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Concepts9

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
∑MathIntermediate

Implicit Differentiation & Implicit Function Theorem

Implicit differentiation lets you find slopes and higher derivatives even when y is given indirectly by an equation F(x,y)=0.

#implicit differentiation#implicit function theorem#jacobian+12
∑MathIntermediate

Taylor Series & Approximation

Taylor series approximate a complicated function near a point by a simple polynomial built from its derivatives.

#taylor series
Advanced
Group:
Calculus & Differentiation
#taylor polynomial
#maclaurin series
+12
∑MathIntermediate

Hessian Matrix

The Hessian matrix collects all second-order partial derivatives of a scalar function and measures local curvature.

#hessian matrix#second derivatives#curvature+11
∑MathIntermediate

Jacobian Matrix

The Jacobian matrix collects all first-order partial derivatives of a vector-valued function, describing how small input changes linearly affect each output component.

#jacobian matrix#partial derivatives#multivariable calculus+11
∑MathIntermediate

Multivariable Chain Rule

The multivariable chain rule explains how rates of change pass through a pipeline of functions by multiplying the right derivatives (Jacobians) in the right order.

#multivariable chain rule#jacobian#gradient+12
∑MathIntermediate

Gradient & Directional Derivatives

The gradient \(\nabla f\) points in the direction of steepest increase of a scalar field and its length equals the maximum rate of increase.

#gradient#directional derivative#partial derivative+12
∑MathIntermediate

Partial Derivatives

Partial derivatives measure how a multivariable function changes when you wiggle just one input while keeping the others fixed.

#partial derivatives#gradient#jacobian+12
∑MathIntermediate

Derivatives & Differentiation Rules

Derivatives measure how fast a function changes, and rules like the product, quotient, and chain rule let us differentiate complex expressions efficiently.

#derivative#product rule#quotient rule+11
∑MathIntermediate

Limits & Continuity

A limit describes what value a function approaches as the input gets close to some point, even if the function is not defined there.

#limit#continuity#epsilon-delta+12