• 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
Youngsub Yoon
한국어
Korean For Korean Laymen For Korean Students
  • About Me
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  • 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
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    Introduction High School Mathematics For Laymen For Mathematically Oriented High School Students For Physics Students The Most Recommended Articles
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    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