Month 1 · ~18.5 h of video + practice

The math that everything else stands on

Your goal this month: become comfortable with vectors, matrices and least squares, because every later course assumes it.

Every robotics course eventually turns into matrices. Rotation is a matrix. A robot's position is a matrix. A camera is a matrix. A controller is a matrix.

If this part is shaky, every lecture after it feels like a foreign language.

month 10/7 · 0%

Watch

ENGR108: Introduction to Applied Linear Algebra ↗54 short lectures, ~18.5 h

Stephen Boyd, Stanford

The most beginner-friendly Stanford math course on YouTube. It ends with control and state estimation examples, which is exactly where robotics picks it up.

Free book: Vectors, Matrices, and Least Squares ↗

What to focus on

→Vectors, norms, distances and angles (lectures 2 to 12)
→Matrix-vector multiplication as "a function that moves things" (lectures 17 to 23)
→Least squares, the single most used idea in robotics (lectures 33 to 36)
→Linear dynamical systems, your first look at how a robot's state changes over time (lecture 26)
→Linear quadratic control and state estimation (lectures 48 and 49), a preview of Month 4

What to skip

–Lecture 47 on portfolio optimization, unless you're curious
–The k-means lectures (13 and 14) can wait

Practice task

Colab notebook coming soon

Install Python with NumPy and Jupyter. Then:

fit a line through 50 noisy points with least squares, first by hand with the formula, then with np.linalg.lstsq, and check you get the same answer
write a function that rotates a 2D point by any angle with a rotation matrix, and plot a square rotating in 10-degree steps
simulate a linear system x(t+1) = A x(t) and plot what happens when you change A

All three come back later: least squares in sensor calibration, rotations in kinematics, linear systems in control.

Milestone: by the end of this month you can

multiply a 2x2 matrix by a vector in your head and explain what it did geometrically
solve a least squares problem and explain why it's "the best fit"
rotate points with a rotation matrix in code
simulate a linear system in a loop and plot it

Get the next checkpoint by email

One topic, one task and one new resource every week.