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27 articles foundClear

๐Ÿ“Math27 articles

Normal distribution probability density functions for different mean and variance
Math
Probability Fundamentals: Distributions, Expected Value, and the Law of Large Numbers
Core probability theory from the axioms through to expectation, variance, common distributions, and ...
๐Ÿ“– 12 min readยทStatistics ยท Engineering Reliability
Monte Carlo estimation of Pi by random point sampling in a unit square
Math
Monte Carlo Methods: Simulation, Integration, and Uncertainty Quantification
How Monte Carlo simulation uses random sampling to solve problems that are intractable analytically ...
๐Ÿ“– 12 min readยทSimulation ยท Reliability Engineering
Math
Eigenvalues and Eigenvectors: The Mathematics Behind Vibration, Stability, and Quantum Mechanics
A comprehensive guide to eigenvalues eigenvectors engineering vibration modal analysis in Mathematic...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Finite Difference Methods: Turning Differential Equations into Spreadsheets
A comprehensive guide to finite difference method PDE numerical methods engineering in Mathematics &...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Genetic Algorithms: How Engineers Borrow Evolution to Solve Impossible Optimisation Problems
Some engineering optimisation problems have billions of possible solutions and no mathematical gradi...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Statistical Hypothesis Testing: How Engineers Decide if Data Is Significant
A comprehensive guide to hypothesis testing p-value t-test engineering statistics in Mathematics & S...
๐Ÿ“– 8 min readยทApplied Mathematics ยท Numerical Methods
Math
The Kalman Filter: The Algorithm That Guides Spacecraft, GPS, and Self-Driving Cars
A comprehensive guide to Kalman filter estimation algorithm state estimation in Mathematics & Engine...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Complex frequency plane s-domain
Math
The Laplace Transform: The Mathematical Tool That Tamed Differential Equations
The Laplace transform converts differential equations into algebraic ones โ€” making control system de...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Monte Carlo Simulation: When Randomness Solves Real Engineering Problems
A comprehensive guide to Monte Carlo simulation uncertainty โ€” the engineering science, history, math...
๐Ÿ“– 7 min readยทApplied Mathematics ยท Numerical Methods
Math
Risk and Reliability Engineering: Quantifying the Probability of Failure
A comprehensive guide to reliability engineering FMEA fault tree analysis failure probability in Mat...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Visual illustration of Bayes theorem with probability regions
Math
Bayesian Inference: The Framework for Updating Beliefs With Evidence
Bayes' theorem is 270 years old and remains the mathematically correct way to update a probability e...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
The Black-Scholes Equation: The Mathematics That Reshaped Financial Markets
A comprehensive guide to Black-Scholes options pricing formula volatility financial engineering in P...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Roulette wheel showing numbered pockets and green zero
Math
Casino Mathematics: The Unbeatable Numbers Behind Every Game on the Floor
Every casino game has a built-in mathematical advantage for the house. Understanding expected value,...
๐Ÿ“– 10 min readยทApplied Mathematics ยท Numerical Methods
Math
Eigenvalues and Eigenvectors: The Mathematics Behind Vibration, Stability, and Quantum Mechanics
A comprehensive guide to eigenvalues eigenvectors engineering vibration modal analysis in Mathematic...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Expected Utility Theory: How Rational Agents Should Make Decisions Under Risk
A comprehensive guide to expected utility theory risk aversion von Neumann Morgenstern decision in P...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Finite Difference Methods: Turning Differential Equations into Spreadsheets
A comprehensive guide to finite difference method PDE numerical methods engineering in Mathematics &...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Prisoner's dilemma payoff matrix
Math
Game Theory and the Nash Equilibrium: The Mathematics of Strategic Decision-Making
John Nash's equilibrium concept โ€” the point where no player can improve their outcome by changing st...
๐Ÿ“– 10 min readยทApplied Mathematics ยท Numerical Methods
Math
Genetic Algorithms: How Engineers Borrow Evolution to Solve Impossible Optimisation Problems
Some engineering optimisation problems have billions of possible solutions and no mathematical gradi...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Statistical Hypothesis Testing: How Engineers Decide if Data Is Significant
A comprehensive guide to hypothesis testing p-value t-test engineering statistics in Mathematics & S...
๐Ÿ“– 8 min readยทApplied Mathematics ยท Numerical Methods
Math
The Kalman Filter: The Algorithm That Guides Spacecraft, GPS, and Self-Driving Cars
A comprehensive guide to Kalman filter estimation algorithm state estimation in Mathematics & Engine...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Sports betting terminal showing odds
Math
The Kelly Criterion: The Mathematician's Answer to How Much to Bet
In 1956, John Kelly derived the optimal bet sizing formula for any situation with a genuine edge. It...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Complex frequency plane s-domain
Math
The Laplace Transform: The Mathematical Tool That Tamed Differential Equations
The Laplace transform converts differential equations into algebraic ones โ€” making control system de...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Markov chain state transition diagram
Math
Markov Chains: Modelling Systems That Have No Memory of the Past
From Google's PageRank to card shuffling, weather modelling to queue theory and board game analysis ...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Monte Carlo Simulation: When Randomness Solves Real Engineering Problems
A comprehensive guide to Monte Carlo simulation uncertainty โ€” the engineering science, history, math...
๐Ÿ“– 7 min readยทApplied Mathematics ยท Numerical Methods
Math
Probability Distributions in Engineering: Matching the Math to the Physical World
A comprehensive guide to probability distributions normal Weibull Poisson exponential engineering in...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Queuing Theory: The Mathematics of Waiting in Line
A comprehensive guide to queuing theory M/M/1 Little's law service systems traffic engineering in Pr...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods
Math
Risk and Reliability Engineering: Quantifying the Probability of Failure
A comprehensive guide to reliability engineering FMEA fault tree analysis failure probability in Mat...
๐Ÿ“– 9 min readยทApplied Mathematics ยท Numerical Methods