Redshift Academy

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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
Stochiometry
The Periodic Table

Classical Mechanics

Blackbody Radiation

Classical Physics

Archimedes Principle
Bernoulli Principle
Center of Mass Frame
Comparison Between Gravitation and Electrostatics
Compton Effect
Coriolis Effect
Cyclotron Resonance
Dispersion
Doppler Effect
Double Slit Experiment
Elastic and Inelastic Collisions
Electric Fields
Error Analysis
Fick's Law
Fluid Pressure
Gauss's Law of Universal Gravity
Gravity - Force and Acceleration
Hooke's law
Ideal and Non-Ideal Gas Laws (van der Waal)
Impulse Force
Inclined Plane
Inertia
Kepler's Laws
Kinematics
Kinetic Theory of Gases
Kirchoff's Laws
Maxwell's Equations
Moments and Torque
Nuclear Spin
One Dimensional Wave Equation
Pascal's Principle
Phase and Group Velocity
Poiseuille's Law
Refractive Index
Rotational Dynamics
Simple Harmonic Motion
Specific Heat, Latent Heat and Calorimetry
The Gas Laws
The Laws of Thermodynamics
The Zeeman Effect
Young's Modulus

Climate Change

Keeling Curve

Cosmology

Baryogenesis
Cosmic Background Radiation and Decoupling
CPT Symmetries
Dark Matter
Friedmann-Robertson-Walker Equations
Hubble's Law
Inflation Theory
Introduction to Black Holes
Olbers' Paradox
Planck Units
Stephen Hawking's Last Paper
Stephen Hawking's PhD Thesis
The Big Bang Model
Vacuum Energy

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

Basis One-forms
Catalog of Spacetimes
Curvature and Parallel Transport
Einstein's Field Equations
Geodesics
Gravitational Waves
Hyperbolic Motion and Rindler Coordinates
Quantum Gravity
Ricci Decomposition
Ricci Flow
Stress-Energy-Momentum Tensor
Tensors
The Area Metric
The Dirac Equation in Curved Spacetime
The Equivalence Principal
The Essential Mathematics of General Relativity
The Induced Metric
The Light Cone
The Metric Tensor
The Principle of Least Action in Relativity
Vierbein (Frame) Fields

Group Theory

Basic Group Theory
Basic Representation Theory
Building Groups From Other Groups
Sets, Groups, Modules, Rings and Vector Spaces
Symmetric Groups
The Integers Modulo n Under + and x

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
Binomial Theorem (Pascal's Triangle)
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
Piecewise Functions
Polar Coordinates
Polynomial Division
Quaternions 1
Quaternions 2
Regular Polygons
Related Rates
Similar Matrices and Diagonalization
Spherical Trigonometry
Stirling's Approximation
Sum and Differences of Squares and Cubes
Symbolic Logic
Tangent and Normal Line
Taylor and Maclaurin Series
The Essential Mathematics of Lie Groups
The Limit Definition of the Exponential Function
Tic-Tac-Toe Factoring
Trapezoidal Rule
Unit Vectors
Volume Integrals

Microeconomics

Marginal Revenue and Cost

Nuclear Physics

Radioactive Decay

Particle Physics

Feynman Diagrams and Loops
Field Dimensions
Helicity, Chirality and Weyl Spinors
Klein-Gordon and Dirac Equations
Regularization and Renormalization
Scattering - Mandelstam Variables
Spin 1 Eigenvectors

Probability and Statistics

Box and Whisker Plots
Buffon's Needle
Categorical Data - Crosstabs
Chebyshev's Theorem
Chi Squared Goodness of Fit
Conditional Probability
Confidence Intervals
Data Types
Expected Value
Factor Analysis
Hypothesis Testing
Linear Regression
Monte Carlo Methods
Non Parametric Tests
One-Way ANOVA
Pearson Correlation
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

Density Operators and Mixed States
Entangled States
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

Bohr Atom
Clebsch-Gordan Coefficients
Commutators
Dyson Series
Electron Orbital Angular Momentum and Spin
Heisenberg Uncertainty Principle
Ladder Operators
Multi Electron Wavefunctions
Pauli Spin Matrices
Photoelectric Effect
Position and Momentum States
Probability Current
Schrodinger Equation for Hydrogen Atom
Schrodinger Wave Equation
Spin 1/2 Eigenvectors
The Differential Operator
The Essential Mathematics of Quantum Mechanics
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 (Faraday) Tensor
Energy and Momentum in Special Relativity, E = mc2
Invariance of the Velocity of Light
Lorentz Invariance
Lorentz Transform
Lorentz Transformation of the EM Field
Newton versus Einstein
Spinors - Part 1
Spinors - Part 2
The Continuity Equation
The Lorentz Group

Statistical Mechanics

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

Bardeen–Cooper–Schrieffer Theory
BCS Theory
Cooper Pairs
Introduction to Superconductivity
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

Hashing
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Hashing is the transformation of a string of characters of arbitrary length into a usually shorter fixed-length value or key that represents the original string. Hashing is used to index and retrieve items in a database/array because it is faster to find the item using the shorter hashed key than to find it by searching character-by-character across the original string. It is also used in many encryption algorithms.

A collision can occur in a situation when two distinct pieces of data have the same hash value. Collisions are likely whenever members of a very large set are mapped to a relatively short bit string. The impact of collisions depends on the application. In some cases such as DNA analysis the hashing functions are designed to maximize the probability of collision between distinct but similar data. On the other hand, when analyzing checksums for example, it is desirable to construct functions that minimize the probability.

Most hash table implementations have some kind of collision resolution strategy to handle such events. There are 2 basic methods. The first method is to use a data structure such as a linked list to store multiple items that hash to the same slot. The second method is to search for other slots using a second function and store the item in the first empty slot found.