believes that both are equally important.

The relationship between logic and mathematics.

Logic is the material for exploring, expounding, and establishing the principles of effective reasoning. It was first created by the ancient Greek scholar Aristotle. Mathematical logic is a discipline that uses mathematical methods, that is, methods to establish a set of symbolic systems to study the form, structure and laws of reasoning.

It includes logical calculus, set theory, proof theory, model theory, recursion theory, etc. Mathematical logic is also known as symbolic logic due to the use of symbols in logic. The main problem in the study of mathematical logic is reasoning.

The so-called reasoning refers to the study of the relationship between the premise and the conclusion and the law of thinking, and the characteristics of mathematical logic are that the narrative is simple and clear, and the general flow is fluent. Logical.

Logical thinking ability refers to the ability to think correctly and reasonably. That is, the ability to observe, compare, analyze, synthesize, abstract, generalize, judge, and reason about things, and the ability to use scientific and logical methods to accurately and methodically express one's own thinking process. It is very different from the ability to think visually

Logical thinking ability is not only necessary to learn mathematics well, but also necessary to learn other subjects well and deal with daily life problems. Mathematics is a discipline that reflects the objective world with quantitative relations (including spatial forms), and it is very logical and rigorous.

Summary: A deep understanding of the application of mathematics in life. At the same time, using the knowledge I learned, I solved a lot of problems in real life.

This semester's mathematics study not only increased my knowledge, but also stimulated my interest in learning mathematics, and I will work harder to study mathematics and apply mathematics in the future!

Mathematics is a general means for humans to strictly describe the abstract structure and pattern of things, and can be applied to any problem in the real world, and all mathematical objects are inherently artificially defined.

Mathematical Logic:Mathematical logic focuses on placing the number guessing back school on a solid axiomatic framework and studying the results of this framework. For its part, it is the source of Gödel's second incompleteness theorem, which is perhaps the most widely circulated achievement of logic Modern logic is divided into recursive theory, model theory, and proof theory, and is closely related to theoretical computer science.

Encyclopedia Mathematics.

My classmates are all studying in Japan from graduate school to doctoral degree, and I especially like mathematics, and when I talked about children's education recently, I suggested that I study logic now.

It is a typical phenomenon: logic is not offered to science and engineering students in China, which leads to the omission of some key steps in the thinking process, and only the result is seen in the learning process, regardless of the process. So a lot of people do math by brushing up on questions.

UNESCO has defined seven basic disciplines: logic, mathematics, astronomy, chemistry, life sciences, astronomy, and geography.

In Europe, the United States, and Japan, the first subject to be taught before learning mathematics is logic. The students said that they felt that they had encountered a ceiling in academic research recently, and the main reason was that they did not learn the basic discipline of logic well, so when they learned mathematics, they couldn't make a mess of the stool and take out reasoning.

Many concepts are limited to prescripts, for example, when learning sets, we all know that empty sets belong to any set, and the teacher did not give an inference at the beginning, only said that it was prescribed, and in fact this conclusion is deduced through logic.

What aspects of mathematics does logic influence?

Mathematics is a science with a high degree of abstraction and rigor, and the correctness of its formulas, theorems, laws, principles, etc., cannot be proved by concrete experiments and empirical practice, but can only be confirmed by strict deductive argument logically.

Without logic, the edifice of mathematics cannot be built, or at least the axiomatic deductive mathematics of the system cannot be constructed. That is, mathematics in the modern sense is impossible to exist.

From the perspective of the emergence and development of mathematics or one of its branches, the development of mathematics has its own laws, but its development stage is also accompanied by the development of logic. It embodies the results of human thinking and ingenuity.

The formation of mathematical theories requires a process of accumulation of relevant empirical materials, then enters the stage of refining and sorting, and then goes through organization and selection of rough fingers, and finally forms a set of systems. There is no doubt that logic needs to be applied throughout the process (inductive logic in the initial stage, and evolutionary logic in the collation stage).

Looking at Douyin, I found that there are really a lot of courses on logical thinking, and I am glad that some people have realized the importance of logic.

But I do know very little about logic, and I plan to seriously study the basics of logic for children aged 3-6.