Chapter 00

Why Basic Math?

Why math is needed to understand deep learning and machine learning, and what math is used.

Math diagram by chapter

Select a chapter to see its diagram below. View the flow of basic math at a glance.

What you learn in Ch01–Ch12

Understanding deep learning and machine learning requires basic math such as functions, exponential and log, limits, derivatives, integrals, and probability and distributions. Ch01–Ch12 cover exactly that. Functions are the basis of input→output; derivatives and gradients are what the model uses to decide where and how much to change parameters when learning; probability and distributions are needed for prediction and uncertainty.

Ch.01
Functions
A function is a rule that assigns one output to each input. Neurons and layers in deep learning are functions.
Ch.02
Exponential and Exponential Functions
Exponentiation is repeated multiplication of the same base; an exponential function fixes the base and uses the exponent as the variable. Used in activation and loss design in deep learning.
Ch.03
Logarithm
A logarithm answers 'how many times we multiply the base to get this number?' It is the inverse of exponentiation and is used with exponentials in loss and probability in deep learning.
Ch.04
Limit and Epsilon-Delta (ε-δ)
A limit describes what happens when we get "arbitrarily close" to some value. Epsilon-delta is the precise way to define that idea and is the basis for derivatives and deep learning.
Ch.05
Continuity
Continuity at a point means the limit exists and equals the function value there. It is the basis for differentiability and for understanding activation and loss functions in deep learning.
Ch.06
Derivative
Differentiation gives the instantaneous rate of change (slope) at a point. The derivative as a function is the basis for gradient descent and backprop in deep learning.
Ch.07
Chain Rule
When you differentiate a function inside another, multiply outer derivative × inner derivative. That's the core of backprop.
Ch.08
Partial Derivative & Gradient
When there are several variables, partial derivative is the derivative w.r.t. one variable with others fixed. The gradient is the vector of those partial derivatives. It's the basis of gradient descent.
Ch.09
Integral
Integration is the inverse of differentiation. It is used for area under a curve, cumulative quantities, and for probability and expectation.
Ch.10
Random Variable & Distribution
A random variable assigns numbers to outcomes of an experiment; a probability distribution summarizes how likely each value is. Used in deep learning for prediction and uncertainty.
Ch.11
Mean & Variance
Ch.12
Uniform & Normal Distribution

Why math is needed to understand deep learning and machine learning

Understanding deep learning and machine learning requires math — They turn inputs (images, text, sound) into numbers, then apply functions and repeated multiplication and addition to produce an answer. That whole process is expressed using functions, limits and derivatives, and probability and distributions. Without that math it’s hard to read *how* the computation works; with it you can interpret why that output was produced.

What math is used — Functions are rules that assign one output to each input; vectors and matrices bundle numbers for batch computation. Derivatives and gradients determine where and how much to change parameters when the model learns; probability and distributions are needed for prediction and uncertainty. So understanding deep learning and machine learning requires this basic math.

Summary — Deep learning and machine learning run on numbers and functions. To understand their internals you need functions, limits, derivatives, and gradients, and probability and distributions. This course (Ch01–Ch12) covers that “math needed to understand deep learning and machine learning” in order.

Why math is needed — Every decision a deep learning or machine learning model makes (next word, recommendation, translation, classification, etc.) is computed from numbers and functions. To understand that process you need functions (input→output), limits and derivatives (gradients used when learning), and probability and distributions (prediction and uncertainty). With that math you can read why that answer was produced.

Where math appears in deep learning and machine learning — Layers are functions that multiply by weights and add; learning is adjusting parameters using gradients to reduce loss. Probability and distributions are used for prediction intervals, uncertainty, and loss design. So understanding deep learning and machine learning means knowing where and how this math is used.

Course order (Ch01–Ch12) — Ch01 Functions → Ch02–03 Exponential and log → Ch04–05 Limits and continuity → Ch06–08 Derivatives, chain rule, partial derivatives, gradient → Ch09 Integral → Ch10–12 Random variables, mean, variance, uniform and normal distributions. Each connects to input→output, learning (gradients), or prediction and uncertainty. Follow the chapter list on the left in order.

How this math connects to understanding deep learning and machine learning — Models have an input→numbers→functions repeated→output structure. Functions (Ch01 onward) are the basic unit; derivatives and gradients (Ch06–08) are used when learning to decide where and how much to change. Probability and distributions (Ch10–12) are used for prediction and loss interpretation. With this basic math you can more easily understand the internal computation of deep learning and machine learning.