1 Learn mathematics as a language, learn the usage of each term, and become familiar with the meaning of each symbol

2 Read "Mathematics Forms Thoughts" instead of "Mathematics Becomes Thoughts" Death Sign".

3 Look at "Language in Mathematics" and "Patterns in Mathematics (Question Types)".

4 Don’t miss any seemingly simple examples - they are often not that simple, or they can lead to a lot of knowledge points

5 Be able to use mathematical formulas and not Show that you can do math.

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If you are not a genius, don’t think about playing games if you want to learn mathematics - you think you have done it, but in fact your mathematics level has not changed with your ability to pass the level. High - In fact, you can always remember: learning mathematics makes you better at playing the big game of "life"!

7 Impetuous people tend to say: Learning mathematics is useless, you should learn something useful; - it’s you who are useless! ?

8 Impetuous people tend to ask: How should I learn? - Don’t ask, just learn.

9 Impetuous people tend to ask: Is it better to write down the teacher’s notes in class or follow the teacher’s thinking without taking notes? - Let me tell you, it's all fine - as long as you learn.

10 There are two types of impetuous people: a) those who just watch without learning; b) those who only learn without persisting.

11 Please don’t be an impetuous person.

12 It is better to keep the conventional problem-solving methods in mind than to talk about novel problem-solving methods.

13 Mathematics is more than just problem solving.

14 One of the best ways to learn to solve problems is to study examples.

15. Never think that you have solved enough problems at any time.

16 Please read the "Mathematics Textbook" to master the standard terms of mathematics.

17 If you understand the examples, please read them carefully; if you do not understand the examples, please read them hard.

18 Don’t expect to remember and grasp anything after reading the book for the first time – please read it a second or third time.

19 Don’t stay at the cradle of basic question types. Learn to treat basic question types as comprehensive questions “assembled” from parts.

20 Don’t assume that just because some words in mathematics look the same as words in natural language, they mean exactly the same.

21 The secret to learning mathematics is: solve problems, solve problems, and solve problems again.

22 Remember: the concepts and objects in mathematics are not exclusive to mathematics. Don’t forget to “use mathematics” in other subjects.

23 Please do the examples in the book yourself.

24 Please find some exercises and use the problem-solving methods you learned in the book!

25 Please pay attention to the detailed errors in problem solving and remind yourself before the exam.

26. Frequently review the problems you have solved before, try new solutions, and apply the new knowledge you have learned.

27 Don’t miss any exercises in the book - please complete them all and record your solution ideas.

28 When you are halfway through a problem-solving idea but find that your method is clumsy, please don’t throw it away immediately. At least come back and try again after solving the problem with a new and better method. Analyze the previous ideas.

29 Don’t stop following some problem-solving rules that you are not proficient in just because the question is “small” – good habits are developed, not memorized once.

30 Whenever you learn a difficult mathematical point, try to explain this knowledge point to others and let them understand it - only if you can explain it clearly will you truly understand it.

31 Save all the exercises you have solved - that is one of your best accumulations.

32 Please love mathematics!

33 Mathematical knowledge is the purest logical thinking activity and the most advanced aesthetic expression of intellectual vitality. ——Prinsham

34 History makes people smart, poetry makes people witty, and mathematics makes people sophisticated.

——Bacon

35 Mathematics is one of the most precious research spirits. ——Hua Luogeng

36 No subject can illustrate the harmony of nature more clearly than mathematics. —— Carlos

37 Mathematics is the referee and master of laws and theories. ——Benjamin

38 Music can inspire or soothe feelings, paintings can make people happy, poetry can move people's hearts, philosophy can make people gain wisdom, science can improve material life, but mathematics can give all the above. ————Klein. 3

39 The essence of mathematics lies in its freedom. ——Cantor

40 In the field of mathematics, the question is asked Art is more important than the art of answering questions. ——Cantor

41 No question can touch people's emotions as deeply as infinity.

Very few There are other ideas that stimulate the intellect to fruitful thoughts like infinity, but there is no other concept that requires so much elucidation as infinity. - Hilbert

42 Mathematics is Infinite science. ——Weil

43 Questions are the heart of mathematics. ——P.R. Halmos 44 As long as a branch of science can raise a large number of questions, it is full of vitality,

while the lack of problems heralds the termination or decline of independent development. - Hilbert

45 Some beautiful theorems in mathematics have such characteristics : They are easily summarized from facts, but the proof is extremely hidden.——Gauss

46 Mathematics is the queen of science, and number theory is the queen of mathematics——Gauss

47 Mathematical metaphors:

The ancient Greek philosopher Zeno is known as the "Father of Paradoxes". He has four mathematical paradoxes that have been passed down to this day. He once said a famous saying: "The big circle has a little more knowledge than the small circle, but because the circumference of the big circle is longer than the small circle, its contact surface with the outside world is larger than that of the small circle, so it feels more Lack of knowledge requires hard work to learn."

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There is a famous adage that mathematics is much bigger than science because it is the language of science. Mathematics is not only used to write about science, but also can be used to describe life. The following introduces the life mottos of several famous people at home and abroad, both ancient and modern. They are all expressed in very simple "mathematics" (numbers, symbols, mathematical concepts, formulas, etc.), and are profound and wonderful.

49 Wang Juzhen’s percentage: Chinese scientist Wang Juzhen has a motto when it comes to experimental failures: “If you keep doing it, there is a 50% chance of success, but if you don’t do it, it will be a 100% failure.”

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Tolstoy’s score: When the great Russian writer Tolstoy talked about his evaluation of people, he compared people to a score. He said: "A person is like a fraction. His actual talent is like the numerator, and his valuation of himself is like the denominator. The larger the denominator, the smaller the value of the fraction."

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Rybakov's constants and variables: Russian historian Rybakov said this about the use of time: "Time is a constant, but for those who are diligent, it is a 'variable'. Use' People who measure time in minutes have 59 times more time than people who measure time in hours. ”

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Hua Luogeng’s minus sign: The famous Chinese mathematician Hua Luogeng is here. When talking about learning and exploration, he pointed out: "We must dare to make subtractions in learning, which means subtracting the parts that have been solved by predecessors to see what problems are still unresolved and need us to explore and solve them."

53 Edison’s plus sign: The great inventor Edison used a plus sign to describe genius when he talked about genius. He said: “Genius = 1% inspiration + 99% blood and sweat.

”

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Dimitrov’s plus and minus sign: When evaluating a day’s work, the famous international workers’ movement activist Dimitrov said: “Use your time , think about what you did during the day, whether it is a 'plus' or a 'minus'. If it is '+', it means progress; if it is '1', you have to learn lessons and take measures. ”

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Einstein’s formula: When Einstein, the greatest scientist in modern times, was talking about the secret of success, he wrote down a formula: A=x+y+Z. And explained: “A stands for success, x stands for hard work, v stands for the right method, and Z stands for less empty words. "

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Zeno's Circle: The ancient Greek philosopher Zeno said this about learning knowledge: "If you use a small circle to represent the knowledge you have learned, use a large circle to represent it. The knowledge I learned is that the area of ??a large circle is a little larger, but the blank space outside the two circles is our ignorance. The larger the circle, the more ignorant surfaces its circumference touches. ”

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Learning language is not only used to express and study science, but also to express people’s thoughts, personality and pursuits exquisitely, and it is so concise and comprehensive. As mentioned above Some mottos reflect their great personalities on the one hand, and the beauty of mathematics on the other. Let us like mathematics, learn mathematics well, and use mathematics well; let us also use those mottos written in mathematics to describe our own life trajectory, our life. The value and contribution to humanity will be unlimited.