High School Mathematics
Elementary School Mathematics
One-to-one correspondence
Comments
Middle School Mathematics
Addition and subtraction of negative numbers
Multiplication and division of negative numbers
Exponents
Root, cube root and nth root
Scientific Notation
Area of a circle
Comments
Linear world
Symbols and Expressions
Linear equations
Linear inequalities
Systems of Linear equations, part I: two unknowns
Systems of Linear equations, part II: three or more unknowns
The Cartesian coordinate system and graph
Arithmetic mean and harmonic mean
Comments
Nonlinear world
Exponents revisited
Root, cube root and nth root, revisited
Polynomials, expansion and factoring
Polynomial division
Dealing with denominators
Quadratic equation
Graphs of quadratic polynomials
Quadratic inequalities and the Cauchy-Schwarz inequality
Arithmetic mean, geometric mean and harmonic mean
Comments
Function and set theory
What is a function?
Composition of functions and inverse functions
Set theory
De Morgan’s laws and the contrapositive
Comments
Triangles
Congruence of triangles
Similarity of triangles
Drawing a triangle with three given sides
The triangle inequality
Comments
Graph
The Cartesian coordinate system and graph
Shifting and reflecting graphs
Graphs of quadratic polynomials
Quadratic inequalities and the Cauchy-Schwarz inequality
Comments
Analytic geometry
The Pythagorean theorem
Distances between points and equations for circles
An algebraic proof of the triangle inequality
Tangent lines to parabolas and circles
Slopes of two perpendicular lines
Comments
Some geometries
Light ray reflecting on a mirror
Inscribed triangle in a circle
Inscribed quadrilateral in a circle
Inscribed circle in a triangle
The center of mass of a triangle
The three altitudes of a triangle always meet at a point
Geometric proofs for algebraic problems
Comments
Arithmetic series and geometric series
Arithmetic series: 1+2+3+…+99+100=?
Convergence and divergence of series
Geometric series
Comments
한국어
Korean
For Korean Laymen
For Korean Students
About Me
Facebook
Quora
Popular Essays
Math and Physics
education
Moving Beyond the Korean System:
On Learning To Love Mathematics and Physics
Surprises in math, the reason why I study physics,
and a recommendation for "The Number Devil"
Is math and science homework mechanical drudgery?
Are memorizing formulas well and good arithmetic
skills essential to become a good theoretical
physicist or a good mathematician?
The difference between explaining theoretical physics
or math and other subjects
Math or Physics
education
Why Math Education Matters
Why Math Education Matters 2
Studying physics as resolving paradoxes
Math and Physics
The mathematical beauty of physics:
simplicity, consistency, and unity
English as a foreign language versus English as a
mother tongue: an analogy for the language of
mathematics and the language of physics
Physics solutions for mathematical problems
Math
The imagination in mathematics:
"Desargues's theorem"
Mathematical maturity in
solving mathematics problems
Turning a complicated multiplication
into a simple addition
The square root 2 as
irrational number
The prisoner's dilemma
Rational numbers and repeating decimal
Math History
The superiority of Hindu-Arabic numeral system
Fermat's Last Theorem
The power of negative number
Nightingale, the statistician
Pythagoras and the musical scale
The calculation of pi, the first part
The calculation of pi, the second part
Why are there as many even
natural numbers as natural numbers?
Physics
The similarity between painting and theoretical physics
Fermat’s principle and the consistency of physics
Did Einstein really prove that Newton was wrong?
The cosmological principle, and my view on philosophy
The case for string theory
Why are theories of crackpots, the self-claimed physicists
who lack proper physics education, wrong and useless?
How are theories and laws in physics created?
About This Page
Found out the reasons for my physics website
Review Articles
Introduction
High School Mathematics
For Laymen
For Mathematically Oriented High School Students
For Physics Students
The Most Recommended Articles
Other Resources
Recommended Physics Books
Other Physics Resources
My Harvard Application Essay
My MIT Application Essay
Ein Monat wie im Traum (in German)
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한국어
Korean
For Korean Laymen
For Korean Students