### Middle School Mathematics

Comments: Even though the concepts dealt in these articles are treated in middle school, I included these articles to remind the adults who have forgotten them.

### Linear world

Comments: In South Korea, after six years of drilling addition, subtraction, multiplication, and division in elementary school, you enter middle school (equivalent to 7th~9th grades). There, you learn somewhat abstract mathematics for the first time and how to express unknown quantities in terms of alphabets such as x, y and z. The first article talks about this abstraction. The second to fourth articles are about equations. Equations involve unknowns, and by solving them you find the unknowns. Even though you may know how to solve systems of linear equations, I encourage you to read “Systems of Linear equations, part II” as I talk about an important concept called “linear independence” in the final comment there. The last article is about the Cartesian coordinate system, first introduced by and named after the great French philosopher René Descartes. (Yes, the one who famously said “I think, therefore I am.”) All the equations considered in these articles are linear equations. You will find the meaning of “linear” in our article “Polynomials, expansion and factoring’ in the “Nonlinear world’’ section.

### Nonlinear world

Comments: Having introduced how to express unknowns abstractly and how to solve linear equations, I introduce how to solve more difficult equations (such as quadratic equations) and how to manipulate the variables arithmetically. In the last article, we introduce the Cauchy-Schwarz inequality, which is essential to prove Heisenberg’s uncertainty principle in quantum mechanics.

### Function

Comments: The concept of a function is very useful and important in mathematics.

### Triangles

Comments: The second article is needed to solve the problem in “Is math and science homework mechanical drudgery?”

### Analytic Geometry

- Slopes of two perpendicular lines

### Some geometries

- Inscribed square in a circle

- Inscribed circle in a triangle

- The center of mass of a triangle

- The orthocenter of a triangle

### Arithmetic series and geometric series

Comments: What would be the sum of all the natural numbers from 1 to 100? The first article introduces a clever trick to answer this problem, discovered by Gauss when he was nine years old. The third article is necessary to understand our later article “composition,” which in turn is important to understand “Approximation of the naïve black hole degeneracy,” my first published research article.