〈Introduction〉 Deductive reasoning is the only way to excel at mathematics.

Part 0.
Elementary Mathematics: The Encounter of Concepts and Letters
Use of characters
The only way to count: counting
The only way to add: multiplication (×)
Subtracting the same number: division sign (÷)
Division by zero
Parentheses and inequalities
Definition of fraction
The great properties of fractions
Percentages and pennies
Proportional
Proportional distribution
Fraction
Gabi's teeth
partial fractions

Part 1.
Numbers and Expressions: How to Read Numbers and Expressions
Positive and negative numbers
port
Commutative and associative laws
absolute value
exponent
Upgrade of mixed calculation order
Expression using letters
coefficient
Degree and exponent
Place value and digit number
Even and odd numbers
Drainage determination method
The characteristic of being divisible by an integer
Law of exponents
When there is 0 in the exponent
factorization
Using parentheses
The development of the food
Factorization
How to factorize
square root
The size of the square root
recurring decimals
Rational and irrational numbers
Rationalization of the denominator

Part 2.
Equations: Expressions that require mastery
equation
Properties of equations
Solving equations using the properties of equations and binomials
Impotence and denial
Indefinite equation
solution (root) of the equation
Denominator removal
simultaneous equations
Simultaneous equations and proportions
Solutions and graphs of simultaneous equations
Quadratic equation
Quadratic equations solved using factorization
Quadratic equations solved using square roots
Quadratic equation root formula
Relationship between roots and coefficients
Junggeun
Discriminant

Part 3.
Inequality: an expression expressing the range or domain of numbers
Properties of inequalities
Reading inequalities
Solution to first-order inequality
Simultaneous inequalities
Application of inequalities
Four basic arithmetic operations for inequalities
Inequalities with absolute value signs
Inequalities and maximum and minimum values
Quadratic and higher-order inequalities
Quadratic inequalities and functions
Various inequalities

Part 4.
Functions: The Final Destination of Mathematics
Definition of a function
react
Correspondence that becomes a function
Coordinate plane
Proportionality emphasizes proportionality
Inverse proportion
Graph of y=ax
inclination
linear function
Creating a linear function relation with two points
A function is an indefinite equation
Special straight lines
Indeterminate line
Quadratic function
Symmetrical movement
parallel translation
Quadratic function and three points
The meeting of quadratic equations and functions
Maximum and minimum values ​​in the range

Part 5.
Equations: Concepts You Need for High School
How to display the terms of a sequence
Properties of equality in sequences
Find repeating patterns
sum of a sequence
Make an equation a proportion
Before solving the problem
hypothetical question

〈Review〉 Mathematics by Concept

“A perfect score on the middle school exam is not preparation for high school.

So it is a fact that the top 70% fail in advanced mathematics.

A child who studies by type cannot break through the wall of the second-grade high school level with his/her skills.

“The kids who do well all the way through high school, the kids who get top grades, all study hard enough to chew on the concepts.”

Solving problems with concepts is deductive reasoning, and deductive reasoning is the only way to be good at math.
However, mathematics is not a discipline in which you can understand concepts on your own, and it is not something that can be achieved just by understanding it.

Therefore, in order to study and digest concepts, you must learn proper 'one-line concepts'.

If the mathematics that teaches logic lacks concepts, you can't even begin to think logically.
Since you can't think about it, you end up thinking that you just have to understand it or somehow solve the problem.
This is the beginning of a huge type problem solving.
Solving type problems is helpless when it comes to new or difficult problems.
Children who are good at math say that it is good because there is nothing to memorize, and children who are bad at math say that it is difficult because there is too much to memorize.
It's the difference between studying as a 'concept' or not.
The author of this book points out that the reason most students are bad at math is not because they lack the ability to apply the concepts, but because they either don't have the concepts in their heads at all or their knowledge is so vague that they can't use them when needed.


Above all, this book explains in an easy-to-understand way the concept of 'numbers', which is necessary from elementary school to high school.
We have covered in more depth topics that high school students find difficult, such as absolute values, functions, and inequalities, so that even students preparing for specialized high schools can access them.
Difficult or confusing content is explained in a conversational manner to make it easy and fun to understand.
The dictionary-style table of contents is easy to find and allows you to study little by little without any burden.
This is the greatest charm of this book.


Polyverse Publishing plans to publish a more systematic compilation of elementary, middle, and high school mathematics by grade level, organized by Director Jo An-ho.
Before that, I hope to use this book to build a comprehensive framework for middle school mathematics.