Calculus
↓ Optimization
The mathematics of finding minima and maxima — from gradient descent's calculus to linear programming's algebra.
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Derivatives
The instantaneous rate of change of a function — defined as the limit of the difference quotient and interpreted as the slope of a tangent line.
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Partial Derivatives
The rate of change of a multivariable function with respect to one variable, holding all others fixed — the building block of multivariable calculus.
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Gradient
The vector of all partial derivatives — pointing in the direction of steepest ascent and encoding how a multivariable function changes locally.
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Gradient Descent
An iterative optimisation algorithm that repeatedly moves in the direction of the negative gradient to find a local minimum of a loss function.
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Linear Programming
Optimizing a linear objective subject to linear constraints — the mathematical core of operations research, from production scheduling to diet planning.
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Convexity
Sets with no dents and functions that curve only one way — the geometric property that turns hard optimization problems into easy ones.