• Theory of Everything

  • Theory of Everything
  • M theory and dualities
  • The fine tuning problem and the hierarchy problem
  • Sum of all the natural numbers
  • Comments
  • Chemistry

  • History of chemistry up until the beginning of 20th century
  • The structure of atoms and the periodic table
  • Comments
  • Some basic mathematics and statistics, the first part

  • What is a vector?
  • Manifold
  • Comments
  • Basic high school physics without calculus, the first part

  • Newton’s first law
  • Newton’s second law
  • The free fall
  • Comments
  • Trigonometric Functions

  • What are trigonometric functions?
  • Polar coordinate and trigonometric functions defined over all values
  • Radian
  • Inverse trigonometric functions
  • Rotation in the Cartesian coordinate system
  • Addition and subtraction rules for trigonometric functions
  • What is Fourier series?
  • Comments
  • Historical Introduction to Quantum Mechanics, the first part

  • Light as waves
  • Blackbody radiation spectrum, the Planck relation and the photoelectric effect
  • Rydberg formula
  • Comments
  • Some prerequisites for "Astronomy"

  • How can we know what chemical elements are there in stars without going there?
  • Doppler effect: How can we know the speed of stars?
  • Conic sections
  • Curved space
  • Why do closer objects seem bigger?
  • Comments
  • Astronomy

  • The round Earth
  • The rotating Earth
  • Why do we have seasons?
  • The phases of the Moon
  • The solar eclipse and the lunar eclipse
  • The Solar System and the apparent motion of planets
  • Parallax: How do we determine distances to stars?
  • History of astronomy up until the mid 17th century
  • History of astronomy from the late 17th century until the early 20th century
  • History of astronomy from the early 20th century to the early 21st century
  • Evidences that the Earth is not flat, but round
  • Comments
  • Bosons and Fermions

  • Supersymmetry: an exposition for laymen
  • Bosons, Fermions, and Pauli’s exclusion principle
  • Pauli's exclusion principle, color charge of quarks, asymptotic freedom and confinement
  • Bosons, Fermions and the statistical properties of identical particles
  • Bosons Fermions in quantum mechanics picture
  • Comments
  • Black hole

  • Why time goes more slowly at a lower place and what a black hole is
  • Comments
  • Some basic mathematics and statistics, the second part

  • Area of a sphere by Archimedes' method
  • Cavalieri's principle and the volumes of cones and spheres
  • Area of a sphere
  • Comments
  • Newton’s Law of Universal Gravitation

  • The inverse square law and the 3-dimensional world
  • Newton's law of universal gravitation
  • Comments
  • Some basic mathematics and statistics, the third part

  • Logarithm
  • Expectation value and Standard deviation
  • Linear regression
  • Semi-log plot and log-log plot
  • Asymptotic behavior of polynomials
  • Exponential function vs polynomial function
  • Pascal's triangle, Combination and the Taylor series for square root
  • Scalar field and vector field
  • Proof by induction
  • Equivalence relation
  • Pentagon, the Fibonacci sequence, and the golden ratio
  • Ellipse revisited
  • Comments
  • Energy and Entropy

  • The conservation of energy
  • Heat as a form of energy
  • Specific heat and latent heat
  • What is entropy? From a microscopic point of view
  • What is entropy? From a macroscopic point of view
  • Comments
  • Loop Quantum Gravity

  • Discrete area spectrum and the black hole entropy I: Loop quantum gravity and the Bekenstein-Hawking entropy
  • Discrete area spectrum and the black hole entropy II: Domagala-Lewandowski-Meissner formula
  • Discrete area spectrum and the black hole entropy III: Newer variables
  • Discrete area spectrum and the Hawking radiation spectrum I
  • Discrete area spectrum and the Hawking radiation spectrum II: Single unit area deduction
  • Discrete area spectrum and the Hawking radiation spectrum III: Maxwell-Boltzmann
  • Discrete area spectrum and the Hawking radiation spectrum IV: Single-partition black hole
  • Comments
  • Complex Numbers

  • Complex numbers
  • Complex conjugate
  • Complex numbers and the trigonometric functions
  • Fundamental theorem of algebra
  • Comments
  • Algebra

  • What is a group?
  • Cyclic group Cn
  • The symmetric group Sn and the alternating group An
  • Finite group
  • Lie group
  • Comments
  • Topology

  • Topology, the Euler characteristic, and the Gauss-Bonnet theorem
  • Moebius strip and Klein bottle
  • The Gauss-Bonnet theorem for triangle on a sphere
  • Algebraic Topology
  • Comments
  • Electricity and Magnetism, the first part

  • Electric charge and Coulomb force
  • Electroscope
  • Magnetic field
  • Electric current makes compass needle turn
  • Magnet exerts force on wire through which electric current passes
  • The force between two parallel wires through each of which electric current passes
  • Comments
  • Special Relativity

  • “Why” is the speed of light constant?
  • Time dilation in Einstein’s theory of special relativity
  • Electromagnetic forces and time dilation in special relativity
  • Lorentz-Fitzgerald contraction: Why is a moving object shortened?
  • Origin of the magnetic force from the perspective of special relativity
  • The relativity of simultaneity
  • Lorentz transformation
  • Lorentz transformation and Rotation, a comparison
  • Light cone
  • Comments
  • Paradoxes in Special Relativity

  • Twin paradox
  • Length contraction paradox
  • Ki yung’s misunderstanding
  • Comments
  • Electricity and Magnetism, the second part

  • Electric field
  • Gauss’s law
  • Why is the electric field inside spherical shell zero?
  • Gravitational field on the surface of the Earth
  • Magnetic monopole and Gauss’s law
  • Comments
  • Basic high school physics without calculus, the second part

  • Constant acceleration in 1-dimension
  • Projectile motion
  • Work and kinetic energy
  • Potential energy and conservation of energy
  • Momentum
  • Center of mass
  • Newton’s third law and conservation of momentum
  • Elastic collision in 1-dimension
  • Elastic collision in 1-dimension in center of mass frame
  • Elastic collision in 2-dimension
  • Normal force
  • Motions on an inclined plane
  • Centripetal force
  • Centrifugal force
  • Rotation
  • Newton’s law of universal gravitation and Kepler’s third law
  • Torque
  • Moment of inertia
  • Angular momentum
  • Hooke’s law and harmonic oscillator
  • Harmonic oscillator and circular motion
  • Electric potential
  • Comments
  • Electricity and Magnetism, the third part

  • Faraday’s law of induction
  • Faraday’s law of induction from the point of view of magnetic force on moving charge
  • Comments
  • Dimensional Analysis, the first part

  • The power of dimensional analysis
  • Natural units
  • Comments
  • CPT

  • The symmetry of physical laws: the CPT theorem for laymen
  • CP violation and the Nobel Prize for Physics 2008
  • Comments
  • Neutrino oscillation

  • Neutrino oscillation
  • Comments
  • Wave

  • Travelling wave
  • The Doppler effect
  • Standing wave
  • Huygens’ principle
  • Snell’s law
  • Young’s interference experiment
  • Interference from thin films
  • Comments
  • A Crash Course in Calculus, the first part

  • What is a limit?
  • What are continuous functions?
  • Intermediate value theorem
  • Derivatives, velocity, and acceleration
  • Addition, subtraction rules for differentiation and Leibniz’s rule
  • Derivatives of the polynomials
  • The sandwich theorem and the limit of sin theta/theta
  • Derivatives of the trigonometric functions
  • Velocity re-visited and extremum
  • The chain-rule
  • Quotient rule
  • L’H?pital’s rule
  • Exponential functions and natural logs
  • Differential and infinitesimal change
  • Implicit differentiation
  • Comments
  • Modified Newtonian Dynamics and Verlinde gravity, the first part

  • The expanding universe
  • Tully-Fisher relation, Modified Newtonian Dynamics, and Verlinde gravity
  • Comments
  • A Crash Course in Calculus, the second part

  • Revisiting the volume of cone
  • Motivating integration
  • Integration and the fundamental theorem of calculus
  • Taylor series
  • Euler’s formula and hyperbolic functions
  • Integration by parts
  • Even functions and odd functions
  • Integration by substitution
  • Comments
  • Applications of Calculus, the first part

  • Area inside a circle, surface area of a sphere and volume inside a sphere
  • The derivation of Snell’s law using calculus
  • Convexity, concavity and the point of inflection
  • Center of mass of a half-ball
  • Fourier transformations
  • Expectation values in quantum field theory (1)
  • Gamma function
  • Comments
  • The products of vectors

  • The law of cosines
  • The dot product
  • The dot product and the law of cosines
  • The cross product
  • Comments
  • The basic statistics

  • Standard deviation of the sum of uncorrelated data
  • Standard deviation of the sample means
  • Probability density function
  • Propagation of error
  • Binomial distribution
  • Gaussian distribution
  • Comments
  • A Crash Course in Calculus, the third part

  • Partial derivatives and the chain-rule
  • Differential equations
  • Partial differential equations
  • Separation of variables method in partial differential equations
  • Multiple integrals
  • Comments
  • Some basic ideas in General Relativity

  • Equivalence principle
  • By how much does time go more slowly at a lower place?
  • Experiments to test equivalence principle
  • Comments
  • Mathematical Introduction to Physics

  • Newton’s first and second laws
  • Newton’s third law and the conservation of momentum with calculus
  • Kinetic energy and Potential energy in one dimension
  • Harmonic oscillator
  • Simple pendulum
  • Kinetic energy and Potential energy in three dimensions, Line Integrals and Gradient
  • Earth’s Gravity near its surface
  • Centripetal force revisited with calculus
  • Newton’s proof of Kepler’s second law
  • Kinetic energy, Potential energy and angular momentum in polar coordinate
  • Re-visiting angular momentum conservation in central force
  • Reduced mass
  • Moment of Inertia revisited
  • Rolling down on an inclined plane
  • A pencil rolling down on an inclined plane, an International Physics Olympiad problem
  • Equilibrium of forces
  • Reflection and transmission of travelling wave
  • Young’s interference experiment, revisited
  • Diffraction
  • Comments
  • Modified Newtonian Dynamics and Verlinde gravity, the second part

  • Verlinde gravity and galaxy rotation curves
  • Comments
  • Electrodynamics

  • Electric potential revisited
  • Lorentz force
  • Magnetic force on a current-carrying wire
  • Magnetic dipole
  • Electric dipole
  • Electron magnetic moment
  • Relativistically moving charges around a square loop, an International Physics Olympiad problem
  • Comments
  • Historical Introduction to Quantum Mechanics, the second part

  • Bohr model
  • De Broglie’s matter waves
  • Schrodinger equation
  • Tunneling
  • Infinite potential well
  • Stern-Gerlach experiment
  • Comments
  • Enumerative Geometry

  • Conic sections in Cartesian coordinate
  • What is enumerative geometry?
  • Conic sections in polar coordinate
  • Comments
  • Dimensional Analysis, the second part

  • The Planck length, the Planck time, the Planck mass and the fine structure constant
  • Comments
Youngsub Yoon
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