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 Physics

Archimedes Principle
Bernoulli Principle
Blackbody (Cavity) Radiation and Planck's Hypothesis
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
Laplace's and Poisson's Equations
Lorentz Force Law
Maxwell's Equations
Moments and Torque
Nuclear Spin
One Dimensional Wave Equation
Pascal's Principle
Phase and Group Velocity
Planck Radiation Law
Poiseuille's Law
Radioactive Decay
Refractive Index
Rotational Dynamics
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
Piecewise Functions
Polar Coordinates
Polynomial Division
Quaternions 1
Quaternions 2
Regular Polygons
Related Rates
Sets, Groups, Modules, Rings and Vector Spaces
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
Trapezoidal Rule
Unit Vectors
Vector Calculus
Volume Integrals

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
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

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
Spinors - Part 1
Spinors - Part 2
The Lorentz Group
Velocity Addition

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

Open Systems Interconnection (OSI) Standard - TCP/IP Protocol
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Virtually all networks in use today are based in some fashion on OSI. The core of this standard is the OSI Reference Model, a set of seven layers that define the different stages that data must go through to travel from one device to another over a network.

Application Set

Transport Set

The OSI Reference Model is really just a guideline. Actual protocol stacks often combine one or more of the OSI layers into a single layer. A protocol stack is a group of protocols that all work together to allow software or hardware to perform a function. The TCP/IP protocol stack is a good example. It uses four layers that map to the OSI model as follows:

A TCP packet consist of:

IP is an Internet protocol (layer 2) that handles the address part of each packet so that it gets to the right destination. Basically, IP is responsible for managing the sending and receiving of data packets over the Internet. An IP packet consists of:

The whole process can be summarized as follows:

IP Routers
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After the IP datagram has been assembled, the local machine ships it down the wire to a router that picks up the frame. Routers are very smart. They can look at the network type and, if necessary, reformat the Data layer information before passing the data onto the destination or another router. The router has a map of the local internet in its memory and each frame is sent off to its destination via the best available route. In the process the IP datagrams are just re-framed with different headers and frame source and frame destination addresses.

The router uses the technique of packet switching and all of the packets in the message may or may not take the same route. In this way the network can dynamically balance the load across various pieces of equipment. If there is a problem with one piece of equipment in the network while a message is being transferred, packets can be routed around the problem, ensuring the delivery of the entire message. The routers that make up the main part of the Internet can reconfigure the paths that packets take because they look at the information surrounding the data packet, and they tell each other about line conditions, such as delays in receiving and sending data and traffic on various pieces of the network.