15yo seeking advice for studying mathematics beyond my grade for graphical engineering.

Hi everyone,

I’m a 15-year-old trying to get into low-level graphics programming. My ultimate goal is to learn c++ and the Vulkan api to build a ray tracer and eventually a path tracer.

I know this requires a lot of heavy mathematics. Right now, I’ve just finished the equivalents Algebra 1 and basic High school geometry (Euclid’s geometry, coordinate system introduction, shapes). I also know early algebra 2 topics like systems of linear equations, polynomials, and quadratic equations. However, I have not learned trig yet.

Based on my research, here are the specific mathematics topics I need. I am looking for advice, textbook recommendations, online tutorials, courses, anything I can find to bridge the gap from where I am now to these topics:

1. Linear algebra (My priority)

Vectors—vector spaces, addition, scaling, dot products, cross products.

Matrices—matrix multiplication, determinants, inverses and 3d affine transformations.

Coordinate spaces—changing bases, transforming between different coordinate systems and such.

2. Geometry and trig

Parametric equations—expressing lines and rays

Geometric intersections

Spherical coordinates

3. Calculus and probability (For path tracing, I believe I’m going to eventually need this)

Integral calculus

Probability & statistics

Monte Carlo methods

Are there any specific resources that teach these concepts with a focus on visual intuition and understanding to implement these concepts through complex problems that demand critical thinking?

I’ve heard 3blue1brown is pretty good and I started doing his essence of linear algebra playlist.

Honestly, I didn’t fully knew what mathematics’ topics is needed for graphics programming, i only knew some topics’ names, therefore I used Gemini to find out what is needed. It might be that it stated some topics that I don’t really need or missed some topics i need, either way feel free to suggest!

Thank you!