(a bit of history on graphics + making a line drawing of a cube!)

(coverage testing as sampling a 2D signals, challenges of aliasing, performing point-in-triangle tests)

(basic math of coordinate spaces and transforms)

(understanding perspective projection, texture mapping using the mip-map)

(occlusion via the depth buffer, alpha composition, the graphics pipeline and modern GPUs)

(implicit and explicit representations, geometric data structures)

(manifoldness, geometry of curves and surfaces, curvature, polygon soup, incidence matrices, halfedge data structure)

(incidence matrices, comparison of polygon mesh data structures, overview of digital geometry processing (DGP), edge flip/split/collapse, remeshing, Delaunay criterion, Loop subdivision, quadric error simplification, Delaunay edge flips, basic Laplacian smoothing, isotropic remeshing)

(quadratic forms, minimizing a quadratic, quadric error simplification, distance queries, point-to-triangle, definition of a ray, ray-sphere intersection, ray-triangle intersection, triangle-triangle intersection)

(acceleration via bounding volume hierarchies and space partitioning structures, rasterization and ray casting as solutions to the same visibility query problem)

(radiometric quantities and units, photometry, radiometry integrals, how real cameras work)

(quadrature, sampling distributions, Monte Carlo integration, importance sampling)

(BRDF, the reflectance equation, transmission and refraction, types of materials)

(the rendering equation, the importance of indirect illumination, path tracing, splitting, Russian roulette)

(Monte Carlo integration, expected value, variance, continuous random variables, variance reduction, bias and consistency, path space formulation of light transport, importance sampling, bidirectional path tracing, Metropolis-Hastings algorithm, multiple importance sampling, sampling patterns, stratified sampling, low-discrepancy sampling, quasi Monte Carlo, Hammersley and Halton sequences, blue noise, Poisson disk sampling, Lloyd relaxation, alias table, photon mapping, finite element radiosity)

(rasterization-based global illumination, packet-tracing, fast-BVH builds)

(history of (computer) animation, splines, natural splines, cubic Hermite/Bezier, B-splines, interpolation, keyframing, rigging, skeletal animation, inverse kinematics, blend shapes)

(physically-based animation, Newton's 2nd law of motion, generalized coordinates, ordinary differential equations (ODE), Lagrangian mechanics, Euler-Lagrange equations, pendulum/double pendulum, n-body systems, mass-spring systems, particle systems, flocking, crowds, particle-based fluids, granular materials, molecular dynamics, hair simulation, numerical integration, forward/backward/symplectic Euler, stability analysis, numerical differentiation, automatic differentiation, symbolic differentiation)

(continuous vs. discrete optimization, standard form of an optimization problem, local vs. global minima, existence and uniqueness of solutions, convex optimization, descent methods, gradient descent, Newton descent, kinematic chains, inverse kinematics)

(PDEs in computer graphics, defintion of a PDE, order and linearity, model equations (elliptic/parabolic/hyperbolic), Laplace equation, heat equation, wave equation, numerical solution of PDEs, Lagrangian and Eulerian discretization, the Laplace operator, discrete Laplacian, Dirichlet and Neumann boundary conditions, Jacobi method)

(linear systems of equations, visualizing linear equations, linear systems in graphics, fundamental linear algebra problems, most important algorithms of the 20th century, NP-hardness of polynomial equations, vector spaces, polynomials, function spaces, numerical linear algebra, visualization of linear maps, matrix representation of linear maps, linear isomorphisms, rotations, reflections, uniform scaling, stretch rotations, shear, symmetric matrices, spectral theorem, determinant as volume scaling, uniqueness of solutions, definiteness, sparse vs. dense matrices, callback functions, direct vs. iterative solvers, linear algebra software)

(frequency decomposition, Fourier transform in computer graphics, modal simulation, sound synthesis, mesh filtering, mesh compression, Fourier analysis in rendering, motion amplification, light field photography, Laplacian eigenfunctions, spectral decomposition, L2 inner product, Fourier transform, spectral theorem, reconstruction, FFT, precomputed radiance transfer)

(tristimulus nature of color perception, color matching experiments, XYZ primaries, luminance vs. brightness, color spaces, gamma correction, tone mapping)

(jpeg compression, image filtering via convolution, separable filters, data-dependent filtering, non-local means, filtering by example)

(sensor to image basics, demosaicing, the light field, light field photography)

(descriptions of fluid motion, Navier-Stokes, material derivative, advection, upwinding, PIC/FLIP, semi-Lagrangian advection, numerical diffusion, numerical dissipation, mass conservation, constrained Lagrangian mechanics, constraint projection, Helmholtz-Hodge decomposition, viscosity)

(VR hardware, latency and resolution challenges, judder, acquiring VR datasets)