Mathematics is a subject that studies the concepts of quantity, structure, change, space and information. The following is a complete collection of contents and materials about first-year mathematics handwritten newspaper compiled by me. Welcome to read.
branch of mathematics
1. History of mathematics
2. Mathematical logic and mathematical foundation? A, deductive logic (also known as symbolic logic) B, proof theory (also known as meta-mathematics) C, recursion theory D, model theory E, axiomatic set theory F, mathematical foundation G, mathematical logic and other disciplines of mathematical foundation
3, number theory
a, elementary number theory B, analytic number theory C, algebraic number theory D, transcendental number theory E, lost. Other disciplines of number theory
4. Algebra
a, linear algebra B, group theory C, field theory D, Lie group E, Lie algebra F, Kac—Moody algebra G, ring theory (including commutative rings and commutative algebras, associative rings and associative algebras, Non-associative rings and non-associative algebras, etc.) H, module theory I, lattice theory J, universal algebra theory K, category theory L, homology algebra M, algebra K theory N, differential algebra O, algebraic coding theory P, algebra other disciplines
5, algebraic geometry
6, geometry
a, geometric foundation B, Euclidean geometry C, non-Euclidean geometry. Vector and tensor analysis F, affine geometry G, projective geometry H, differential geometry I, fractal geometry J, computational geometry K, other disciplines of geometry
7, topology
a, point set topology B, algebraic topology C, homotopy theory D, low-dimensional topology E, homology theory F, dimension theory G, lattice topology H, fiber bundle theory I. Differential topology l, other disciplines of topology
8, mathematical analysis
a, differential calculus b, integral calculus c, series theory d, other disciplines of mathematical analysis
9, nonstandard analysis
1, function theory
a, real variable function theory b, simple complex variable function theory c, multiple complex variable function theory d, function. Other disciplines of function theory
11, ordinary differential equation
a, qualitative theory b, stability theory c, analytical theory d, ordinary differential equation other disciplines
12, partial differential equation
a, elliptic partial differential equation b, hyperbolic partial differential equations c, parabolic partial differential equation d, nonlinear partial differential equation e, partial differential equation other disciplines
13. Differential dynamic system B, topological dynamic system C, complex dynamic system D, other disciplines of dynamic system
14, integral equation
15, functional analysis
a, linear operator theory B, variational method C, topological linear space D, Hilbert space E, function space F, Banach space G, operator algebra H, measure and integral I, generalized function theory J, nonlinearity. Other disciplines of functional analysis
16, computational mathematics
a, interpolation and approximation theory b, numerical solution c of ordinary differential equations, numerical solution d of partial differential equations, numerical solution e of integral equations, numerical algebra f, discretization method g of continuous problems, random numerical experiment h, error analysis I, other disciplines of computational mathematics
17, probability theory
a, geometric probability b. Limit theory D, stochastic process (including normal process and stationary process, point process, etc.) E, Markov process F, stochastic analysis G, martingale theory H, applied probability theory (specifically applied to related disciplines) I, other disciplines of probability theory
18, mathematical statistics
a, sampling theory (including sampling distribution, sampling survey, etc.) B, hypothesis test C, hypothesis test C. Correlation regression analysis F, statistical inference G, Bayesian statistics (including parameter estimation, etc.) H, experimental design I, multivariate analysis J, statistical decision theory K, time series analysis L, other disciplines of mathematical statistics
19, applied statistical mathematics
a, statistical quality control B, reliability mathematics C, insurance mathematics D, statistical simulation
2, other disciplines of applied statistical mathematics. Operations research
a, linear programming b, nonlinear programming c, dynamic programming d, combinatorial optimization e, parametric programming f, integer programming g, stochastic programming h, queuing theory I, game theory also known as game theory j, inventory theory k, decision theory l, search theory m, graph theory n, overall planning theory o, optimization p, other disciplines of operations research
22, combinatorial mathematics. Fuzzy mathematics
24, quantum mathematics
25, applied mathematics (specifically applied to related disciplines)
26, development history of other disciplines of mathematics
Mathematics (Hanyu Pinyin, shù xué；; Greek, μ α θ η μ α τ κ; English, Mathematics), derived from the ancient Greek word μθημα(máthēma), has the meaning of learning, learning and science. Ancient Greek scholars regarded it as the starting point of philosophy and the "foundation of learning". In addition, there is a narrow and technical meaning-"mathematical research". Even in its etymology, its adjective meaning related to learning will be used to refer to mathematics.
its plural form in English and its plural form in French +es as mathématiques can be traced back to the Latin neutral plural (Mathematica), which was translated by Cicero from the Greek plural τ α α θ ι α ι κ (tamath ē matiká).
In ancient China, mathematics was called arithmetic, also known as arithmetic, and it was finally changed to mathematics. Arithmetic in ancient China was one of the six arts (called "number" in the six arts).
Mathematics originated from the early production activities of human beings, and the ancient Babylonians had accumulated certain mathematical knowledge from ancient times and could apply practical problems. From the mathematics itself, their mathematical knowledge is only obtained by observation and experience, and there is no comprehensive conclusion and proof, but they should also fully affirm their contribution to mathematics.
The knowledge and application of basic mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be seen in ancient mathematical texts in ancient Egypt, Mesopotamia and ancient India. Since then, its development has continued to make small progress. But algebra and geometry at that time were still in an independent state for a long time.
Algebra can be said to be the most widely accepted "mathematics". It can be said that since everyone began to learn to count when he was a child, the first mathematics he came into contact with was algebra. Mathematics is a subject that studies numbers, and algebra is also one of the most important parts of mathematics. Geometry is the earliest branch of mathematics studied by people.
Until the Renaissance in the 16th century, Descartes founded analytic geometry, which linked algebra and geometry which were completely separated at that time. From then on, we can finally prove the theorem of geometry by calculation; At the same time, abstract algebraic equations can also be vividly represented by graphics. And then more subtle calculus was developed.
At present, mathematics has included many branches. The Bourbaki School in France, founded in 193s, believes that mathematics, at least pure mathematics, is a theory to study abstract structures. Structure is a deductive system based on initial concepts and axioms. They believe that mathematics has three basic parent structures: algebraic structure (group, ring, field, lattice …), ordered structure (partial order, total order …) and topological structure (neighborhood, limit, connectivity, dimension …).
Mathematics is applied in many different fields, including science, engineering, medicine and economics. The application of mathematics in these fields is generally called applied mathematics, and sometimes it will arouse new mathematical discoveries and promote the development of new mathematics disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without aiming at any practical application. Although a lot of work begins with the study of pure mathematics, it may find suitable applications later.
specifically, there are sub-fields used to explore the connection between the core of mathematics and other fields, from logic and set theory (mathematical basis) to empirical mathematics in different sciences (applied mathematics), and more modern research on uncertainty (chaotic and fuzzy mathematics).
as far as the vertical degree is concerned, the exploration in the respective fields of mathematics is getting deeper and deeper.
the number in the figure is the national two disciplines number.
How to improve mathematics learning ability
1. Improve visual perception function.
Mathematics is a "quantity and spatial form" for studying the objective world. It should have a strong visual perception function, and distinguish "number and shape" from the length, size and dotted line of the complicated objective world. The basic strategy is to try more visual sports based on sports.
2. Improve the understanding of mathematical language.
Mathematics is a language system of "literature and the structure of numbers and symbols". First of all, we should improve the reading ability of words, and then cultivate the understanding of "numbers and symbols". If there are problems in understanding, we should remedy them accordingly.
3. Improve the generalization ability of mathematical materials.
firstly, cultivate the ability of abstract generalization of mathematical materials, secondly, cultivate the ability of generalization and reasoning of mathematics, and finally cultivate the ability of generalization and reasoning of graphics.
4. Improve the computing power.
mathematical famous sayings
1. Mathematics is a variety of proof skills. Wittgenstein
2. Infinite! No other problem has touched the human mind so deeply. D Hilbert
3. Reading history makes people wise, reading poetry makes people witty, mathematics makes people rigorous, physicists make people profound, ethics makes people grave, logic and rhetoric make people able to distinguish; Every scholar becomes a character. Bacon
4. Law contains the story of how many centuries a nation has experienced, so it can't be studied just as a theorem formula in a math textbook. In order to know what law is, we must understand its past and future trend. Holmes
5. The main goal of mathematics is the public interest and the explanation of natural phenomena. Fourier
6. Mathematics points out that the maximum value of a function is often taken at the most unstable point, and people will lose their inner balance if they pursue extremes.
7. When mathematicians derive equations and formulas, they are as happy as seeing statues, beautiful scenery and listening to beautiful tunes. Copnin
9. New mathematical methods and concepts are often more important than solving mathematical problems themselves. Hua Luogeng
1. History makes people wise, poetry makes people elegant, mathematics makes people noble, natural philosophy makes people deep, morality makes people steady, and ethics and rhetoric make people good at arguing. Bacon
11. Mathematics is the queen of science, while number theory is the queen of mathematics. Gauss
12. The essence of mathematics lies in its freedom. Cornel
13. What delights me most in mathematics is what can be proved. Russell
14, reading makes a full person; Talks make people agile; Writing and taking notes make people precise. Historical lessons make people wise; Poetry makes people clever; Mathematics makes people fine; Natural history makes people deep; Ethics makes people solemn; Logic and rhetoric make people eloquent.
15. Asking a question is often more important than solving a problem, because solving a problem may only be a mathematical or experimental skill. Asking new questions and new possibilities, looking at old problems from a new perspective, requires creative imagination and marks the real progress of science.
16. Some beautiful theorems in mathematics have such characteristics: they can be easily summarized from facts, but the proofs are extremely hidden. Gauss
17. It sounds funny that people who study Chinese go abroad for further study. In fact, only those who study China literature have to study abroad. Because all other subjects, such as mathematics, physics, philosophy, psychology, economy, law, etc., have been instilled from abroad, and have long been foreign; Only when the Chinese language is a local product and needs foreign signs can it maintain its position, just as the money exploited by China officials and businessmen in their own country needs to be exchanged for foreign exchange to maintain the original value of the national currency. Qian Zhongshu
18. One reason why mathematics is respected more than all other sciences is that his proposition is absolutely reliable and indisputable, and other sciences are often in danger of being overthrown by newly discovered facts. Einstein
19. Reading makes a full person, conversation makes a quick person, writing and taking notes make a precise historical lesson and make a wise person; Poetry makes people clever; Mathematics makes people fine; Natural history makes people deep; The study of ethics makes people solemn; Logic and rhetoric make people eloquent. Bacon
2. It is not good to study literature books. Previous literary youth often hated mathematics, physics and chemistry, history and geography, and biology, thinking that these were insignificant, but later they became even common sense. Lu Xun
21. In mathematics, the main tools for us to find truth are induction and simulation. Laplace
22. The incomparable permanence and omnipotence of mathematics and his independent action on time and cultural background are the direct consequences of its essence. Eber
23. This is a reliable law. When the author of a mathematical or philosophical work writes in vague and abstruse words, he is talking nonsense. Whitehead
24, the first is mathematics, the second is mathematics, and the third is mathematics. Roentgen
26 or 2 years old is a confusing age. Shi Yuzhu, who is in his twenties, is studying mathematics at Zhejiang University, Ma Yun, who is in his twenties, is hitting the wall everywhere, and Wang Shi, who is in his twenties, is a car soldier in the Gobi Desert. There has never been a job called more money, less work and being close to home. In the three most powerful 1 years of life, we need to rely on ourselves in a down-to-earth manner.
27. Mathematics makes an important contribution to the observation of nature. It explains the simple primitive elements in the regular structure, and the celestial bodies are built with these primitive elements. Kepler
28. Mathematicians are fascinated by nature. Without fascination, there is no mathematics. Nouvelles
29. The essence of mathematics lies in its freedom. Cantor
31. Love is really subtle. It is not that mathematics cannot be added or subtracted, nor that physics cannot be calculated. It is really puzzling. Some love comes from imagination, and the result may not be what you think. Some love comes from longing. The more you want it, the less you can get it. Like possessed. So the commander (person) must stay awake.
32. What gives me the greatest happiness is not knowing knowledge, but learning constantly. Not what you already have, but what you constantly acquire; Not the height that has been reached, but the continuous climbing. Gaussian
33, direct direction