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Description
Book Introduction
Step-up math that builds the basics step by step!
Let's build up the concepts one by one!
This book introduces how to be good at math.
The author, who has taught mathematics for over 30 years, says that when studying mathematics, it is important to understand the process by which formulas are created, or the "story."
Once you understand the story, you can derive the answer by setting up the equation yourself without having to memorize the entire formula.
If you feel like you've been studying incorrectly, try this "non-memorization" study method now! You'll be at a much higher level in a year or two.
Let's build up the concepts one by one!
This book introduces how to be good at math.
The author, who has taught mathematics for over 30 years, says that when studying mathematics, it is important to understand the process by which formulas are created, or the "story."
Once you understand the story, you can derive the answer by setting up the equation yourself without having to memorize the entire formula.
If you feel like you've been studying incorrectly, try this "non-memorization" study method now! You'll be at a much higher level in a year or two.
- You can preview some of the book's contents.
Preview
index
As you enter, learn math through ‘stories’!
Homeroom ① Memorizing the entire formula is useless.
Homeroom ② Learn math through the story of 'origin'!
Homeroom ③ 3 Steps to Studying Math
Introduction Math Review
Introduction: Breaking Down the Obstacles of Mathematics
Division ① Two types of division (equal division and inclusion)
Division ② Why do we calculate division of fractions by reversing them?
Division ③ Triangle of Fraction Calculation
Division ④ Let’s think of ratios as subject, modifier, and predicate!
Chapter 1: Shapes
Chapter 1: Overview Diagram - The Formation of City-States
Proof ① The era when mathematicians were philosophers
Proof ② Proof is connecting assumptions and conclusions.
Proof ③ The century's bestseller, "Principles"
Drawing ① 'Showing' is the best proof
Construction ② Two constructions that appear in all textbooks
Construction ③ Possible and impossible constructions
Parallel Lines ① Euclid's Fifth Postulate and Reduction
Parallel Lines ② Surprisingly Difficult! The Relationship Between Two Parallel Lines and Corresponding and Alternate Angles
Parallel Lines ③ The most difficult proof in middle school math is solved with this!
Angle ① Why is the sum of the interior angles of a triangle 180°?
Angle ② Properties of polygon angles
Congruence ① The conditions for congruence of triangles are an 'efficient checklist'.
Congruence ② It is fun to prove that 'the base angles of an isosceles triangle are equal'
Similarity ① Let's prove that the similarity condition is correct.
Similarity ② Measurement technology developed through similarity.
Circle ① The most beautiful shape is the circle 87
② The 'inverse of the central angle theorem' proven by the 'conversion method'
Pythagorean Theorem ① The Pythagorean Order, a group of mathematicians of exceptional caliber
The Pythagorean Theorem ② The Pythagorean Theorem: The End of Middle School Mathematics
The ancient Greeks treated solid figure 5 specially.
Solid Figure ② Rules for 'seeing' the 'invisible' parts of solid figures
3D Figure ③ Why is the volume of the ‘~horn’ ⅓?
Chapter 2 Numbers and Formulas
Chapter 2: Overview: Numbers and Food: The Beginning of Trade
Number ① Prime numbers are the most precious and mysterious numbers.
② '1 million won debt' is '-1 million won profit'
Number ③ Extreme, but subtraction is no longer necessary
Number ④ Why is (-1) × (-1) = (+1)?
Number ⑤ Calculation mixed with the four basic arithmetic rules
Number ⑥ Why can't we divide by 0?
Alphabet ① 'Algebra' developed in non-European countries
Text format ② The surprisingly short history of '＋, -, ×, ÷'
Character expression ③ Why use character expression?
Character expression ④ Calculation and use of character expression
Linear Equation ① The basis of truth lies in the process.
Linear Equation ② The '＝' in the equation has two meanings.
Linear Equation ③ Let's solve a one-dimensional linear equation using the properties of equations.
Linear Equation ④ Let's solve the linear equation.
Linear Equation ⑤ To solve an equation with two unknowns
Linear Equation ⑥ Let's solve the two-way simultaneous linear equation.
Polynomial ① Let's think of the product of polynomials as the area!
Polynomial ② Very convenient expansion formulas
Polynomial ③ Factorization and its meaning
Square root ① The irrational number that troubled Pythagoras
Square root ② A 'number' that definitely exists but cannot be expressed numerically
Let's do a calculation that includes square root ③ √
Quadratic Equation ① Solving Quadratic Equations by Factoring
Quadratic equation ② Perfect square and quadratic equation root formula
Quadratic Equation ③ Let's solve the one-dimensional quadratic equation.
Chapter 3 Probability
Chapter 3: Overview of Probability: The Development of an Aristocracy
Probability ① Galileo's foresight
Probability ② Correspondence between Pascal and Fermat
Case 1: 〈Development〉 4 ways to count
Case 2: The '!' of succession is the '!' of exclamation point
Probability ③ Empirical probability, mathematical probability, and subjective probability
Probability ④ Various Probabilities That Are Easily Misunderstood
Chapter 4 Functions
Chapter 4 Overview Functions—The Scientific Revolution Takes Place—
Function ① Vending machines and functions are similar.
Proportion ① Proportion is the easiest function
② What is the graph of a proportional function?
Proportional ③ Inverse proportion means that y is proportional to 1/x.
Linear function ① A linear function is a development of a proportional relationship.
Linear Function ② 〈Development〉 Differentiation
Linear function ③ The function graph is dynamic, and the equation graph is static.
Linear function ④ Why is the point where the graphs intersect the solution to the simultaneous equations?
Quadratic function ① A quadratic function derived from a number proportional to its square
Quadratic function ② The graph of a quadratic function is a parabola
Quadratic Function ③ 〈Development〉 What is integration?
Function ② A slightly unusual function
Chapter 5 Statistics
Chapter 5: Overview Statistics - The Large-Scale Development of the Nation
Statistics ① History of descriptive and inferential statistics
Descriptive Statistics ① The goal of descriptive statistics is 'easy understanding'.
Descriptive Statistics ② Frequency Distribution and Histogram
Technical Statistics ③ Understanding the Whole with Three Representative Values
Technical Statistics ④ Five-Number Summary to See Data 'Dispersion' at a Glance
Descriptive Statistics ⑤ Box and whisker plots are for viewing data without preconceptions.
Technical Statistics ⑥ 〈Development〉 Variance and Standard Deviation
Technical Statistics ⑦ 〈Development〉 Beware of Correlation ≠ Causality
Inferential Statistics ① Two methods of inferential statistics: population and sample
Inferential Statistics ② 〈Development〉 Normal distribution and deviation
Coming out
References
Homeroom ① Memorizing the entire formula is useless.
Homeroom ② Learn math through the story of 'origin'!
Homeroom ③ 3 Steps to Studying Math
Introduction Math Review
Introduction: Breaking Down the Obstacles of Mathematics
Division ① Two types of division (equal division and inclusion)
Division ② Why do we calculate division of fractions by reversing them?
Division ③ Triangle of Fraction Calculation
Division ④ Let’s think of ratios as subject, modifier, and predicate!
Chapter 1: Shapes
Chapter 1: Overview Diagram - The Formation of City-States
Proof ① The era when mathematicians were philosophers
Proof ② Proof is connecting assumptions and conclusions.
Proof ③ The century's bestseller, "Principles"
Drawing ① 'Showing' is the best proof
Construction ② Two constructions that appear in all textbooks
Construction ③ Possible and impossible constructions
Parallel Lines ① Euclid's Fifth Postulate and Reduction
Parallel Lines ② Surprisingly Difficult! The Relationship Between Two Parallel Lines and Corresponding and Alternate Angles
Parallel Lines ③ The most difficult proof in middle school math is solved with this!
Angle ① Why is the sum of the interior angles of a triangle 180°?
Angle ② Properties of polygon angles
Congruence ① The conditions for congruence of triangles are an 'efficient checklist'.
Congruence ② It is fun to prove that 'the base angles of an isosceles triangle are equal'
Similarity ① Let's prove that the similarity condition is correct.
Similarity ② Measurement technology developed through similarity.
Circle ① The most beautiful shape is the circle 87
② The 'inverse of the central angle theorem' proven by the 'conversion method'
Pythagorean Theorem ① The Pythagorean Order, a group of mathematicians of exceptional caliber
The Pythagorean Theorem ② The Pythagorean Theorem: The End of Middle School Mathematics
The ancient Greeks treated solid figure 5 specially.
Solid Figure ② Rules for 'seeing' the 'invisible' parts of solid figures
3D Figure ③ Why is the volume of the ‘~horn’ ⅓?
Chapter 2 Numbers and Formulas
Chapter 2: Overview: Numbers and Food: The Beginning of Trade
Number ① Prime numbers are the most precious and mysterious numbers.
② '1 million won debt' is '-1 million won profit'
Number ③ Extreme, but subtraction is no longer necessary
Number ④ Why is (-1) × (-1) = (+1)?
Number ⑤ Calculation mixed with the four basic arithmetic rules
Number ⑥ Why can't we divide by 0?
Alphabet ① 'Algebra' developed in non-European countries
Text format ② The surprisingly short history of '＋, -, ×, ÷'
Character expression ③ Why use character expression?
Character expression ④ Calculation and use of character expression
Linear Equation ① The basis of truth lies in the process.
Linear Equation ② The '＝' in the equation has two meanings.
Linear Equation ③ Let's solve a one-dimensional linear equation using the properties of equations.
Linear Equation ④ Let's solve the linear equation.
Linear Equation ⑤ To solve an equation with two unknowns
Linear Equation ⑥ Let's solve the two-way simultaneous linear equation.
Polynomial ① Let's think of the product of polynomials as the area!
Polynomial ② Very convenient expansion formulas
Polynomial ③ Factorization and its meaning
Square root ① The irrational number that troubled Pythagoras
Square root ② A 'number' that definitely exists but cannot be expressed numerically
Let's do a calculation that includes square root ③ √
Quadratic Equation ① Solving Quadratic Equations by Factoring
Quadratic equation ② Perfect square and quadratic equation root formula
Quadratic Equation ③ Let's solve the one-dimensional quadratic equation.
Chapter 3 Probability
Chapter 3: Overview of Probability: The Development of an Aristocracy
Probability ① Galileo's foresight
Probability ② Correspondence between Pascal and Fermat
Case 1: 〈Development〉 4 ways to count
Case 2: The '!' of succession is the '!' of exclamation point
Probability ③ Empirical probability, mathematical probability, and subjective probability
Probability ④ Various Probabilities That Are Easily Misunderstood
Chapter 4 Functions
Chapter 4 Overview Functions—The Scientific Revolution Takes Place—
Function ① Vending machines and functions are similar.
Proportion ① Proportion is the easiest function
② What is the graph of a proportional function?
Proportional ③ Inverse proportion means that y is proportional to 1/x.
Linear function ① A linear function is a development of a proportional relationship.
Linear Function ② 〈Development〉 Differentiation
Linear function ③ The function graph is dynamic, and the equation graph is static.
Linear function ④ Why is the point where the graphs intersect the solution to the simultaneous equations?
Quadratic function ① A quadratic function derived from a number proportional to its square
Quadratic function ② The graph of a quadratic function is a parabola
Quadratic Function ③ 〈Development〉 What is integration?
Function ② A slightly unusual function
Chapter 5 Statistics
Chapter 5: Overview Statistics - The Large-Scale Development of the Nation
Statistics ① History of descriptive and inferential statistics
Descriptive Statistics ① The goal of descriptive statistics is 'easy understanding'.
Descriptive Statistics ② Frequency Distribution and Histogram
Technical Statistics ③ Understanding the Whole with Three Representative Values
Technical Statistics ④ Five-Number Summary to See Data 'Dispersion' at a Glance
Descriptive Statistics ⑤ Box and whisker plots are for viewing data without preconceptions.
Technical Statistics ⑥ 〈Development〉 Variance and Standard Deviation
Technical Statistics ⑦ 〈Development〉 Beware of Correlation ≠ Causality
Inferential Statistics ① Two methods of inferential statistics: population and sample
Inferential Statistics ② 〈Development〉 Normal distribution and deviation
Coming out
References
Detailed image
Into the book
Thales was the first person in human history to prove the properties of figures such as 'the two base angles of an isosceles triangle are equal' and 'the opposite vertical angles are equal'.
Although these facts were known long before Thales was born, one cannot be called a mathematician simply by discovering them.
If you can't prove why it's so, then you can't call that knowledge mathematics.
Mathematics that 'builds up proofs' = The history of argumentative mathematics began with Thales.
--- From "Chapter 1: Shapes"
Using negative numbers adds 'direction' to the world of numbers.
If you use only positive numbers, the numbers only go in one direction.
But when we bring in negative numbers, the number becomes a factor to consider not only 'magnitude' but also 'direction'.
At first, using negative numbers may feel unnatural, but it enriches your mathematical expressions.
--- From Chapter 2, Numbers and Formulas
The ratio obtained from actual experimental data is called empirical probability (or statistical probability).
Meanwhile, the probability defined as the ratio of the number of cases in which a specific event occurs to the number of all possible cases is called mathematical probability (or a priori probability).
However, the 'cases' used in this calculation are all assumed to be equally certain (expected to occur with similar probability).
--- From "Chapter 3 Probability"
The shape that is created when all (x,y) that satisfy an equation are collected is called the graph of that equation.
Anyway, please keep in mind that the same graph can be the graph of a function or, at the same time, the graph of an equation (obtained by transforming the formula of the function).
It's important to be able to change the perspective from which you view the same graph, depending on the situation.
Although these facts were known long before Thales was born, one cannot be called a mathematician simply by discovering them.
If you can't prove why it's so, then you can't call that knowledge mathematics.
Mathematics that 'builds up proofs' = The history of argumentative mathematics began with Thales.
--- From "Chapter 1: Shapes"
Using negative numbers adds 'direction' to the world of numbers.
If you use only positive numbers, the numbers only go in one direction.
But when we bring in negative numbers, the number becomes a factor to consider not only 'magnitude' but also 'direction'.
At first, using negative numbers may feel unnatural, but it enriches your mathematical expressions.
--- From Chapter 2, Numbers and Formulas
The ratio obtained from actual experimental data is called empirical probability (or statistical probability).
Meanwhile, the probability defined as the ratio of the number of cases in which a specific event occurs to the number of all possible cases is called mathematical probability (or a priori probability).
However, the 'cases' used in this calculation are all assumed to be equally certain (expected to occur with similar probability).
--- From "Chapter 3 Probability"
The shape that is created when all (x,y) that satisfy an equation are collected is called the graph of that equation.
Anyway, please keep in mind that the same graph can be the graph of a function or, at the same time, the graph of an equation (obtained by transforming the formula of the function).
It's important to be able to change the perspective from which you view the same graph, depending on the situation.
--- From “Chapter 4 Functions”
Publisher's Review
No need to memorize the entire formula!
Middle school math becomes one story!
Any problem can be solved in just 3 steps!
Is there a secret to excelling at math? This question, asked by the author, who has been teaching students struggling with math for over 30 years, is a frequent one.
Whenever I get asked that question, the author's answer is always, "Don't memorize it!"
Most people who find math difficult seem to think that studying math is simply plugging numbers into memorized formulas and solving problems.
However, if you continue to study focusing on memorization, you will usually reach a limit at some point and become frustrated.
Even in middle school math, there are over 100 formulas. Imagine how difficult it would be to memorize them without even understanding their meaning! The crucial difference between those who struggle with math and those who excel at it lies in their study methods—in other words, whether they memorized the entire math curriculum.
When studying mathematics, it is important to understand the process by which formulas are created, that is, the 'story'.
Once you understand the story, you can derive the answer by setting up the equation yourself without having to memorize the entire formula.
In this book, the 'origins' of each unit are mixed in between to understand the 'story' of mathematics, and the whole thing is rebuilt into one story.
The structure is different from school textbooks in that it proceeds in the order of ‘Shapes’, ‘Numbers and Formulas’, ‘Probability’, ‘Functions’, and ‘Statistics’.
The beginning of mathematics is strongly connected to real-life situations and events.
Why did our ancestors need to create formulas, laws, and even mathematics itself? There was a compelling reason, even if it was complex.
Knowing the reason will bring a vivid 'story' to even the most inorganic and abstract mathematics.
This book contains all of the author's accumulated know-how in mathematics teaching.
Through this book, mathematics will become wisdom you will never forget.
Middle school math becomes one story!
Any problem can be solved in just 3 steps!
Is there a secret to excelling at math? This question, asked by the author, who has been teaching students struggling with math for over 30 years, is a frequent one.
Whenever I get asked that question, the author's answer is always, "Don't memorize it!"
Most people who find math difficult seem to think that studying math is simply plugging numbers into memorized formulas and solving problems.
However, if you continue to study focusing on memorization, you will usually reach a limit at some point and become frustrated.
Even in middle school math, there are over 100 formulas. Imagine how difficult it would be to memorize them without even understanding their meaning! The crucial difference between those who struggle with math and those who excel at it lies in their study methods—in other words, whether they memorized the entire math curriculum.
When studying mathematics, it is important to understand the process by which formulas are created, that is, the 'story'.
Once you understand the story, you can derive the answer by setting up the equation yourself without having to memorize the entire formula.
In this book, the 'origins' of each unit are mixed in between to understand the 'story' of mathematics, and the whole thing is rebuilt into one story.
The structure is different from school textbooks in that it proceeds in the order of ‘Shapes’, ‘Numbers and Formulas’, ‘Probability’, ‘Functions’, and ‘Statistics’.
The beginning of mathematics is strongly connected to real-life situations and events.
Why did our ancestors need to create formulas, laws, and even mathematics itself? There was a compelling reason, even if it was complex.
Knowing the reason will bring a vivid 'story' to even the most inorganic and abstract mathematics.
This book contains all of the author's accumulated know-how in mathematics teaching.
Through this book, mathematics will become wisdom you will never forget.
GOODS SPECIFICS
- Date of issue: January 24, 2025
- Page count, weight, size: 312 pages | 420g | 148*210*18mm
- ISBN13: 9791168623125
- ISBN10: 116862312X
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