Introduction to String Theory

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Astronomy

Astronomical Distance Units .

Celestial Coordinates .

Celestial Navigation .

Location of North and South Celestial Poles .

Chemistry

Avogadro's Number

Balancing Chemical Equations

Classical Physics

Blackbody (Cavity) Radiation and Planck's Hypothesis

Center of Mass Frame

Comparison Between Gravitation and Electrostatics

Double Slit Experiment

Elastic and Inelastic Collisions .

Gauss's Law of Universal Gravity .

Gravity - Force and Acceleration

Hooke's law

Ideal and Non-Ideal Gas Laws (van der Waal)

Kinetic Theory of Gases .

Kirchoff's Laws

Laplace's and Poisson's Equations

One Dimensional Wave Equation .

Pascal's Principle

Phase and Group Velocity

Planck Radiation Law .

Simple Harmonic Motion

Specific Heat, Latent Heat and Calorimetry

Stefan-Boltzmann Law

The Gas Laws

The Laws of Thermodynamics

The Zeeman Effect .

Wien's Displacement Law

Young's Modulus

Climate Change

Keeling Curve .

Cosmology

Baryogenesis

Cosmic Background Radiation and Decoupling

CPT Symmetries

Dark Matter

Friedmann-Robertson-Walker Equations

Geometries of the Universe

Hubble's Law

Inflation Theory

Introduction to Black Holes .

Olbers' Paradox

Penrose Diagrams

Planck Units

Stephen Hawking's Last Paper .

Stephen Hawking's PhD Thesis .

The Big Bang Model

Finance and Accounting

Amortization

Annuities

Brownian Model of Financial Markets

Capital Structure

Dividend Discount Formula

Lecture Notes on International Financial Management

NPV and IRR

Periodically and Continuously Compounded Interest

Repurchase versus Dividend Analysis

Game Theory

The Truel .

General Relativity

Accelerated Reference Frames - Rindler Coordinates

Catalog of Spacetimes .

Curvature and Parallel Transport

Dirac Equation in Curved Spacetime

Einstein's Field Equations

Geodesics

Gravitational Time Dilation

Gravitational Waves

One-forms

Quantum Gravity

Relativistic, Cosmological and Gravitational Redshift

Ricci Decomposition

Ricci Flow

Stress-Energy Tensor

Stress-Energy-Momentum Tensor

Tensors

The Area Metric

The Equivalence Principal

The Essential Mathematics of General Relativity

The Induced Metric

The Metric Tensor

Vierbein (Frame) Fields

World Lines Refresher

Lagrangian and Hamiltonian Mechanics

Classical Field Theory .

Euler-Lagrange Equation

Ex: Newtonian, Lagrangian and Hamiltonian Mechanics

Hamiltonian Formulation .

Liouville's Theorem

Symmetry and Conservation Laws - Noether's Theorem

Macroeconomics

Lecture Notes on International Economics

Lecture Notes on Macroeconomics

Macroeconomic Policy

Mathematics

Amplitude, Period and Phase

Arithmetic and Geometric Sequences and Series

Asymptotes

Augmented Matrices and Cramer's Rule

Basic Group Theory

Basic Representation Theory

Binomial Theorem (Pascal's Triangle)

Building Groups From Other Groups

Completing the Square

Complex Numbers

Composite Functions

Conformal Transformations .

Conjugate Pair Theorem

Contravariant and Covariant Components of a Vector

Derivatives of Inverse Functions

Double Angle Formulas

Eigenvectors and Eigenvalues

Euler Formula for Polyhedrons

Factoring of a³ +/- b³

Fourier Series and Transforms .

Fractals

Gauss's Divergence Theorem

Grassmann and Clifford Algebras .

Heron's Formula

Index Notation (Tensors and Matrices)

Inequalities

Integration By Parts

Introduction to Conformal Field Theory .

Inverse of a Function

Law of Sines and Cosines

Line Integrals, ∮

Logarithms and Logarithmic Equations

Matrices and Determinants

Matrix Exponential

Mean Value and Rolle's Theorem

Modulus Equations

Orthogonal Curvilinear Coordinates .

Parabolas, Ellipses and Hyperbolas

Similar Matrices and Diagonalization .

Spherical Trigonometry

Stirling's Approximation

Sum and Differences of Squares and Cubes

Symbolic Logic

Symmetric Groups

Tangent and Normal Line

Taylor and Maclaurin Series .

The Essential Mathematics of Lie Groups

The Integers Modulo n Under + and x

The Limit Definition of the Exponential Function

Tic-Tac-Toe Factoring

Microeconomics

Marginal Revenue and Cost

Particle Physics

Feynman Diagrams and Loops

Field Dimensions

Helicity and Chirality

Klein-Gordon and Dirac Equations

Regularization and Renormalization

Scattering - Mandelstam Variables

Spin 1 Eigenvectors .

The Vacuum Catastrophe

Probability and Statistics

Box and Whisker Plots

Categorical Data - Crosstabs

Chebyshev's Theorem

Chi Squared Goodness of Fit

Conditional Probability

Permutations and Combinations

Pooled Variance and Standard Error

Probability Distributions

Probability Rules

Sample Size Determination

Sampling Distributions

Set Theory - Venn Diagrams

Stacked and Unstacked Data

Stem Plots, Histograms and Ogives

Survey Data - Likert Item and Scale

Tukey's Test

Two-Way ANOVA

Programming and Computer Science

Hashing

How this site works ...

More Programming Topics

MVC Architecture

Open Systems Interconnection (OSI) Standard - TCP/IP Protocol

Public Key Encryption

Quantum Computing

The Qubit .

Quantum Field Theory

Creation and Annihilation Operators

Field Operators for Bosons and Fermions

Lagrangians in Quantum Field Theory

Path Integral Formulation

Relativistic Quantum Field Theory

Quantum Mechanics

Basic Relationships

Bell's Theorem

Bohr Atom

Clebsch-Gordan Coefficients .

Commutators

Dyson Series

Electron Orbital Angular Momentum and Spin

Entangled States

Heisenberg Uncertainty Principle

Ladder Operators .

Multi Electron Wavefunctions

Pauli Exclusion Principle

Pauli Spin Matrices

Photoelectric Effect

Position and Momentum States

Probability Current

Schrodinger Equation for Hydrogen Atom

Schrodinger Wave Equation

Schrodinger Wave Equation (continued)

Spin 1/2 Eigenvectors

The Differential Operator

The Essential Mathematics of Quantum Mechanics

The Observer Effect

The Quantum Harmonic Oscillator .

The Schrodinger, Heisenberg and Dirac Pictures

The WKB Approximation

Time Dependent Perturbation Theory

Time Evolution and Symmetry Operations

Time Independent Perturbation Theory

Wavepackets

Semiconductor Reliability

The Weibull Distribution

Solid State Electronics

Band Theory of Solids .

Fermi-Dirac Statistics .

Intrinsic and Extrinsic Semiconductors

The MOSFET

The P-N Junction

Special Relativity

4-vectors .

Electromagnetic 4 - Potential

Energy and Momentum, E = mc²

Lorentz Invariance

Lorentz Transform

Lorentz Transformation of the EM Field

Newton versus Einstein

Statistical Mechanics

Black Body Radiation

Entropy and the Partition Function

The Harmonic Oscillator

The Ideal Gas

String Theory

Bosonic Strings

Extra Dimensions

Introduction to String Theory

Kaluza-Klein Compactification of Closed Strings

Strings in Curved Spacetime

Toroidal Compactification

Superconductivity

BCS Theory

Introduction to Superconductors

Superconductivity (Lectures 1 - 10)

Superconductivity (Lectures 11 - 20)

Supersymmetry (SUSY) and Grand Unified Theory (GUT)

Chiral Superfields

Generators of a Supergroup

Grassmann Numbers

Introduction to Supersymmetry

The Gauge Hierarchy Problem

The Standard Model

Electroweak Unification (Glashow-Weinberg-Salam)

Gauge Theories (Yang-Mills)

Gravitational Force and the Planck Scale

Introduction to the Standard Model

Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

Quantum Flavordynamics and Quantum Chromodynamics

Special Unitary Groups and the Standard Model - Part 1 .

Special Unitary Groups and the Standard Model - Part 2

Special Unitary Groups and the Standard Model - Part 3 .

Standard Model Lagrangian

The Higgs Mechanism

The Nature of the Weak Interaction

Topology

Units, Constants and Useful Formulas

Constants

Formulas

Redshift Academy