AI Math Fundamentals

AI, short for Artificial Intelligence, is the technology that enables machines to learn patterns from data and make decisions, while mathematics is the precise language for describing patterns and characterizing changes.

AI sets the goal, and mathematics provides the path to achieve it—from data representation to model training, mathematics is at work behind every step.

It can be said that mathematics is the skeleton of AI. Without math, AI is only a vague idea. With math, AI can be computed, verified, and truly realized.

This is also why understanding AI cannot be separated from understanding the mathematics that supports it.

AI Math Fundamentals Related Content

The AI Math Fundamentals related content includes the following modules:

  • Linear Algebra— The language for describing data. An image, a piece of text, or a user profile ultimately becomes vectors or matrices in a computer.
  • Calculus— The language for describing change. How does a model learn? It relies on continuously calculating gradients and adjusting parameters.
  • Probability and Statistics— The language for describing uncertainty. The world is random, data has noise, and a model's output is essentially a probabilistic judgment.
  • Information Theory— The language for describing the amount of information. It is used to measure how far predictions are from reality and how much the model has learned.
  • Optimization Theory— The language for describing how to find the optimal solution. Training a model is essentially solving an optimization problem.

These five modules are not isolated knowledge points, but an interlocking chain:

Data (Linear Algebra) → Modeling (Probability & Statistics) → Measuring Error (Information Theory) → Solving (Calculus + Optimization)

Each subsequent lesson will keep returning to this chain, helping you map abstract formulas to concrete AI applications.

Why learn this math?

You might ask: now that you can use AI by calling an API, why do you still need to learn math?

If you only use AI toolsHonestly, you don't need much math; being able to write prompts and call APIs is enough.

If you want to understand how AI worksthen you need a certain mathematical foundation, so that you can know the reasons behind the following questions:

  • Why does loss decrease during model training?
  • Why does the model sometimes fail to learn (gradient vanishing/exploding)?
  • Why does adjusting the learning rate make training better or worse?
  • Why does Transformer need normalization and softmax?

The answers to all these "whys" are hidden in mathematics. Without a mathematical foundation, you can only memorize these phenomena by rote. With the mathematical foundation above, you can derive that these phenomenawill inevitably occur.。

If you want to create new AI methodsthis is where mathematics truly unleashes its power. Every breakthrough you've heard of—gradient descent, backpropagation, the attention mechanism, diffusion models—all began with mathematical derivation before any code was implemented. To do original work, mathematics is an unavoidable foundation.

To sum up in one sentence: mathematics is not the decoration of AI, but the skeleton of AI. Code is just translating mathematics into a language that machines can execute.

Who is this course for?

This course is suitable for the following types of people:

  • Those who want to switch careers to AI / algorithms: you need to build a solid underlying foundation, not just know how to call libraries
  • Current students (computer science, software engineering, and related majors): who want to establish systematic mathematical intuition early
  • Developers who can already write AI applications but want to understand the "why" behind them: you can run code, but you can't understand the formulas when reading papers
  • People who are curious about the underlying principles of AI: simply want to understand "what AI is really all about"

Cases where it's less suitable: if your goal is just to quickly use off-the-shelf models to complete business requirements (for example, calling large model APIs to build product features), then it's not necessarily for you.

What prerequisite knowledge is needed?

Mathematical foundation

  • High school math level is sufficient (being able to compute derivatives and understanding basic set and function concepts is better, but not required)
  • No prior university-level linear algebra, calculus, or probability theory is required—the course starts from the most basic definitions

Programming foundation

  • Ability to read and write basic Python code (variables, loops, functions)
  • No need to know NumPy in advance; you'll learn it as you go in the course

Other

  • A bit of patience is needed: mathematical intuition doesn't develop overnight; it's recommended to follow the exercises in each lecture and do the calculations and run the code yourself
  • No prior knowledge of AI/machine learning is required; the course will gradually introduce related concepts while teaching the mathematics
Other extensions