basics:

Cartesian coordinate system.
Geometry [Points, Primitives, Winding, Surfaces, Manifolds]
Trigonometry and Vector Math.
Geometry manipulation [SOPs] Point clouds.
Different spaces in 3D [World, Object, Camera, UV space, etc.]
Data types in computer graphics.
Introduction to VEX and VOPs

Data flow:

Linear[SOPs] vs Non-linear[DOPs] data flow.
Explaining Time-depending solving with Point-based dynamics.
first simulation [Particles].

Optimizations:

Camera-Space-based cache Optimization.
Geometry [Packed: On-Disk, In-Memory, Fragments]
Reduce memory usage FPS optimization.

Volumes:

Volumes [VDBs, Signed SDF, Unsigned, Density Fog fields]
Volume sourcing, manipulation [Volume VOPs]
Smoke and Fire simulation:
Fire Characteristics [Gas, Wood, tire, etc.]
Fire Shading [Fitting, Remapping, data manipulation]
Rendering fire [ACES color-space workflow]
Rendering Optimization

Scattering:

Scattering Techniques.
Controlled Organized Randomization. [lookDev]

Advanced Transformations:

Transformations Matrices.
Rotations, decomposing matrices, quaternions
inversed transformations, Scene absolute. scene axis alignment.

RBDs:

Geometry [Primitives, Convex, Concave]
Rigid Body Dynamics [Bullet Solver]
Fracture Technicians, Constraints.
Guided Simulations.
Collision Detection Optimization.

Houdini in the Pipeline:

Send Geometry with simulation attributes to other DCCs. [Maya]
Preserve hierarchy, Attributes, and Shading Groups of incoming Geometry.
Using Reference system in Maya to work on Shading, Animation, and Simulation in parallel.
Deformation vs Transformation Alembic cache.

Explosions:

Characteristics of a good Explosions:
Shaping explosions to get a good composition in your shot.
Rendering explosions. [ACES]

Grains:

Grain sourcing, constraints.
Grain optimizations.
Grains shading and rendering [Mantra].
About Sending grains to other DCCs.