Mathematical notation and special-character aliases. Everything is an expression: operators, functions, data structures. Symbolic computation principles. Patterns and replacement rules, variables and functions as global replacements. Functional programming, listable functions, higher-order functions. Localized replacement rules. Solving algebraic and differential equations. Plots, graphics, dynamic outputs and interactive expressions. Parametric animation and spline animation, exporting frame sequences. Converting expressions to and from LaTeX code, rendering formulae (MaTeX paclet).

Adobe Photoshop interface and document structure, shortcuts for navigation and layer manipulation directly from the document window. Navigator, History, Layers, and Tools panels. Drawing basics: Brush and Eraser tools, Fill options, plotting arrows. Changing image and canvas size, Free Transform mode. Selecting and cutting image regions, Marquee and Polygonal Lasso tools. Layer alignment and distribution. Nondestructive editing: Masks, Vector masks, and Clipping masks, Smart objects, Paths. Making use of RGB Channels. Brightness adjustments: Curves and Levels functions, Adjustment Layers, Histogram, Dodge and Burn tools. Retouching: Stamp and Healing Brush tools, Content-Aware Fill. Nonlinear history, History Brush tool. Assembling animations from frame sequences. Automation: Actions panel, Batch and Variables functions, scripting.

Mathematical foundations, Bézier curves. Adobe Illustrator interface and document structure: similarities and differences with Adobe Photoshop, distinctions in the Layers panel, Isolation mode. Making and editing splines: Pen tool and its controls, inserting spline points, Anchor Point tool, joining splines. Compound paths: Pathfinder panel, Shape Builder tool, Clipping Masks. Appearance panel, dashing and arrowheads, Expand Appearance, selecting objects by properties and types. Text layers, text block threading, typing along splines, convertion to outlines. Embedding external files, combining vector and raster images, linking between Illustrator and Photoshop, tracing raster images. Importing rendered LaTeX documents, dealing with font issues (font sources from CTAN, selectively replacing missing fonts, Flatten Transparency), in-place LaTeX expression rendering (plugin LaTeX2AI and scripts). Vector image formats, exporting as raster image.

Unreal Engine interface: Viewport navigation and basic tools, Outliner, Details, and Content Drawer panels. Setup for low-end PC. Adding basic shapes and scene composition: left-handed coordinate system!, the order of Euler angles, object parenting. Keyframe animation (Bézier splines), Sequencer panel, Movie Render Queue plugin, render settings for high-quality video. Actors, programming with Blueprints, real-time physics simulations. Importing animation keyframes, table data, and 3D meshes from Wolfram Mathematica. Importing LaTeX expressions via Adobe Illustrator, Widgets, 2D and 3D rendering of text and imported formulae. Trajectory visualization with Niagara. Materials: basic properties, Blueprints, Material Instances. Lighting and camera settings, Post Process Volume, HDRI environment maps. Native 3D graphics in Wolfram Mathematica: materials and lighting, generating and exporting 3D meshes.

Reducing problems to functions, arbitrary function construction, the Universal Approximation Theorem. Forward pass and backpropagation in a classification neural network. Training: loss function, gradient descent, stochastic gradient descent. Interpretability, convolutional neural networks (CNN), U-Net. Neural networks for image and video restoration: training data synthesis, available implementations. Image generation: reverse classifiers and generative adversarial networks (GAN), mode collapse. Autoencoders: training data synthesis, compression, latent space and generalized coordinates, variational autoencoders (VAE). Diffusion models: full image space and target distribution, forward process and Schedule types, reverse process and Sampling methods (ODE solvers), differential equation, step size (Sampling steps). Unguided vs guided generation, image-text cross attention, classifier-free guidance (CFG) scale, Control Net. Latent diffusion, Stable Diffusion (SD) 1.5 and interfaces (Automatic1111, ComfyUI, InvokeAI, Fooocus, Google Colab). Generation from source images (img2img), inpainting, diffusion models for image restoration.

HTML basics: tags, attributes, styles. Cascading Style Sheets (CSS): selectors, specificity, inheritance, combinators, pseudo-classes, custom properties (variables). CSS <length> units, absolute and relative units. Box model: padding, margin, border, and outline. Element positioning: display and position properties, flexbox and grid layouts, inset shorthand. Raster graphics (<canvas>). Vector graphics (inline <svg>), <path> tag and Bézier spline syntax, presentation (CSS) attributes, <filter> tags. Structuring SVG with <g>, <def>, and <use>. CSS animation (transitions and @keyframes), SVG animation (<set> and <animate>). HTML domain object model (DOM), accessing objects with JavaScript. Basic interface elements: buttons, sliders, checkboxes, dropdowns. Interactivity: onclick attribute, event listeners, setTimeout and setInterval methods. Rendering LaTeX expressions (MathJax library).

Adobe After Effects interface: Project, Composition, Timeline, and Preview panels, accessing History. Importing video, frame sequences, raster and vector images. Layers: raster, vector, text, compositions. Layer properties, Transform, reference frames and parenting, Null Objects. Effects, Effect Controls panel, adjustment layers. Keyframe animation (Bézier splines), temporal interpolation, Graph Editor, animating with Pen tool. Expressions, pick whip, JavaScript basics, After Effects Object Model, Expression Controls. Scripts and Plugins. Composition settings, Motion blur, and Frame Blending. Render Queue and export settings. Importing animation keyframe tables from Wolfram Mathematica. 3D graphical elements, right- and left-handed coordinates, Space Transforms, 3D rotation properties, lookAt method. Text and vector layer extrusion, Camera and Light layers, material properties.

Foundational design principles: repetition, contrast, proximity. Visual communication means: size, position, alignment, tangents, fonts, colors. Optical compensation. Typeface anatomy, serif vs sans-serif, typographical point. Repetition and contrast in font attributes: family, size, weight, tracking. Optical compensation in fonts, kerning. Font libraries, file formats. Color schemes: analogous, complementary, and tetrad palettes, connection to proximity and contrast principles, correlation with the other visual means. Color and gradient libraries. Microsoft PowerPoint: Selection Pane, native vector graphics and alignment tools, importing vector images and LaTeX expressions, extracting source files from presentations. Interactive elements, dynamic references, animation and transitions, layer naming convention for the Morph transition. Baking presentations, exporting to video.

RGB color space from the first principles. Curvilinear coordinates in the color space: HSL, HSV, and LAB. Nuances of color terminology: Hue, Shade, Tone, and Tint. Conversion of images to grayscale and CMYK, gray component replacement. Color (bit) depth, HDRI. Blending modes in Adobe Photoshop and Wolfram Mathematica, multiply and screen as a substitute for masking. Hue/Saturation adjustment, selective color editing, gamma correction. Colorizing grayscale images: working with channels, gradient maps in Wolfram Mathematica, Adobe Photoshop, and After Effects. Color decomposition, combination with frequency (wavelet) decomposition, application in retouching.

Image convolution, linear and box kernels, separation of variables. Motion (directional) blur, camera blur, Gaussian blur. Drop shadows and glow. Spatial frequencies, wavelet decomposition. Convolution filters: Sharpen, High Pass, Unsharp Mask, Edge detection. Image deconvolution and denoising, loss-of-information obstacles (out-of-bounds blur, noise infinite frequency). Random number generation (LCG and Mersenne Twister from the first principles, connection to logistic map and Lorenz attractor), random seed. Gaussian and fractal noise, implementation in Adobe Photoshop and After Effects. Reaction-diffusion patterns.

Mathematical foundations: ray tracing vs projection (rasterization) rendering. Ray tracing variations: path tracing, ray marching, cone marching. Physically based rendering (PBR) and materials: the Rendering equation, Bidirectional Scattering Distribution Function (BSDF), metallic-roughness model. Specular reflections: Fresnel coefficients, Schlick's approximation, highlight models. Mesh geometry and normals: Phong shading, normal maps. Global illumination and ambient occlusion (AO), implementation with Fibonacci lattice. Anti-aliasing (AA), motion blur, and depth-of-field blur with combined supersampling technique. Shaders: GLSL basics, real-time GPU simulations and rendering, integration into HTML with <canvas>, Unreal Engine material blueprints. Native 3D functionality in Wolfram Mathematica: materials and lighting, generating and exporting 3D meshes.