Perceptual, sensory, emotional and impulsive thinking is gradually replaced by rational thinking.
In the process of everyone's growth, understanding and exploring the spiritual world is a real wisdom competition, sharpening and enterprising.
People's spiritual development, people's unique ability, survival ability, the core key to creation and invention, spread wisdom through writing books.
Hegelian dialectics, metaphysical criticism, the highest methodology of philosophy.
In the scientific stage, people's way of thinking is based on mathematics and physics.
Theological system → philosophical system → mathematical system → physical system.
With a scientific and systematic way of thinking, the systematization of scientific knowledge led by mathematics, physics, chemistry, astronomy and medicine has become the key direction and driving force for the development of civilization for centuries.
Now mathematics has become a huge empire with more than 100 main branches in science.
Mathematics is a kind of knowledge education, which is essentially a kind of quality education.
Education is an important matter related to a person's growth.
The foundation of science building lies in education. Take mathematics as an example. The foundation of mathematical architecture lies in primary school mathematics. Has this foundation been laid?
I need a comprehensive, systematic and conceptual noun to write a math topic.
Mathematics learning is systematic, connected and phased. Different stages will have different emphases, and the understanding of these abilities will also affect the next stage of learning.
Mathematics in primary school and enlightenment stage is a critical period for cultivating, learning mathematics and interest.
There are many factors that lead to high school mathematics difficulties, such as the neglect of mathematical ability and thinking habits, and training.
For example: oral calculation, quick calculation, mental calculation. It is very important to learn this well.
Number summarizes two aspects of everything in the world, the quantitative relationship in the real world and the scientific big data in spatial form.
The formation, internalization and skillful application of concepts need a process.
The cultivation of ability and thinking also needs a process.
A magnificent epic of mathematics and physics, composed of heroes Newton, Gauss, Riemann, Maxwell, Einstein, Ramanukin, Hawking …
It is no exaggeration to say that mathematics and physics are created by intelligent minds.
From the control of nature to the gradual improvement of mankind, scientific literacy, mastery of energy and energy shortage restrict the further development of mankind.
What is the energy that the future world of mankind depends on?
The development of mathematics and physics will tell you.
The development of mathematics and physics tells you that the development of science is the mainstream trend of human development.
Physics is a natural science that studies the material world, the most basic structure, the most common interaction, the most general law of motion, the experimental means and thinking methods used.
There are three main points in primary school mathematics: the cultivation of mathematical interest, the cultivation of mathematical thinking, the improvement of calculation ability and good mathematical study habits.
Arithmetic, elementary algebra, advanced algebra, number theory, abstract algebra.
Keywords elementary geometry, projective geometry, analytic geometry,
Keywords non-Euclidean geometry, topology,
Keywords calculus, differential equation, differential geometry, function theory, functional analysis,
Why should we review the history of mathematics and historical figures repeatedly?
The history of the past is the reality of today.
First of all, we have a basic understanding of the great mathematicians in the history of mathematics.
Diophantine is a representative figure of Greek mathematics around 250 AD.
The book Arithmetic is mainly an equation and a master of solving equations. It is called the originator of algebra.
Of the original 13 books, only six survived.
His tombstone says
1/6 of his life was a happy childhood.
112 of life is adolescence.
It was his life before he got married 1/7.
After five years of marriage, he had a child who died when he was only half the age of his father.
After the death of his child, he lost Pantu and was heartbroken.
He lived another four years, ending his earthly career.
Passerby, do you know how old Pantu is?
This tombstone is engraved with his life history of pursuing mathematics all his life.
Born in Milai, the capital of Ionia, from about 624 BC to 546 BC, he was an ancient Greek thinker, scientist and philosopher.
Known as the father of science and philosophy.
He used the shadow of the sun to measure the height of the pyramid and accurately predicted the solar eclipse in 585 BC.
Many theorems of plane geometry were discovered.
1) The diameter bisects the circumference.
2) Equiangles of two equilateral sides of a triangle
3) Two straight lines intersect and the vertex angles are equal.
4) The two corners of the triangle and its clamping edges are known, and the triangle is completely determined.
5) The circumferential angle of a semicircle is a right angle.
6) The inscribed triangle on the circle diameter must be a right triangle.
Around 820 AD, Arab mathematician Hua Razimi wrote a book Algebra after returning from India.
The book clearly puts forward the general solution of quadratic equation for the first time, and puts forward the methods of shifting term, merging term and similar term.
Hua Lazimi's Algebra is called the originator of mathematics textbooks.
Eratosthenes, a pioneer in searching for prime numbers.
The four mathematicians Archimedes, Newton and Euler are all math teachers.
Riemann is a mathematical genius. In high school, he completely read the 859-page masterpiece Number Theory in only six days.
Prince of Gauss Mathematics (born from 1777 to 1855) is a famous German mathematician, physicist, astronomer and geodesist.
Gauss, Newton, Archimedes and Euler are considered as the four greatest mathematicians in history.
If you are 9 years old, you will get1+2+3+4 …+100 = 5050.
/kloc-binomial theorem for independent discovery at the age of 0/2.
8 1297+8 1495+8 1693+…+ 100899
This is a question of peace in arithmetic progression.
Gauss's life, a typical literati life, has always maintained the simplicity of the farmhouse, which is unimaginable. He is the greatest professor and mathematician in the world.
Imagine mathematicians in the18th century as a series of high mountains, and the last awe-inspiring peak is Gauss. If we think of mathematicians in the19th century as rivers, then its source is Gauss.
His thoughts went deep into the mysteries of mathematics, space and nature, and measured the trajectory of stars, the shape of the earth and natural forces.
Euclid's Elements of Geometry, the Father of Geometry.
Descartes, the founder of analytic geometry.
Galileo once said: The book Nature is written in the language of mathematics. You learn its language first, and the scientific language of mathematics is very accurate.
This language is also universal, including addition, subtraction, multiplication, division, power, root, exponent, logarithm, emblem, integral and constant.
Without the support of mathematics, it is difficult to make great progress. Mathematicization and high technology of natural science are one kind of mathematical technology.
Mathematical thinking or: What is mathematical thinking?
Classification, modeling, combination of numbers and shapes, induction and analogy ... Aren't these mathematical thoughts the processes of logical thinking, classified thinking, abstract thinking and inductive thinking?
Classified thinking is an important kind of thinking. In the ever-changing world, many changing conditions and factors need to be classified to clarify the thinking.
Abstract thinking, from line segment abstraction to quantitative relationship, seeks the relationship through the combination of quantity represented by line segment diagram and graph.
Inductive thinking is a very important way of thinking in mathematics, and many of them appear in the form of conjecture. After induction, hypothesis conclusion, and then proof, the mathematical theorem is obtained.
Primary school mathematics is the best time to lay a good foundation and improve the ability of calculation and mental arithmetic.
Whether primary school mathematics can be learned well is particularly critical. Do you love math or not?
Through mathematical training, the key to solving calculation problems quickly and accurately lies in the active thinking ability, the improvement of practical ability, the ability to find key points and difficulties, and the ability to practice solving problems efficiently.
1) natural number, and the number used to represent the number of objects is called natural number.
0 is also a natural number, 1.2.3.4.5.6, etc.
Counting unit, ten 10000 is called 100000, ten 100000 is called 100000, and so on.
Even number, even number divisible by 2.
2,4,6,8, 10, 14, 16, 18,20,22,24,26,28,33, 12,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,99, 12,94,96,98, 100。
Odd numbers, numbers that are not divisible by 2 are called odd numbers.
1,3,5,7,9, 1 1, 13, 15, 17, 19,2 1,23,25,27,29,3 1,33,35,37,39,4 1,43,45,47,49, 5 1,53,55,57, 59,6 1,63,65,67,69,7 1,73,75,77,79,8 1,83,85,87,89,9 1,93,95,97,99。
A prime number is called a prime number if it only has 1 and its two divisors.
What is a prime number?
Among all integers greater than 1, there is no divisor except 1 and itself. This number is called prime number, and there are infinitely many.
Prime numbers are also called prime numbers.
For example, prime numbers greater than 100,10, 40 1, 60 1, 70 1.
* * */kloc-25 pieces within 0/00,
100 to 1000*** 143
10 1, 103, 107, 109, 1 13, 127, 13 1,65438.
Prime numbers are also called prime numbers. Integers greater than 1 in natural numbers cannot be divisible by other natural numbers except 1 and the integer itself.
In other words, a natural number with only two positive factors (1 and itself) is a prime number.
Numbers greater than 1 but not prime numbers are called composite numbers.
The distribution law of prime numbers is 36N(N 10 1). With the increase of the number of prime numbers, the number of prime numbers gradually increases in the form of waves, and the twin prime numbers also have the same distribution law.
A number is called a composite number if it has other divisors besides 1 and itself.
composite number
4,6,8, 10, 12, 14, 16,18,20,2122,24,25,26.
2) Fraction, that is, dividing the unit 1 into several parts on average, indicating the number fraction of such one or several parts.
A fraction is the ratio of an integer a to a positive integer b that is not equal to an integer.
When expressing fractions, a fraction of one number is a fraction of another number.
1/2, 1/3, 1/4, 5/8, 3/4… and so on.
Addition and subtraction rules of fractions
Add and subtract fractions with the same denominator, only add and subtract numerators, and the denominator remains the same.
Fractions with different denominators should be added and subtracted first, and then added and subtracted.
proper fraction
Fractions with numerator less than denominator are called true fractions.
improper fraction
Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions.
Error score is greater than or equal to 1.
mixed number
Writing a false score as an integer and a true score is called taking a score.
3. Decimals, take a few tenths, a few percent, and a few thousandths, whichever is smaller.
The decimal unit is110 (0,1) ...
The percentile unit is1%(0,01) …
The thousandth unit is1‰ (0,001) …
Converting decimals into percentages usually means converting fractions into decimals first, and then converting decimals into percentages.
Learn to divide fractions into fractions and fractions into decimals.
Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
Endless decimal
The number of digits in the decimal part is a finite decimal, which is called a finite decimal.
Endless decimal
The number of decimal places, infinite decimal, is called infinite decimal.
repeating decimal
A decimal, starting from somewhere in the decimal part, and one or several numbers are repeated in turn. Such decimals are called cyclic decimals.
For example, 3. 14 14
Pure cyclic decimal system
Mixed cyclic decimal
Learn to recite the formula of 99 multiplication and learn the basic addition, subtraction, multiplication and division.
Additive commutative law
Two numbers are added to exchange the positions of addends, and their sum remains the same.
a+b=b+a
associative law of addition
Add three numbers, first add the first two numbers and then add the third number.
Or add the last two numbers first, and then add the first number, and their sum remains the same.
(a+b)+c=a+(b+c)
Improve the multiplication table and learn to mix basic geometric figures.
Commutative law of multiplication
Multiply two numbers, exchange the positions of factors, and their products remain unchanged.
axb=bxa
Multiplicative associative law
Multiply three numbers, first multiply the first two numbers, and then multiply the third number.
Multiply the last two numbers first, and then multiply the first number. Their products have not changed.
(axb)xc=ax(bxc)
Powder companion
When the sum of two numbers is multiplied by a number, you can multiply the two addends by this number respectively, and then add the products of the two numbers.
(a+b)xc=axc+bxc
Fractions are decimal.
least common multiple
greatest common divisor
If the number A is divisible by the number B, then A is called a multiple of B and B is called a divisor of C..
Multiplication refers to the quotient of dividing two numbers, which can be an integer, a decimal or a fraction.
Multiplication is only within the divisible range of a number. Compared with divisor, the concept of number represents a number that can be divisible by natural numbers.
The multiple of 4 is 4,8, 12, 16. ...
The multiple of 6 is 6, 12,18,24. ...
The common multiple of several natural numbers is called the common multiple of this number.
Refers to two or more integers, and * * * has the greatest divisor, also called the greatest common factor.
There are many ways to find the greatest common divisor, and the common ones are prime factor decomposition, short division, phase division and phase subtraction.
Four methods for finding the greatest common divisor.
1, exhaustive method, 2, divide by division,
3, subtraction over and over again, 4, recursion
To find the greatest common divisor of 24 and 60, first decompose the prime factor.
24=2x2x2x3
60=2x2x3x5
All common factor of 24 and 60 are 2, 2, 3,
Their product is 2x2x3= 12.
So (24,60) =12.
How to calculate the greatest common denominator?
The positive divisor of 12: 1, 2,3,4,6, 12.
The positive divisor of 18: 1, 2,3,6,9, 18.
So (12, 18)=6.
17th century French mathematicians Marin and Mei Sen, founders of French Academy of Sciences,
The first pheromone is 2 minus 1 equal to the square of 3.
The second Mason number is two minus one equals the cube of seven.
Two minus one to the fifth power is equal to 3 1.
The 40th mersenne prime was discovered in 2003, the second one was 209960 1 1, and the second one was 1.
In 2003, the 4th1mersenne prime, and the 24036583rd square of 2.
The American Electronic New Field Foundation announced to the world that any individual or organization that finds Mr. Mei Sheng Zhou with a figure of more than 6.5438+million will receive a prize of $6.5438+million from the Foundation.
The 46th mersenne prime in 2008 was 4,365,438+065,438+02609 Times Square 1, 1.
The study of it promotes the study of number theory called the queen of mathematics.
Fermat number
Fermat, father of modern number theory, king of amateur mathematicians.
Fermat number is a set of natural numbers named after the mathematician Fermat.
All prime numbers of 2n ten 1 must be fermat number.
Fermat number revealed the relationship between decimal and binary.
3,5,17,257,65537, and later fermat number, proved to be a composite number. Why?
All fermat number are obviously odd numbers.
Fermat's conjecture, why was it later proved wrong?
Because it involves a deeper topic of number theory, this paper will not discuss and analyze it.
Geometry, plane graphics and three-dimensional graphics.
The intersection of points, lines and lines is the point, which is the most basic graph of set graph.
The intersection of lines, faces and faces is a straight line, which can be divided into straight lines and curves.
The face surrounding the body is divided into plane and curved surface.
Shape, geometry, also known as shape, moves from point to point into a line, and the line moves into a plane moving body.
algebra
Classification of rational numbers,
Rational numbers are divided into positive rational numbers and negative rational numbers by sign.
Integers and fractions are generally called rational numbers.
Two numbers with opposite values, one number is opposite to the other.
For example, -2 and +2 are reciprocal.
The antonym of positive number is negative number, and the antonym of negative number is positive number. Irrational numbers also have antonyms.
Mathematically, the number axis can be represented by points on a straight line, which is called the number axis.
Two mutually perpendicular number axes of the same origin can form a plane rectangular coordinate system.
Three mutually perpendicular masses with the same origin can form a spatial rectangular coordinate system to determine the position of an object.
Countdown,
Absolute value,
function
constant
changeable
coefficient
known number
Unknown number
equation
monomial
multinomial
Analytic geometry
origin
axis
Circular axis curve
parabola
hyperbola
Asymptote
tangent
normality
circular
spiral line
spiral
(being perfected)