The number of real world relations and the spatial form of science. Practice in human long-term production and development activities. Originated in the count and measure, with the development of productive forces, are increasingly demanding quantitative study of natural phenomena; the same time as the development of mathematics itself, it is highly abstract, rigorous logic and broad applicability. Are broadly divided into basic mathematics (also known as pure mathematics) and applied mathematics major categories. The former include mathematical logic, number theory, algebra, geometry, topology, function theory, functional analysis and differential equations and other branches; which include probability theory, mathematical statistics, computational mathematics, operations research and combinatorial mathematics and other branches.
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No. 2
That the number of patients. Ancient on astronomy, calendar, divination of knowledge
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No. 3
Refers to the ancient science of astrology. Song Yu Wen Bao, "recorded four sword blow": "Health Day taboo hide their math, temperature and species of peony public, President said: One day late in the morning practice dead horse. Sun, must rein went to the horse stables. This non-mathematical but what?" "Vision and Kingdoms" before the set: "Taejo transfer position and Taizong, Emperor Taizong want to be in Kyoto, was alarmed by Mr. Chen Xiyi name Tuan Hua, table Detu Nan, and good at math, predict the future things." clear Qingchengzi " Deng Zhiyi sequel will be ":" with great concentration in mathematics, accounting for more than something odd experience. "
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Of the real world of space science and the relationship between form and quantity
Of the real world the relationship between spatial form and quantity of science, including arithmetic, algebra, geometry, trigonometry, calculus and so on. Qing Qian Yong "Garden Cong would carry out the number of arts": "Mathematics through in astronomy, law calendar, although one of the six arts, the law the general subtle, can greatly from school to do also."
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Introduction
Definition Mathematics is the study of quantity, structure, change, and the concept of spatial models of a discipline. Abstract and logical reasoning through the use of the counting, calculating, measuring and observing object shape and movement of produce. Mathematicians develop these concepts, in order to guess the new formulation and _select_ed from the right to establish rigorous definition of axioms and deduce the truth. Name source China's ancient mathematics called arithmetic, also known as arithmetic, and finally changed to mathematics. History of mathematics Basic mathematical knowledge and use of personal and community life is always an integral piece. The basic concept of refining as early as in ancient Egypt, Mesopotamia and ancient India, the ancient mathematical texts within a matter of considerable see. Since then, its development has continued to progress slightly, until the 16th century Renaissance, because of new scientific discovery phase and the role of innovation led to the generation of mathematical knowledge to accelerate, until today. Today, mathematics is used in different areas of the world, including science, engineering, medicine and economics. The application of mathematics to these areas often referred to as applied mathematics, sometimes sparking new mathematical discovery, and lead to new disciplines. Mathematicians also study pure mathematics, is mathematics itself, without any practical application as the goal. While many began to study pure mathematics, then will find many applications. Founded in the 1930s the French Bourbaki school of thought: mathematics, pure mathematics at least, is the study of abstract structure of the theory. Structure, that is, the initial concepts and axioms of the deductive system. Cloth school of thought, there are three basic abstract structure: algebraic structures (groups, rings, fields ...) order structure (partial order, total order ...), topology (neighborhood, limits, continuity, dimension ... ... ).
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The nature of mathematics
What is the nature of mathematics? Why mathematics can be used in all other subjects? Mathematics is the number and shape of things, the law subjects. If you want to in-depth study of its nature and its extension problem, we must introduce civilization] [Complete Works of proper nouns of course. In fact, the nature of mathematics: a study of subjects [storage space]. The natural world has its own storage space, a phenomenon called the [blank] Chu. To determine whether a thing as a "storage space" is actually very simple: to _set_ in "in the × ×" × × is the "storage space" (including concrete and abstract). Then, we will find that all things can be _set_ into one that is: the natural world are just different "storage space" only. So people also found that: [[algebra] is to study the amount of storage space] subjects; [] is a study of the geometric shape of [storage] space subjects. And since natural things are just different storage space only, then the mathematics course will be common to all subjects among the! 1 more evidence As a storage space in addition to the vacuum outside the storage compartment are all [] (empty reservoir diaphragm), and then use it in other subjects must be used [number] to distinguish between the various units of storage space, such as: a, head , bar, hours, cattle, Joule, Ohm, Ampere, etc., can be said to leave the unit, was nearly meaningless. And the definition of the term [] is related to the storage compartment storage space, a place that is different from other things. Recalcitrant space computational model Recalcitrant waited in vain for type type] [recalcitrant waited in vain for example: one person is equal to 5 different apples, that is: a person can get five apples, five apples, or a man linked to (any contact can be); different The following is the equal sign = equal sign plus a o (storage empty flag); so that you can simply describe the many calculations encountered in daily life. And you can reserve through the right of the [different] space computational model (the simplest model), to calculate the number of things. 3 Other areas of geometry Of course there is, in fact, there have been two huge areas of geometric been long ignored, that is [text] and [functional geometry geometry]. (1) text geometry: when some specific meaning of the text by special arrangement and shape of a combination of down will be a variety of special functions and features. As our most common "chemical periodic table", "text diagrams", "mathematical model" and so on. (2) the geometric features: a variety of shapes are holding a variety of functions! If you can expand capacity to accommodate spherical material, the material is conducive to cross-spread and so on. Therefore, we should carefully study and explore a variety of special features of various shapes! However, using the Complete Works of civilized logic: If the natural world have a common nature and law, then they can certainly be used to deduce the nature and laws of the various subjects, and to infer the subjects of the new content. So we found the study of mathematics is the "storage space" of a subject, and reasoning out a variety of new areas. Note: (equations, arithmetic, solution of equations of the nature reserve can be used [blank] out of the internal laws of reasoning)
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In all areas of mathematical research
The main subjects mathematics first commercially produced in the calculation of the need to understand the relationship between numbers, land measurement and prediction of astronomical events. Require roughly four and quantity, structure, space and change (ie, arithmetic, algebra, geometry and analysis) and other mathematically related to a wide range of sub-fields attached. In addition to these main concerns, there are also used to explore other areas by the core on mathematical link between the sub-fields: to logic, to _set_ theory (basic), to experience different mathematical sciences (applied mathematics), and more modern to rigorous study of uncertainty. Quantity Number of learning from a few, at the beginning of the familiar natural numbers and integers and is described in the natural number arithmetic and integer arithmetic. Integer nature of deeper study in number theory was, if this theory includes the famous Fermat's Last Theorem results. Number theory has been widely explored, including two unsolved problems: the twin prime conjecture and Goldbach's conjecture. Further development when the number system, integers are recognized as a sub_set_ of rational numbers, and rational numbers are included in the real numbers, the number of consecutive real numbers that are represented. Real number can be further generalized into the plural. Number can be further generalized to include continuous quaternion and eight metadata. Consideration of natural numbers can lead to transfinite numbers, which formulated the concept of counting to infinite. Another area of study for its size, this led to the base and the other after a concept of the infinite: the number of ALEPH, which allows unlimited size collection can be done between a meaningful comparison. Structure Shown with a collection of functions and many other mathematical objects have a containing structure. Structural properties of these objects are discussed in the group, ring, body and other objects of the abstract itself this system. This is the field of abstract algebra. In this there is a very important concept, namely the vector, and generalized to the vector space, and research in linear algebra. Vector of a combination of three basic areas of mathematics: quantity, structure and space. Vector analysis will be extended to a fourth of its basic areas that change. Space And philosophical basis To understand the foundations of mathematics, mathematical logic and _set_ theory was developed out of other areas. Cantor (Georg Cantor ,1845-1918) first _set_ theory, boldly, "infinity" to enter for the various branches of mathematics is to provide a solid foundation, but the content itself is quite rich, made a real infinite exist for the future development of mathematics an invaluable contribution. Cantor's work to bring about a revolution in the development of mathematics. Because of his theory beyond the visual, so when some mathematicians have been the opposition, even as the "profound and full of initiative," the mathematician Pioncare also interesting to compare the _set_ theory of the "pathological cases", even his Cantor is the Kronecker teachers fight back, "neurotic," "beyond the numbers into the hell." censure and blame for these, Cantor is still full of confidence, he said: "I like the theory of solid rock in general, any who oppose it will move from shooting ourselves in the foot. "He also said:" The essence of mathematics lies in its freedom, not bound by traditional ideas. "This argument continued for decades. As often in the spirit of Cantor being suppressed, resulting in him in 1884 suffering from schizophrenia, died of a mental hospital. However, after all, a fair assessment of the history of his creation, _set_ theory in the early 20th century, has gradually penetrated into every branch of mathematics, has become the analytical theory, measure theory, topology and mathematical sciences, an indispensable tool. Early 20th century, the world's greatest mathematician Hilbert spread in Germany, Cantor's ideas, called him "a mathematician's Paradise" and "the most amazing product of mathematical thought." British philosopher Russell to Cantor's work as "this day and age can boast of the most significant work." Focus on mathematical logic placed in a solid mathematical axioms architecture, and study the results of this framework. For its part, the second Godel incompleteness theorem for the origin, and this is perhaps the most widespread logic results - there is always one that can not be proven true theorems. Modern logic is divided into recursion theory, model theory and proof theory, and theoretical computer science and is closely correlated. Engels said: "Mathematics is the relationship between the number of the world are given form and space science."
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Mathematical classification
Discrete Mathematics Fuzzy Branch of mathematics 1 Arithmetic 2 Elementary Algebra 3 Advanced Algebra 4 Number Theory 5 European Geometry 6 Non-European-style geometry 7. Analytic Geometry 8. Differential Geometry 9. Algebraic geometry 10. Projective geometry learning 11. Geometric Topology 12. Topology 13. Fractal geometry 14 calculus 15 Real Variable Theory 16 Probability and Statistics 17 complex variables 18 Functional analysis 19 Partial Differential Equations 20. ODEs 21 Mathematical Logic 22 Fuzzy Math 23 Operations Research 24. Computational Mathematics 25 The mutation theory 26. Mathematical Physics Broad classification of mathematical From the vertical division: 1, elementary mathematics and ancient mathematical: This refers to the 17th century mathematics. Mainly built during the age of ancient Greece Euclidean geometry, ancient China, ancient India and ancient Babylon during the establishment of arithmetic, developed during the European Renaissance of algebraic equations. 2, the variable math: is 17 - 19 century to establish and develop math. Half of the 17th century, the beginning of math time variable can be divided into two phases: the creation of the 17th century stage (Heroic Age) and the 18th-century stage of development (creating the era). 3, Modern Mathematics: is the nineteenth-century mathematics. Modern mathematics during the 19th century is the comprehensive development of mathematics and the mature stage, mathematics has undergone profound changes, most branches of mathematics have been formed during this period, the mathematics show emerged full prosperity. 4, modern mathematics: refers to the 20th century mathematics. In 1900 the famous German mathematician Hilbert (D. Hilbert) Congress of Mathematicians in the world made a famous speech, made 23 predictions and know the future development of mathematics in mathematical problems (see below), beginning the 20th century prelude to modern mathematics. Note: Hilbert's 23 problem - In 1900 Paris International Congress of Mathematicians, Hilbert published a report entitled "Mathematics problem" of the famous speech. He is the nineteenth century, especially the past results of mathematical research and development trends, made 23 of the most important mathematical problems. This is known as Hilbert 23 problem issues, and later became a mathematician trying to overcome the many difficulties of modern mathematical research and development had a profound impact and played a positive role in promoting, in some Hilbert problem is has been satisfactorily resolved, some still with us. Expounded in his speech to the letter of every mathematical problem can be solved beliefs, for mathematicians is a great encouragement. (1) base of Cantor's continuum problem. (2) arithmetic axiom system without contradiction. (4) straight line distance between two points in the most short-term problem. (5) topology of a Lie conditions (topological group). (6) play an important role in mathematical physics axiomatic. (7) certain number of transcendence proof. (8) distribution of prime numbers, especially on the Riemann hypothesis, Goldbach conjecture and the twin factors of the problem. (9) General reciprocity in any number of field evidence. (10) through a finite number of steps to determine whether the uncertain existence of rational integer solutions of equations? (11) within the general quadratic algebraic number theory. (12) class domains pose a problem. (13) General seven algebraic equations with two variables to solve continuous function of the combination is not likely. (14) Department of limited function in some complete proof. (15) to establish the basis for algebraic geometry. (16) algebraic topology of curves and surfaces. (17) square and positive semidefinite forms, said. (18) with congruent polyhedra constructed space. (19) is the variational solution of the problem is always an analytic function? (20) study the general boundary value problem. (21) with the given singularities and single valued group of Fuchs class of linear differential equations to prove existence of solutions. (22) automorphic functions with a single value of analytic functions. (23) Development of variations methods of research. From the horizontal division of: 1, Basic Mathematics (Pure Mathematics). Also known as the theory of mathematics or pure mathematics, is the core of mathematics, including algebra, geometry, analysis of the three branches, respectively, of the number, shape and several shaped relationship. 2, Applied Mathematics (Applied mathematics). Simply put, that the application of mathematics. 3, Computational Mathematics (Computstion mathematics). Studies such as the calculation method (numerical analysis), mathematical logic, symbolic mathematics, computational complexity, programming and other issues. The subject is closely related with the computer. 4, Probability and Statistics (Probability and mathematical statistics). Sub-probability theory and mathematical statistics the two blocks. 5, Research and Cybernetics (Op-erations research and csntrol). Operations research is the use of mathematical methods, based on the model, to solve the manpower, materials, money, and the operation of complex systems, organization, management, and the problems of a discipline.
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Symbols, language and rigorous
In modern notation, simple expressions can describe a complex concept. This image is a simple equation that is generated. We are now used by most of the mathematical symbols are to the 16th century before being invented. Before that, mathematics was written out of the text, this is a hard mathematical development will be locked into the program. For today's expert in terms of mathematical symbols makes it easier to control for, but beginners often feel they are prohibitive. It is extremely compressed: a few symbols contain a large number of messages. Like music notation in general, today's mathematical symbols have a clear syntax and other methods is difficult to write the message encoding. Mathematical language also find it difficult, for starters. How to make these words have a more precise than everyday language meaning. Also annoying with beginners, words such as open fields and in mathematics has a special meaning. Mathematical terms as the embryos and may also include the plot and other proper nouns. However, exclusive use of these special symbols and terminology have their reasons: the Mathematical need more precision than everyday language. Language and logic of a mathematician accuracy of this requirement as "stringent."
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History of mathematics
History of world mathematics Mathematics, originated in early human production activities, as one of six arts in ancient China, was also the philosophy of the ancient Greek scholar as a starting point. Greek mathematics μαθηματικ?? (Mathematikós) means "knowledge base", from μ? Θημα (máthema) ("science, knowledge, learning"). About the evolution of mathematical abstraction can be seen as the continued development or extension of the theme. The first is about the concept of abstract numbers, its two apples and two oranges have a certain kind between the same perception of things is a major breakthrough in human thought. In addition to understanding how to count the actual amount of material, prehistoric man also learned how to count the number of abstract material, such as time - days, seasons and years. Arithmetic (Math) is also naturally produced. The ancient stone has been confirmed at the geometric knowledge. Further you need writing or other digital recording systems, such as wood or symbol in the Inca Empire used to store data, Chip. Historically there were many differences between the count and the system. From a historical era beginning, the main principle of mathematics is to do the tax and trade-related terms, in order to understand the relationship between numbers, to measure land, and in order to predict the formation of astronomical events. These needs can easily be summed up as the number of mathematics, structure, space and time for research. To the 16th century, arithmetic, elementary algebra, and trigonometry and other elementary mathematics has been largely complete. 17th century produced the concept of variable so that people began to study changes in the volume and the amount of mutual relations and mutual transformation between the graphics. In the study of classical mechanics in the process, the method was invented calculus. With the natural sciences and technology, further development, the basis for the study of mathematics and mathematical logic, _set_ theory produced, also began to slowly develop. Mathematics since ancient times has been continuously extended, and a wealth of interaction with science, and to benefit both. In the history of mathematics there are many discoveries, and until today have also been discovered in. According to Mikhail B. Sevryuk in the American Mathematical Society Bulletin in January 2006 in the journal said, "exists in the Mathematical Reviews database, the number of papers and books since 1940 (the founding year of Mathematical Reviews) is now more than one hundred ninety million copies, and each year has increased over seventy-five thousand copies of the breakdown. Xuehai the bulk of this new mathematical theorem and its proof. "
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Foreign Math Masters
Gauss Mathematical genius ─ ─ Gauss Gauss is the German mathematician, physicist and astronomer. Gauss born, all phenomena and things on the very curious, and determined to get hold of the bottom. 7 years old, Gauss first school. In the world of a widely circulated story that the Bute Na Gauss calculated the age of 10 will be out to students of all integers from 1 to 100 combined math problems, Bute Na was out to the children is a The addition of more difficult questions: 81297 +81495 +81693 + ... +100899. Gaussian can be considered finished and finished writing the answer to a small stone to pay up, when he wrote the answer is only correct, but the other kids are wrong. Mathematical historians tend to think that Gauss had already mastered the arithmetic series summation method. A 10-year-old only child, independently found that mathematical methods it is very common. Gauss's academic status has always been admired by people very high. He has "Prince of Mathematics", "mathematician king" reputation. Newton Newton is a British physicist and mathematician. At school, Newton was a strange child, we like to design their own hands, do Feng Zheng, sundial, drip like objects. He was curious about everything around, but it does not seem particularly clever. Later, the family told him to suspension, to go help his mother's farm. In his mother's farm and saw an apple fall to the ground, began to fathom that this force will pull down the apple will also control the moon. Which Newton deduced the rate of change objects falling speed is proportional to the size and gravity, and gravity size and square of the distance from the center of the earth. Newton's prism experiment was also made him famous. There are two famous Newton is known to everyone. He wrote in a letter: "If I see far more than others, it is because I stood on the shoulders of giants." Said he talked: "I do not know how I see the world; but I seems like only a child playing on the beach, from time to time to find a smooth than the others, a more beautiful pebbles or shells are happy, and I in front of the vast ocean of truth, still a complete mystery. History of ancient Chinese mathematics Math ancient mathematics, ancient Chinese science an important subject, according to the characteristics of the development of mathematics in ancient China can be divided into five periods: embryonic; formation of the system; development; prosperity and integration in Western mathematics. The seeds of ancient Chinese mathematics Primitive end of private ownership and exchange of goods produced, number and type of concept has been further developed, Yangshao pottery unearthed during the above said 1234 has been marked with the symbol. To the primitive stage, has begun to use symbols instead of text Jieshengjishi the. Xi'an Banpo pottery useful for one to eight dots composed of equilateral triangles and sub-square pattern of 100 small squares, Banpo Ruins of houses are round and square base. To draw a circle for the side to determine the straight, it also created the rules, moments, quasi-, rope and other mapping and measurement tools. According to "Historical summer of the century," record, Yu flood control when using these tools. Commercial mid, Oracle has produced a _set_ in decimal numbers, and notation, with the largest numbers to 30,000; At the same time, Yin with ten Heavenly Stems and twelve Earthly Branches composed of six decades, Yi Chou, Bingyin, Dingmao other 60 names to remember the date 60 days; in the Zhou Dynasty, before again using yin and yang symbol consisting of gossip that eight kinds of things develop hexagrams that 64 kinds of things. The first century BC "Zhou Bi Suan Jing 'early Western Zhou Dynasty that moment measurements with high, deep, wide, far way, citing Gougu Xing hook three shares of four, five strings and rings can be round, etc. Examples of moments . "Book of Rites in" articles mentioned the age of nine from the Western Zhou children of the nobility would have to learn numbers and counting methods, they want gifts, music, shooting, Yu, books, a few of the training as "six arts," one of the few has started to become specialized courses. The occasion of the Spring and Autumn, has been generally contemplated the application contemplated notation has been used decimal value system, this notation on the development of mathematics in the world there is a landmark. The measurement of mathematics in this period the production has been widely used in mathematics, there is also a corresponding increase. Warring States period, contending also contributed to the development of mathematics, especially for the rectification of names and some of the propositions of mathematics concerned with the issue directly. After famous term that through the abstract concept of different entities with their original, they proposed "Moment side, not as round regulations," the "freshman" (infinity) is defined as "Tai no outside" and "little one" ( infinitesimal) is defined as "to small no inside." Also proposed the "foot of the Chui, whichever half day, eternally inexhaustible" and other propositions. The name comes from the material Mohist believes that, were from different areas and different depths reflected objects. Mohist give some mathematical definitions. Such as round, square, flat, straight, sub-(tangent), end (point) and so on. Mohist do not agree with "one foot of the Chui," the proposition put forward a "non-half" of the proposition to be refuted: the line segment by split half and half to go on infinitely, it will no longer split the emergence of a "non-half", the "non-half" is the point. Masters thesis discusses the limited length can be divided into an infinite sequence, Mohist proposition is that this infinite division of the changes and results. Mohist famous and the mathematical definition and discussion of mathematical propositions, on the development of the theory of ancient Chinese mathematics is of great significance. The formation of ancient Chinese mathematical system Qin and Han period is the rise of feudal society, economy and culture have been developing rapidly. Mathematical system in ancient China was formed in this period, its main indicator is the arithmetic has become a specialized discipline, as well as the "Nine Chapters on Arithmetic", represented by the emergence of mathematical works. "Nine Chapters on Arithmetic" has several notable features: the use of disaggregated _set_ of chapters in the form of mathematical problems; formula are contemplated from the notation developed; to arithmetic, algebra, and few involve graphic nature; attention applications, the lack of theoretical understanding and so on. These characteristics are the same social conditions was closely related with academic thought. Qin and Han Dynasty, when all the science and technology should be to establish and consolidate the feudal system, and the development of social production services, emphasizing the application of mathematics. Finally a book on the Eastern Han Dynasty's "Nine Chapters on Arithmetic" eliminate the Warring States period, contending that appear in the famous and Mohist attention and logical discussion of the term defined, with emphasis on production at that time, living in close combination of mathematical problem and its solution, This was the development of society is exactly the same. "Nine Chapters on Arithmetic" in the Sui and Tang dynasties had spread to Korea, Japan, and was a math textbook in these countries. Some of its achievements, such as the decimal value of the system, this has surgery, earned less than surgery so also to India and Arabia, and through India, Arabia to Europe to promote the development of mathematics in the world. Development of mathematics in ancient China Wei, Jin period occurs in the spirit, not bound for the Confucian classics, thinking more active; it's long debate win, but also the use of logical thinking, analysis, argumentation, all of which contribute to improved mathematical theory. Note Zhao Shuang Wu, "Zhou Bi Suan Jing ', Han Chu-Jiang Wei Xu Yuezhuan" Nine Chapters on Arithmetic "Note, the late Jin Wei Liu Hui early essays," Nine Chapters on Arithmetic "Note," IX re-difference map "are there during this period. Zhao Shuang Liu Hui's work with the mathematical system in ancient China has laid a theoretical foundation. Zhao Shuang was ancient China to prove mathematical theorems and formulas and the derivation of one of the earliest mathematicians. In his "Zhou Bi Suan Jing 'book to add the" Pythagorean circle Quadrant and Notes "and" high map and note on "is a very important mathematical literature. In the "Pythagorean circle Quadrant and Notes" in which he proposed to prove the Pythagorean theorem reconciliation Gougu Xing chord diagram of the five formulas; in the "high figure, and note on", he proved with the graphics area of the universal application of the weight difference between the Han Dynasty formula, Zhao Shuang's work with the groundbreaking, the development of mathematics in ancient China occupies an important position. Liu Hui and Zhao Shuang about the same time, he inherited and developed the famous and the Warring States period Mohist ideas, particularly ideas of some mathematical terms it is important to give a strict mathematical definition of the concept, that of mathematical knowledge must be "reasonable analysis" in order to close to simple mathematical works, which will help the reader. His "Nine Chapters on Arithmetic" note not only of the "Nine Chapters on Arithmetic" method, formulas and theorems for general explanation and derivation, but also in the process of discussion of a great development. Liu Hui create cutting round operation, using the limits of thought that the circle area formula, and the first circle with the theoretical approach considered was 157/50 and 3927/1250. Liu Hui's method of infinitesimal division side proved right angle right angle tetrahedral cone with a 2:1 volume ratio constant, to solve the general three-dimensional volume of the key issues. In that side cone, cylinder, cone, round table size, the Liu Hui to solve the volume of the ball made a correct way. Eastern Jin Dynasty, the Chinese long period of war and the state of North-South divide. Zu and his son after the work is the economic and cultural southward, the South representative of the development of mathematics work, they note in Liu Hui "Nine Chapters on Arithmetic" on the basis of the traditional mathematics greatly step forward. Their mathematical work are: to calculate pi 3.1415926 - 3.1415927 in between; proposed ancestral (Riheng) principle; proposed the solution of quadratic and cubic equations, etc. Presumably, Zu Chong Zhi Liu Hui cut round in the surgery, based on the calculated inscribed regular 6144-gon-gon and the area is 12288, which has been the result. He also used a new method to get the value of pi two points, namely the rate of about 22 / 7 and close rates of 355/113. Zu this work, the Chinese in the calculation of pi, than in the West about a thousand years ahead; Zu Zu's son (Riheng) summarizes Liu Hui's work, that "the potential power of both the plot with the intolerance," that the two high-dimensional, if any of its high level of cross-sectional area equal to the volume of two-dimensional equal, this is the famous ancestors (Riheng) axioms. Zu (Riheng) application of this axiom to solve the Liu Hui unresolved ball volume formula. Emperor ambitious, massive construction projects, the objective to promote the development of mathematics. Early WANG Xiao Tong's "Ji Gu Suan Jing ', focuses on civil engineering, earthwork calculations, engineering division, acceptance, and the computation of the warehouse and cellar, reflecting the situation of mathematics during this period. WANG Xiao-Tong mathematical symbols not in the case of legislation the number of cubic equations, not only to solve the needs of society at that time, but also for the subsequent establishment of technique Tianyuan basis. In addition, the traditional solution of Gougu Xing, WANG Xiao-Tong also used the number of cubic equations to solve. Sui and early Tang dynasty feudal rulers inherited the system, _set_ up 656 years of arithmetic in the Imperial Museum, has a PhD in computer and teaching assistants, students 30. Taishi compiled by the comment that Li Chunfeng, etc. "count by 10 book", as the arithmetic Hall textbooks for students, Ming Yi Yi these operators count Examination books prevail. Li Chunfeng other compilation "considered by the 10 books', the preservation of mathematical classics, for the research literature in mathematics is of great significance. They "Zhou Bi Suan Jing", "Nine Chapters on Arithmetic" and "considered by the island" by the comments, it is helpful to the reader. Sui and Tang dynasties, the calendar needs, day mathematicians created a quadratic function of interpolation, rich in ancient Chinese mathematics content. Computer chip is the main computational tools in ancient China, it has a simple image, the specific advantages, but there are a large cloth chip footprint, logistics easier when playing with speed errors caused by errors and other shortcomings, so very early reform. Tai-count which, appearances count, three are considered and the abacus abacus with beads slot, is technically important reform. Especially the "abacus", which inherits the contemplated five liters decimal place value system with the advantages and overcome the count and _set_ the aspect contemplated to raise inconvenient shortcomings, the advantages are clear. But then the multiplication algorithm is still not carried out in a row. Not wearing a file count beads, convenient to carry, so still not widely used. After the mid-Tang, commercial prosperity, figures increased urgency for reform is calculated from the "New Book of Tang" and other literature left to count the book titles, this algorithm can be seen that the main reform is to simplify the multiplication, addition algorithm, the Tang Dynasty multiplication and division algorithms reforms carried out in a row operations, both for contemplated, also applies to the abacus. The prosperity of ancient Chinese mathematics 960 years, the establishment of the Northern Song Dynasty Five Dynasties and Ten Kingdoms carved over the situation. Song of agriculture, handicrafts, commerce unprecedented prosperity, scientific and technological advances, gunpowder, the compass, printing three great inventions is high in this economic situation has been widely used. 1084 Secretary of the Province, the first print publication of the "count by 10 book", 1213 Martin has conducted a roll of the carved turn. These are the development of mathematics to create good conditions. From 11 to 14 century about 300 years, there has been a number of famous mathematicians and mathematical works, such as Jia constitution of the "Yellow Emperor IX algorithm Xicao," Liu Yi's "discussion of ancient roots," Horner's "book number nine chapter, "Li Ye's" round the sea mirror test "and" benefit the ancient speech segment, "Yang Hui's" Nine Chapters Detailed algorithm "," daily algorithm "and" Yang Hui's algorithm, "Zhu Shijie's" arithmetic Enlightenment, "" four yuan Yu Kam, "and so on, many areas have reached the peak of ancient mathematics, some of which was also the world's mathematical achievements of the peak. From the open square, open cube to more than four times the square root, is a leap in understanding, to achieve this leap is Jia Xian. Yang Hui in the "Nine Chapters on Algorithms compile class" contains Jia Xian "increase by Kaiping method", "increasing by open method"; in the "Detailed IX algorithm" Jia constitution contained the "prescribing practices origin" Figure , "by seeking inexpensive way to take grass," and used by open method to open by the fourth power of example. According to these records to determine the constitution has been found two JIA coefficient table, created by by open method. These two achievements of the Song and Yuan dynasties mathematics major impact, including Jia Xian triangular Pascal triangle than in the West long before the 600 years. Increased by the open method is extended to higher number of equations (including the case of a negative factor) solution is Liu Yi. "Yang Hui's algorithm" in the "Tian Mu Jie method than the class of multiplication and division," volume, the book describes 22 of the original quadratic equation and a quartic equation, which is used by more than three times by open method to solve the equation of the earliest examples of high- . Astronomers Wang Xun Yuan, Kuo Shou-ching, etc. in the "timing calendar" in the three functions to solve the problem of interpolation. Horner in the "push technique augmented Star" title, Zhu Shijie in the "four yuan Yu Kam" "such as elephant tricks" mentioned interpolation problem (poor technique they called strokes), Zhu Shijie get a four function interpolation formula. With Tianyuan (equivalent to x) as unknown symbols stand out high-equation, the ancient technique known as Tianyuan, which is first introduced in the history of Chinese mathematics symbols, and use symbolic computation to solve the problem of the establishment of high-order equation. The earliest surviving surgery Tianyuan Li Ye's book is "round the sea mirror test." From Tianyuan surgery extended to the binary, ternary and quaternary of the high-simultaneous equations, the Song is another outstanding mathematician created. Been transmitted so far, and this excellent discussion is to create a system of Zhu Shijie "four yuan Yu Kam." Zhu Shijie quaternary high-order simultaneous equations representation in Tianyuan surgery developed on the basis of his constant on the central, quaternary all the power on, down, left, and right directions, the other on four quadrants. Zhu Shijie's greatest contribution is to propose four yuan elimination method, the method is to choose one yuan for the unknown, the other element as it composed of unknown polynomial coefficients, fitted to a number of one yuan higher equations, and application interoperability by destructive method gradually eliminate the unknown. Repeat this step will eliminate the other unknown, and finally by open method of solving multiplication. This is a linear method of solution of the major development groups, similar methods than in the West as early as 400 years. Gougu Xing solution in the new development during the Song and Yuan, Zhu Shijie in the "arithmetic of Enlightenment" made known to hook under the string volume and the stock strings and solving Gougu Xing approach complements the "Nine Chapters on Arithmetic" deficiencies. Li Ye in the "round the sea mirror test" of the Pythagorean circle issues capacity of a detailed study, to be nine round capacity formula, which greatly enriched the content of geometry in ancient China. Known angle between the ecliptic and the equator and the sun from winter solstice to the vernal equinox by running over the yellow arc, seeking more than ascension and declination degree arc, is a solution of spherical right triangle problem, the traditional calendar is calculated using interpolation. Yuan Wang Xun, Guo Shou-jing and other solution is to use traditional Gougu Xing, Shen Kuo Tianyuan with surgery and surgery will be round to solve this problem. But they get is a similar formula, the result is not precise enough. But their steps throughout the projection is correct, from a mathematical sense, this method opens up the way leading to spherical trigonometry. Computing technology in ancient China is the climax of the reform in Song and Yuan Dynasties. Yuan, Ming and the history of literature contains a large number of practical arithmetic books of this period, their number is more than the Tang Dynasty, the main elements of the reform is still multiplication and division. And algorithms reforms, abacus beads may have occurred in the Northern Song Dynasty. But if the modern abacus abacus beads as both, there are a complete _set_ of algorithms and formulas, then it should be finalized in the Yuan Dynasty. The integration of mathematics in the West China from the Ming Dynasty, late into the feudal society, feudal rulers of the implementation of totalitarian rule, publicity idealist philosophy, the implementation of stereotyped examination system. In this case, in addition to Abacus, the development of mathematics and gradually decline. 16 century, the West into China one after another elementary mathematics, the mathematical study of Chinese and Western integration through the emergence of a situation; after the Opium War, the beginning of modern mathematics into China, China will be transferred to a mathematical study of Western mathematics-based period; to the late 19th early 20th century, modern mathematical research began in earnest. From the early Ming Dynasty Ming, commodity economic development, and this commercial development is compatible with the popularity of abacus. The early Ming "Quebec with four words of this hybrid of the word" and "Luban wood by" the emergence of shows abacus has been very popular. The former children's books picture flashcards, which the abacus as a household essential items included in the general manual of wood furniture. With the popularity of abacus, abacus algorithms and formulas are also becoming more and more perfect. For example, Wang Su and Cheng Dawei to increase and improve the hit go, from a formulas; XU Xin Lu and Cheng Dawei by adding, by formulas in the division is widely used in return except, in order to achieve the abacus arithmetic all the formulas of; Zhu _set_ out moisture and Cheng Dawei to prepare for making the open square and open cubic method applied to the abacus, abacus solution process with a large number of second place, three equations, and so on. Cheng Dawei book widely circulated at home and abroad, a significant influence. In 1582, the Italian missionary Matteo Ricci in China, 1607 years later, he met with Xu translated "Geometry" before the six-volume "measurement justice 'roll, and Li algae build" capacity won more justice "and" with the text count means. " 1629, Xu was appointed governor repair calendar rites, under his auspices, the compiler "Chongzhen almanac" 137 volumes. "Chongzhen almanac" is to introduce the European astronomer Tycho's geocentric theory. As part of this theory of mathematics, Greek geometry, trigonometry several European Yushan, and Napier count chips, the proportion of regulations and other computational tools Galileo also introduced come. In the incoming mathematics, the greatest impact is the "Geometry." "Geometry" is the Chinese translation of the first mathematics books, most of the mathematical terms are first, many of which are still in use. Xu that it "need not doubt," "not changed", "no one is universally wrong to learn." "Geometry" is the reading of the Ming and Qing dynasties mathematician math book, for their influential research. Second, is the most widely used trigonometry, trigonometry book introduces the West has "big test", "cutting a round eight-line" and the "Measuring the whole meaning." "Big test" shows the main triangle eight lines (sine, cosine, tangent, cotangent, secant, cosecant, is vector, I vector) the nature, methods of making and using table table method. "Measuring the whole meaning of" in addition to add some "big test" for the missing plane triangle, the more important is the product of and spherical trigonometry and differential equations. All of these are at the time with the translation work calendar with use. There are clear for beginners of Chinese and Western mathematical ideas and write books, many handed down, a greater impact Xi explain, "Graphics", Mei Wen-ting, "Medvedev Books series to" (of which 13 kinds of math books 40 volumes), in Greece Yao, "inspection" and so on. Mei Wen-ting is the culmination of those who focus on Western mathematics. His traditional mathematical solution of linear equations, Gougu Xing solution and the high power of positive roots methods, seeking to collate and study the verge of withering of the Ming Dynasty mathematics there life. Xi Yao in the "inspection" is China's first books to introduce Western science perspective. The sum can be seen on the Western Qing mathematicians will pass a lot of math work and made many original results. These results, such as traditional mathematical comparison, there is progress, but more and contemporaries is obviously lagging behind the West. After Yongzheng's reign, foreign inward, causing China to stop the importation of Western science, domestic pressure to implement the policy, resulting in general can not contact with Western scholars in mathematics, did not dare to interfere study of statecraft, and therefore hard to study ancient rule. Qian Jia was gradually formed between a textual criticism based Qian-Jia school. With the "count by 10 book" Song math works with the collection and annotation, there is a tradition of research in mathematics climax. Which can break through the old box and have inventions have Jiao Xun, Wang Lai, Li Rui, Li Shanlan and so on. Their work, and the Song and Yuan Dynasties era algebra comparison is excel rather than blue; and more Western algebra, in time a bit late, but these results are not being under the influence of modern Western mathematics independently obtained. Have a climax with the traditional mathematical research while Ruan Yuan and Li Rui and other astronomical mathematician wrote a biography - "domain preach," collected from the Yellow Emperor Jiaqing four times to the late astronomer and mathematician more than 270 people (including mathematics books handed down less than 50 people), since the introduction of Western astronomy and mathematics Ming missionaries 41. This book entirely, "Duoshi history books, Tsuen extraction group membership, screening and recording of the" made to collect the raw data is entirely first-hand, influential in the academic community. After the Opium War in 1840, started modern Western mathematics into China. The first is the establishment of British rule a sea of ink in the Shanghai Library, introduced Western mathematics. After the Second Opium War, Tseng Kuo-fan, Li and other bureaucrats to carry out "Westernization Movement", also called for introduction of Western mathematics and learning, the organization works translated a number of modern mathematics. The more important are the Lishan Lan and Wylie translation of "Algebra" "on behalf of the calculus Steps to Christ"; Hua Hengfang and Englishman John Fryer joint translation of "algebraic technique", "micro-product traceability" "casuistry Mathematics"; Zou Liwen Di Cowen compiled with "-shaped device aims to study" "algebra prepared Zhi", "written calculation math"; Xie Wen Hong Shen He Yi Pan and Dalai's "generation-shaped combination of all," "Eight-line equipment purpose" and so on. "On behalf of the calculus Steps to Christ" is the first Chinese translation of calculus; "algebra" is written by the British mathematician De Morgan algebra symbol translation; "casuistry Mathematics" is the first translation of probability theory. In these translations, the creation of a number of mathematical terms and the terms are still used, but generally used by mathematical symbols have been eliminated. After the Hundred Days Reform, _set_ up around the new law school, some of these works will become the main textbook. In the translation of Western mathematical works, the Chinese scholars have conducted some research, write some books, the more important are the Lishan Lan's "" tip Reform solution "" test roots of law "; Xia Xiang bend the" square hole surgery diagrams "" To music technique "" To the song graphic "and so on, all will pass and Western academic research ideas. Since the input of modern mathematics requires a process of digestion and absorption, coupled with the late Qing Dynasty rulers are corrupt, under the impact of the Taiping movement, the imperialist powers of the plunder, the bruised and battered, to attend to mathematical research. Until after the May Fourth Movement of 1919, China's modern mathematical research began in earnest.
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Ancient China and its major contribution to the well-known mathematician
Liu Hui (born around the year 250 AD) Liu Hui Liu Hui (born about AD 250), three post-Wei who is an outstanding mathematician of ancient China, Chinese classical mathematical theory is one of the founders. The birth and death, life story, the history books rarely recorded. It is speculated that the limited historical data, he is the Wei-Jin era Zouping people. Life is not official. His history of mathematics in the world, also occupies a prominent position. His masterpiece, "Nine Chapters on Arithmetic Note" and "considered by the island", is the most valuable mathematical heritage. "Considered by the island," a book, Liu Hui careful _select_ion of the nine measurement issues, these topics of creativity, complexity and representative, have attracted the attention of the West at that time. Liu Hui quick thinking, flexible method to promote both intuitive reasoning and ideas. He is the earliest clear the way advocate the use of logical reasoning to prove mathematical propositions people. Liu Hui's life is hard for the math to explore life. Although he is low status, but noble character. He is not mediocre fame, but insatiable in learning a great man, he left us with a valuable wealth of the Chinese nation. Zu (AD 429 AD 500 years ─) Zu outstanding achievements in mathematics, on the calculation of pi. Qin and Han dynasties past, people with "Drive one week three" as pi, which is the "old rate." Error rate was found too old, pi should be "more than a round Path and Wednesday," but how many more than are divergent views. Until the Three Kingdoms period, Liu Hui made a calculated pi of the scientific method - "cut round operation," with inscribed regular polygon to approximate the circumference of the perimeter. Liu Hui's calculation to the inscribed 96-gon, obtain π = 3.14, and that the inscribed regular polygon of side a few more, the more accurate value of π obtained. Zu on the achievements of our predecessors, through diligent study and repeated calculations, find π in between 3.1415926 and 3.1415927. And obtained an approximation of the form π score, taking 22 / 7 about the rate, take the 355/113 to close rate, which take six decimals is 3.141592 355/113, which is the numerator and denominator in the 16604 score of less than the value closest to π . Zu exactly the method used to reach this result, now unable to examine. If the idea of him to Liu Hui's "cut round operation" approach to seeking, then we would calculate to the 12288-gon inscribed circle, which takes much time and how much to pay a huge labor ah! This shows his tenacity on the scholarship and intelligent talent is admirable. Zu calculated density rate, foreign mathematicians get the same result, is a thousand years later things. To Jinian Zu Chong Zhi outstanding contribution to some foreign math historian suggested that π = called "ancestral rate." Zu Exhibition at the famous classic, seek truth from facts, he personally measured the calculation of large amounts of data in the comparative analysis found that the past calendar of serious errors, and be willing to improve on his 33 when the preparation of the success of the "Ming Li," opened up new era in the history of the calendar. Zu Zu with his son microscopy (also a famous mathematician) together with a clever solution to the sphere volume calculations. They were using a principle is: "both with power potential, the product can not be different." Means, located between two parallel two-dimensional plane, two plane by Ren Yiping line in the plane of the cut, if two constant cross-section area equal to the volume of two-dimensional equivalent. This principle, known as the Western Cavalieri principle, but it is a thousand years after the progenitor's only by the card's discovery. To Jinian Zu's son found a significant contribution to this principle, we call this the principle of "ancestral microscopy principle." Ancient China and its major contribution to the well-known mathematician ▲ Zhang Qiu Jian - <count by Zhang Jian Qiu> "Zhang Jian Qiu considered by the" three volumes, according to Qian Bao-cong test, about a book in AD 466 ~ 485 years, Zhang Jian Qiu, Northern Wei Dynasty Qing (now Linqing area) who's life is unknown. Least common multiple applications, the elements of arithmetic sequence and find each other, "one hundred chickens surgery" and is the main achievement. "Hundred chicken technique" is a world famous Diophantine equation problem. 13th century Italian Fibonacci "considered by" the 15th century Arab Al Casey <<math of the key "and other writings have appeared have the same problem. ▲ Zhu Shijie: "four yuan Yu Kam" Zhu Shijie (around 1300), the word Hanqing, No. Pine Court, resident Yanshan (now near Beijing), "famous travel around the lakes in mathematics more than twenty years," "heel and scholars gathered in the door." Zhu Shijie mathematical representative of the "arithmetic of Enlightenment" (1299) and "four yuan Yu Kam" (1303). "Arithmetic Enlightenment" is a popular mathematical classics, has spread overseas, affecting Korea, Japan, the development of mathematics. "Four yuan Yu Kam" is the peak of Chinese Song and Yuan Dynasties mathematical another sign, one of the most outstanding mathematical creation of "Quaternion" (multi-column style high-equation solution and elimination), 'stack plot Law "(high order Arithmetic sum) and "bad move technique" (high-order interpolation) ▲ Jia Xian: <<Yellow Emperor IX considered by Xicao>> Chinese classical mathematician reached a peak in the Song and Yuan Dynasties, the prelude to the development of "Jia Xian Triangle" (two expansion coefficients table) and the discovery of closely related high-open approach ("by by open method") creation. Jia Xian, Song of people, about 1050 or so to complete <<count by Emperor IX Xicao>> the original books get lost, but its main content is Yang Hui (about 13th century) writings of transcription, due to be handed down. Yang Hui <<Detailed IX algorithm>> (1261) contains "the origin of prescribing practices," map, marked "Jia Xian using this technique." This is the famous "Jia Xian triangle", or "Yang Hui's triangle." <<Detailed IX algorithm>> Jia also recorded the high power of prescribing the constitution of "increasing by open method." Jia Xian triangle in the Western literature called "Pascal Triangle", in 1654 the French mathematician Pascal B · rediscovered. ▲ Horner: <<Number of books nine chapters>> ▲ Li Ye: "round the sea mirror test" - Kaiyuan surgery With the numerical solution of high-technology development equation, the methods of the corresponding row equation, and this is the so-called "New Century surgery." Song mathematics in the writings handed down the first system described technique is Kaiyuan Li Ye's "round the sea mirror test." Li Ye (1192 ~ 1279) formerly known as Li Zhi, No. Jingzhai, Jin really be Luancheng, a former Jun state (Yu County, Henan Province today) governor, 1232-Jun state was broken by the Mongolian army, then retreat scholarship, was Kublai Khan appointed Imperial Academy, only one year, will resign to go home. 1248 Zhuancheng "round the sea mirror test", its main purpose is to explain the column technique with Kaiyuan equation method. "Kaiyuan surgery" modern algebra equation wears a similar column, "Li Tianyuan one for certain," the equivalent of "Let x be a certain" symbolic algebra can be said that the attempt. Li Ye have another math book "The benefits section of the ancient play" (1259), but also to explain the Kaiyuan surgery. ▲ Liu Hui: "count by the island," "Nine Chapters on Arithmetic Note," "Nine weight difference map" 263 years, Liu Hui found that when the inscribed regular polygon of infinitely variable increases, the area of the polygon approaches area of circle can be unlimited, so-called "fine cut of the indemnity, the indemnity loss less, but cut the cut, so that can not be cut, and the circumference is Fit and carry nothing to lose. "Liu Hui used to direct generation of music, unlimited closer," folder inside and outside the force, "the idea, the creation of a" cut round operation. " "Re-poor" was originally "Nine Chapters on Arithmetic Note" vol. X, later, "considered by the island", the content is a measure of the high and far target is calculated. Weight difference method is an important method of measurement in mathematics. ▲ Zu: (AD 429 AD 500 years ─) is China's outstanding mathematicians, scientists. Northern and Southern Dynasties people, Han Chinese, the word text far. He was put pi to the nearest 7 (3.1415926 <pi <3.1415927), than in the West ahead of 1500, and came to a close rate 355/113, 22 / 7 about the rate. Writing a book "augmented technique", recorded his method of calculating pi, but has been lost.
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Famous mathematical
* The number of ruled the universe. - Pythagoras * Mathematics, science Queen; number theory, mathematical Queen. - CoFo Gauss * God created the integers, all the rest of the numbers are artificial. - Lo Kelongneike * God is an arithmetic home - Jacobi • A poem without a bit of a mathematician can never become popular a complete mathematician. - Weierstrass Pure Mathematics, the science and then the modern stage of development of the human spirit can be said that the most original creation. - Whitehead • You can rule the whole number is an amount of the world, and the four arithmetic operations can be seen as a mathematician of all equipment. - Maxwell * Number theory is the oldest of human knowledge, a branch, but some of his deepest secrets and their most mundane truth is closely linked. - Smith * Unlimited! No other problems so deeply moved over the human mind. - Do Hilbert * That each new group is in the form of math, because we can not have other guidance. - CoGo Darwin * Of the universe to the great building is now a pure mathematician emerged. - JoHo Jing Si * This is a reliable rule, when a mathematical or philosophical works of the author when writing the words of profound ambiguity, he is talking nonsense. - AoNo Whitehead * Give me five factors, I will draw an elephant; give me six factors, the elephant will shake the tail. - AoLo Cauchy If the diagonal of a square who do not know the side is incommensurable with the amount of people that he does not deserve the title. - Plato * A simple integer form, several centuries been a source of new life to mathematics. - GoDo Birkhoff * Permanent and universal mathematical incomparable nature and cultural background of his time and independent line is a direct consequence of its nature. - Ao Ebo * Math prominent human development - Lin Yi Man
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Mathematics-related terms
* The number of mathematics • Basic * Negative * Positive * Integer * Score * Binary fraction * Unit fractions * Decimal * Limited fraction * Infinite decimal * Circulator * Rational * Irrational number * Quadratic irrational number * Composite number * Real * Imaginary * Gaussian integers * Eisenstein integers * Algebraic number * Algebraic integers * Number of rules * Transcendental number * Extension * Double complex * Hypercomplex * Quaternion * A total of quaternion * Complex quaternion * Octonion * Number of sixteen yuan · Tessarine * Number of super- * Large real number * A very real • For even * Nominal value * Serial Number * Transfinite numbers * Ordinal * Base * Prime number * Composite number · P into several * Number of rules * Calculate the number of * Sequence of integers * Mathematical constants * Large numbers * Pi π = 3.14159265358 ... · E = 2.718281828 ... * Imaginary unit i ^ 2 = - 1 (i squared) * Infinite ∞
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Encyclopedia
Mathematics mathematics Value terms) to determine the unknown function, constitute the calculus of variations (vanational False! Min Wu 1) of the topic, so that, in addition to the number of equations as unknowns Outside, there was another type of equation, some of which function is unknown , And pending. With the movement of graphics and the introduction of the concept of transformation geometry. Geometry The object of study also greatly expanded. Geometry began to study movement And transform itself, for example, in projective geometry learning (proJ. Shen i remember both g] nletry) , The plane or projective transformation of space is the basic object of study of a collection A However, the development of conscious thought is only in the 18th century Last century and early 19th centuries. A long time ago, with analytic geometry learning (an- alytjeg India nletry) established in the 17th century, its geometry with math He played a fundamental relationship between the branch changes then have to find a common Approach to geometric problems into algebra and analysis to learn the language and spirit Clever to use algebra and analysis methods to solve; the other hand, found The algebraic geometry and analysis methods used to express the fact that (icon) of the Wide range of possibilities, such as using graphics to represent a function. 4 Modern Mathematics in the 17th and 18th centuries the mathematical analysis of the Branch, in the 19th and 20th century are to continue to develop great strength. However, in addition to this quantitative growth and, in the 18th century and Development of mathematics in the early 19th century also there are some essentially new Characteristics. In the 17th and 18th century built up a large number of actual data, Making in-depth analysis and logical analysis to this point of view with the new phase Combined into the necessary back while the relationship between mathematics with natural sciences, although However, the extent of the substance does not close diminished, they are very complex In the form of a. Major new theory of production, not only because of the natural sciences The direct or technical needs, but also because of the inherent requirements of mathematics itself .19 In the mid-century, leaves and all the mathematical analysis of the complex occupies a central position Variable function theory (Ibnctio Long Bai of a con1Plex currency able, thcoryof), It is this developed largely as the internal development of the mathematical results If the rise of another wonderful example of the theory and a few hasty 6 Xiang Ming eBc What school (1 knife bache-ming g] n order to worship try). More directly and continuously rely on the needs of mechanics and physics Grow up, is the vector and tensor analysis of the concept of transfer vector and tensor To the infinite-dimensional volume, it is in functional analysis (Qin nalanal Ict fine old is) Occurred within the framework and the needs of modern physics is closely Contact. In this way, because the internal needs of mathematics, but also because of the natural sciences New needs, the study of mathematical and spatial relationship between the number of forms greatly Expansion up; introduced in mathematics in existence between the elements in any group , The vector between the function space operator relationship between the Various kinds of forms of arbitrary dimensions of space, and so on. In the 19th century this stage of the development of mathematics, its essence, new Differences are is to study the relationship between the number of forms to expand the scope and space The problem itself has become mathematicians consciously and actively interested in Objects. If in the past, for example. The introduction of negative numbers and complex numbers Accurate algorithm to form long-term effort, it is now mathematical Development requires a number of ways to develop a conscious, planned to build The new geometry and algebra systems.
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English Expression
n.: math, mathematics, maths, science of numbers, quantity and space, of which eg arithmetic, algebra, trigonometry and geometry are branches, point at which a curve crosses itself （
elementary mathematics