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TUTBB · 2026-09-14T21:00:26+0100

Learn the vectors, matrices, calculus and probability robots actually run on, derived from scratch and proved in Python
What you'll learn

Derive the dot product from the law of cosines, and use it to project one vector onto another

Use the cross product to compute the torque a robot arm feels, and know why direction needs a direction of its own

Build rotation matrices from a robot's heading, and see exactly why composing them in the wrong order breaks

Chain homogeneous transforms from a camera's eye all the way to a robot's world frame

Read eigenvectors and eigenvalues as the directions a transform refuses to rotate, and how much it stretches them

Compute a Jacobian and use it to relate every joint's motion to the robot hand's motion at once

Run gradient descent on a real objective and see why an arm overshoots before it learns to stop

Derive Bayes' rule and use it to update a belief instead of replacing it

Build a one-dimensional Kalman filter from scratch, including where the Kalman gain actually comes from

Combine all four ideas into a single control loop that catches a moving object it can only estimate
Requirements

Comfortable with high school algebra: rearranging an equation, reading a graph

Able to read basic Python: variables, functions, a for loop. You do not need to be a programmer

No prior linear algebra, calculus or probability needed. Every idea is derived from the start

Python 3 with numpy and sympy if you want to run the proof scripts yourself, which is encouraged but optional
Description
This course contains the use of artificial intelligence.
Most robotics courses assume you already know the mathematics, and most mathematics courses never tell you which parts a robot actually uses. This course is the bridge. It teaches the four ideas a robot runs on, vectors, matrices, calculus and probability, and it derives every one of them rather than asking you to accept a formula.
Proof before formula, always. Nothing here is asserted. The dot product is derived from the law of cosines. The inertia of a rotation is derived, not quoted. The Kalman gain is built up from two noisy estimates until the formula falls out on its own. Every number spoken on screen was computed by a script that asserts its own claims, and those scripts ship with the course so you can run them yourself.
Every section runs one concrete robot storyline and ends on a payoff that connects the mathematics back to a real robot capability: steering a rover with nothing but vector sums, finding a robot's true position through three chained frames, an arm that corrects its own aim in real time, and a robot that tracks a moving target through occlusion.
The capstone puts all four ideas in one control loop. A robot arm must catch a moving object it can only estimate. You locate the object in the arm's own frame with vectors and matrices, compute the fastest correction with calculus, decide how much to trust the estimate with probability, and then run the whole thing as one loop with no gaps.
What this course is not. It is not a proof-heavy pure mathematics course, and it is not a formula reference. It is the working subset a roboticist needs, taught slowly and honestly. If a derivation needs twenty scenes to be understood, it gets twenty scenes.
53 lectures, roughly nine hours, plus the complete source archive for every lecture.
Who this course is for

Robotics students who can follow the code in a ROS 2 or simulation course but lose the thread when the mathematics appears

Self-taught engineers who want the vectors, matrices, calculus and probability robots actually use, without a full mathematics degree

Anyone who has copied a rotation matrix or a Kalman filter from a tutorial and wants to understand why it works

Developers moving into robotics, computer vision or control from another area of software

Not for you if you want rigorous proofs in the pure mathematics sense, or a quick formula cheat sheet
Homepage

Code:

https://www.udemy.com/course/math-foundations-for-robotics-vectors-matrices-calculus

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Math Foundations for Robotics Vectors, Matrices, Calculus

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