Introduction: Mathematics is a profound subject. Learning mathematics well requires hard research and knowledge accumulation. The master of mathematics can improve his academic level by writing a thesis, and he needs to submit an opening report before writing. Watch the opening report of the master's thesis in mathematics with me. I hope it helps!
First, the connotation of mathematical culture
As a scientific language, tool and technology, mathematics has penetrated into all aspects of modern science and technology, which is an indisputable fact, but the status of modern mathematics in people's minds is far from reaching the height it should reach. With the improvement of mathematics specialization, it seems to be getting farther and farther away from people. Professional knowledge is difficult to understand because it is only in the hands of a few people, and it can't be enjoyed by the public, which directly leads to new achievements that no one understands and awards that no one pays attention to, so mathematicians are "lonely". Loneliness leads to arrogance, and arrogance leads to alienation. This is misunderstanding and helplessness. So we emphasize culture, because mathematics without cultural foundation can only be farther and farther away from people.
Influenced by the present situation of school education, many people think that mathematics is superior and useless except as a tool for further study. In this way, even some well-educated people ignore mathematics, a subject with profound cultural connotation, and ignorance of mathematics has become a very common social phenomenon, which is a very worrying fact. Just as beautiful pictures are more than lines and colors, moving music is more than notes and beats, and mathematics is more than numbers, symbols and operations. Everyone who knows mathematics knows that operation is only a trivial aspect of mathematics, but the spirit, ideas and methods of mathematics contain incomparable profound connotations and penetrate into every corner of science. If mathematics is compared to a big tree, the vitality of this big tree is vigorous, which is reflected in every process of the origin, development, perfection and application of mathematics, and mathematical culture, like soil, has nourished this big tree for hundreds of thousands of years and made it flourish. Therefore, mathematics education rooted in cultural soil is very necessary, which is also what we need very much at present, which will be discussed in detail in chapter 5.
The decades from the end of 19 to the beginning of the 20th century are the golden age in the research field of mathematical philosophy. The discussion on the basis of mathematics is very active, and different schools have been formed, including logicism, formalism, intuitionism and axiomatic chemistry of set theory. Everyone plans to build a solid philosophical foundation for mathematics. Although several schools have their own advantages and disadvantages, they all contribute to the rigor of mathematical foundation. However, Godel's work shattered their illusions and made the study of mathematical philosophy once fall to the bottom. Until the 1960s, western scholars put forward the concept of mathematical culture and put forward new viewpoints and methods for the study of mathematical philosophy from a new standpoint. The first American mathematician who systematically completed this pioneering work was R. Wilder, who put forward the philosophy of mathematics as a cultural system. Wilder is an excellent mathematician, mainly engaged in the research of topology and mathematical foundation. His Introduction to Mathematical Basis and Preliminary Study on the Evolution of Mathematical Concepts are of far-reaching significance to the study of mathematical basis. Influenced by anthropologist friends, he became interested in anthropology, boldly investigated the essence and development of mathematics from the perspective of anthropology, integrated anthropological research experience into mathematics research, and published books such as Evolution of Mathematical Concepts and Mathematics as a Cultural System.
In his works, he investigated mathematics from the perspective of cultural generation and development theory, took the lead in putting forward the concept of mathematical culture, constructed the theoretical system of mathematical culture, and formed the first mature mathematical philosophy that has appeared for a long time, emphasizing the cultural connotation of mathematics, such as development motive force, development law and way of thinking, and emphasizing the influence of heredity, environment, human beings and human culture on mathematics.
Second, the significance of mathematical culture research
Different from other cultures, mathematical culture has a unique research object, research perspective and value evaluation standard. Its appearance puts forward new ideas and methods for mathematical research, which enables us to cut into mathematics, understand mathematics and deconstruct mathematics from any angle of human culture, and expand the research ideas and scope to the greatest extent.
Mathematical culture first studies mathematics itself, including studying mathematical science from the perspective of scientific system and studying mathematical philosophy from the perspective of philosophy. The study of mathematical science is the study of mathematical theory in a general sense, while the study of mathematical philosophy is the discussion of mathematical foundation, mathematical paradox and mathematical ontology, including the object, nature, characteristics, position and function of mathematics, the philosophical significance of new branches and topics of mathematics, the philosophical thoughts of famous mathematicians and mathematical schools, mathematical methods, and the reality and truth of mathematics.
At the same time, mathematical culture studies the interaction between mathematics and other disciplines, mathematical culture and other cultures, such as the infiltration between mathematics and literature, mathematics and economics.
The study of mathematical culture considers the evolution and development of mathematics from cultural factors, which provides a new thinking direction for the study of mathematical history. The study of mathematical cultural history is different from that of mathematical history, which pursues the perfection of mathematical knowledge and the evolutionary history of mathematical thoughts. The historical study of mathematical culture is based on the overall perspective, thinking about the interactive relationship between mathematics and other cultural systems, and paying attention to the influence and enlightenment of these relationships on the development of modern mathematics.
For example, China's traditional culture and practical philosophy make China's traditional mathematics pay attention to practicality, so it is the essence of China's traditional mathematics to work out the algorithm of practical problems, which is also the basic point for the existence and development of China's mathematics. The mathematical thought of ancient Greece was born in the atmosphere of city-state maritime trade, and the speculative thought of inclusiveness and pursuit of independence gave birth to deductive mathematics, which is the deep penetration of ancient Greek philosophy and the embodiment of cultural values. From the perspective of cultural differences between China and the West, we have found the reasons for the great differences in the mathematical systems between the East and the West. This is not the requirement of mathematics itself, but the requirement of culture.
The study of mathematical culture emphasizes and highlights the role of social cultural psychology, values and human culture in mathematics, and explains the reasons for the emergence, development, stagnation or extinction of some theories from a new perspective. For example, mathematics in ancient Greece flourished because the Greeks regarded mathematics as the basis of all learning, and the dualistic world outlook also guided scientists to separate matter from themselves and make scientific and effective objective analysis. China's Confucianism put mathematics at the end of the six arts, and the world outlook of harmony between man and nature made orientals show that they are good at intuition and short of abstraction, good at synthesis and not good at analysis. This is also the reason why ancient oriental mathematics could not flourish.
Third, the cultural characteristics of mathematics
1. Mathematical abstraction
In the early human civilization, at the beginning of mathematics, human beings learned to think about numbers and perform some operations. Soviet mathematician A.D.Aleksandrov said: "Abstraction has been shown in simple calculations. We use abstract numbers, but we don't intend to associate them with concrete objects every time. What we learn at school is an abstract multiplication table-always numbers. The multiplication table is not the number of boys multiplied by the number of apples, or the number of apples multiplied by the price of apples, and so on. "
Mathematics has become an abstract subject, and people remember this great contribution of the Greeks. The Pythagorean school considers abstract problems purely by the mind, and thinks that number is the ultimate component of real matter and the element of the universe. Complete deductive reasoning proves that it deepens the abstraction of mathematics. The Greeks consciously acknowledged and emphasized that mathematical things such as numbers and figures are abstractions of thinking, which are completely different from actual things or actual images. Material entities are transient and imperfect, while abstract concepts are eternal and perfect. Although abstraction is more difficult than entity, its advantage is beyond the reach of entity, that is generality. In the abstract world, points have no size, lines have no width, and surfaces have no thickness. Piled stones and bundles of branches can both represent quantitative relations.
2. Mathematical certainty
Mathematics pursues completely certain and reliable knowledge. This result benefits from the special and effective method of mathematical system, that is, starting from a series of self-evident axioms, accurately describing the concepts and definitions to be discussed, and drawing clear conclusions through strict logical reasoning, which is also the driving force for the rapid development of mathematics. For thousands of years, the truth of mathematics has been highly recognized and respected.
However, after19th century, this truth position of mathematics has been greatly impacted again and again. The paradox of non-Euclidean geometry, quaternion theory and set theory casts a shadow on the image of "the embodiment of truth" in mathematics, which makes mathematics lose the rigor of revealing the objective world and its own foundation. Morris Kline mentioned in "Mathematics: The Loss of Determinism", "The current dilemma of mathematics is that there are many kinds of mathematics instead of only one kind, and each kind cannot satisfy the opposing schools for various reasons. Obviously, the generally accepted concept and the correct reasoning system-the noble mathematics in1800 and the pride of people at that time-have now become wishful thinking. Uncertainty and doubt related to future mathematics have replaced past certainty and complacency. The differences based on the "most certain" science are not only surprising, but also embarrassing to put it mildly. "
3. Inheritance of mathematics
Scientific knowledge is formed in the long-term historical development process, and its process shows that knowledge has inheritance. Without inheritance, there is no accumulation. I think inheritance should be understood from two aspects.
Personally, I think we can learn some knowledge and master the achievements accumulated by a subject for thousands of years in a short time without going through the arduous practice process of scientists again. This inheritance is realized through education, which has greatly accelerated the development of science and technology, so now a middle school student has more knowledge than some famous scientists in ancient times. "Only by effectively inheriting human knowledge and mastering the most advanced scientific and technological knowledge in the world can we move forward half a step, that is, the most advanced level and first-class scientist (Steven Weinberg, winner of the Nobel Prize in Physics)." Because of this, the field of knowledge can develop into today's face. Poincare, a famous French scientist, is known as an "all-round mathematician" because he has made outstanding contributions in almost every field of mathematics, astronomy and physics. However, today, it is impossible for a person to master one-third of all mathematical knowledge.
Four. summary
catalogue
Chapter 1 Overview
The cultural connotation of 1. 1
1.2 the connotation of civilization
1.3 the connotation of mathematical culture
1.4 Significance and present situation of mathematical culture research
Chapter two: Cultural characteristics of mathematics.
2. 1 Cultural characteristics of mathematics
2. 1. 1 mathematical abstraction
2. 1.2 Mathematical certainty
2. 1.3 Inheritance of Mathematics
2. 1.4 Simplicity of Mathematics
Mathematics 2. 1.5 in one
2.2 the functional characteristics of mathematics
2.2. 1 mathematical permeability
2.2.2 the spread of mathematics
Mathematical tools
2.2.4 Predictability of mathematics
2.3 the artistic characteristics of mathematics
2.3. 1 Mathematical Art
2.3.2 Mathematics and Music
Math and art
Mathematics and literature
Chapter 3 Mathematics and Human Civilization
3. 1 Mathematics is the source of human logical ability.
3.2 Mathematics Awakens Human Rational Spirit
3.3 Mathematics has promoted the liberation of human thought.
3.4 Mathematics improves human life
3.5 Mathematics Perfecting People's Character
3.6 Mathematics to improve human cultural quality
Chapter IV Mathematics and Social Civilization
4. 1 Mathematics promotes social progress
4.2 Mathematics promotes knowledge development
Chapter 5: The research progress of mathematics culture and mathematics education in China.
5. 1 Summary of Research on Mathematics Culture and Mathematics Education
5.2 Progress of Mathematical Culture and Mathematical Education Activities
Chapter VI Reflection on Mathematics Education
6. 1 Mathematics literacy is an important part of national cultural quality.
6.2 Status of Mathematics Education
6.3 Problems and suggestions to be solved urgently in mathematical culture education
Concluding remarks
refer to
Express gratitude/gratitude
Problems and suggestions to be solved urgently in verb (abbreviation of verb)
1. The cultivation of mathematical skills and mathematical literacy should be closely integrated into an organic whole. On the one hand, it can improve students' interest in learning mathematics, on the other hand, it can help students deepen their understanding of mathematics, improve their logical thinking ability and form the habit of rational thinking. A common problem in the education of mathematical culture in colleges and universities is that mathematical culture is out of touch with the cultivation of mathematical skills. At present, math culture courses or math education courses are optional courses, which are essentially "make-up courses", usually offered after students enter school for one or two semesters. When the mathematics culture class arouses students' interest and thinking about mathematics, the basic mathematics course has been completed or will be completed soon. Therefore, for students, math culture class has a feeling of "meeting each other late". As some students have reflected, if we set up a math culture class earlier and understand the cultural connotation of mathematics earlier, we will learn advanced mathematics better. Due to the long-term accumulation of exam-oriented education, students mainly accept knowledge of mathematical skills in junior and senior high schools, and rarely contact with knowledge of mathematical culture. Therefore, after entering colleges and universities, students' understanding of mathematics culture is almost blank. This also objectively caused the disconnection between mathematical culture and skill training.
2. In recent years, due to the demand of workers in various fields for modeling ability, mathematical modeling education has been paid more and more attention. The main goal of mathematical modeling education is to cultivate students' innovative consciousness and thinking ability in the process of modeling and cultivate students' good mathematical literacy. A study by Louisiana State University in the United States shows that, similar to the survival and development of bacteria, students' exploration and acceptance of knowledge is not only an individual behavior, but the communication network formed between students will make students interact and promote each other, thus having a qualitative impact on teaching results. The educational form of mathematical modeling has just broken through the limitation of time and space and changed the traditional single teaching of "teacher to student".
Schedule of intransitive verbs
20xx165438+1October 01-165438+1October 7.
20xx165438+1October 08-165438+1October 20, initially collect the relevant information of graduation thesis and fill in the task book.
20xx165438+1October 26th-165438+1October 30th to further familiarize yourself with the graduation thesis materials and write the opening report.
20xx65438+February10-65438+February 19 confirm and submit the opening report.
20XX 0 1.04-0.02 15, complete the first draft of graduation thesis and submit it to the tutor.
20XX Finish the paper revision from February 16 to February 20.
20XX Finalize, print and bind from February 2/KLOC-0 to March 20.
20XX thesis defense on March 21-April 10.
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[4] Qin Huangan. On the essence and function of mathematical culture and its role in human cultural changes [J]. Journal of Shaanxi Normal University, 1993 (2): 54-6 1.
[5] Zheng Yuxin. The content and significance of mathematical philosophy [J/OL].
[6] Ordinary high school mathematics curriculum standards (experiment) [M]. Beijing: People's Education Press, 2003.
[7] Gu Pei. Mathematical culture [M], Beijing: Higher Education Press, 2008.
[8] Introduction to Mathematics Culture Course of Nankai University.
[9] Jilin University undergraduate mathematical culture course syllabus-mathematical culture.
Maurice Klein. Ancient and modern mathematical thoughts (Volume I) [M]. Shanghai: Shanghai Science and Technology Press, 2002.
Zheng Yuxin. Mathematical methodology [M]. Nanning: Guangxi Education Press, 200 1.
Zhang Weizhong. Mathematics: Losing certainty? [J] Study on Dialectics of Nature, 1998, 14 (1 1).
[13], often, On the Cultural Characteristics of Mathematics [J].par Journal of Mathematics Education, 2005, 14 (3): 25-27.
[14] Jiang Lan. On the beauty of mathematics [J]. Journal of Wenzhou Vocational and Technical College, 2003,3 (2): 38-42.
[15] Yang Yi. On sports mathematics and sports science [J]. Journal of Hengyang Normal University, 2002,23 (3): 95-96.
Sichuan Key Laboratory of Mathematical Geology.
Lin. I ching and fuzzy mathematics [J]. Journal of Minjiang University, 2002,22 (2):116-118.
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