AI Math Quest

Tracks

1. 01🌌A High-Dimensional Universe

   0/5 lessons

   Rethinking what you experience

   Everything is data in disguise. The Afogato is a matrix. Your cat is a tensor. Your day is a trajectory. Welcome to the lens.

   Lesson list (5)

   • 01
     The Afogato Matrix~10 min · dimensions, data, intuition, high-dimensional
   • 02
     From Cat to Cat-Woman~12 min · dimensions, representation, arrays, oop
   • 03
     The Lifespan Puzzle and the Resolution of the World~10 min · complexity, bits, lifespan, elden-ring
   • 04
     Objects: The Zenith of Dimensional Representation~10 min · oop, abstraction, encapsulation, self-reference
   • 05
     Everything Is Data — The Big Reveal~8 min · dimensions, data, philosophy, self-reference

   ✓Quiz · 4 questions→

2. 02🔢Taming the Infinite

   0/5 lessons

   How the brain (and the GPU) survives the continuous

   Sampling, normalization, standardization, and the re-frame of arithmetic as expansion vs compression. The infinite is the default; finite hardware copes by approximating well.

   Lesson list (5)

   • 01
     How Many Numbers Are Between 1 and 2?~8 min · infinity, continuity, discretization
   • 02
     Your Brain Is a Lossy Codec~10 min · sampling, perception, lossy-compression, memory
   • 03
     Normalize vs Standardize: Two Ways to Tame Numbers~12 min · normalization, standardization, z-score, preprocessing
   • 04
     The Scalar Trap (and the Equal Sign Re-Met)~10 min · scalars, matrices, vector-arithmetic, equilibrium
   • 05
     Expand and Compress: Re-meeting Arithmetic~8 min · arithmetic, normalization, denormalization

   ✓Quiz · 4 questions→

3. 03↗️Vectors: Magnitude × Direction

   0/6 lessons

   The carrier across multidimensional space

   Scalars vs vectors, the 0-D bug, dot products as alignment, norms as choosable rulers, and the five operations you'll reuse forever.

   Lesson list (6)

   • 01
     Scalar vs Vector: Solo Star vs Dynamic Duo~8 min · scalars, vectors, magnitude, direction
   • 02
     0-D vs 1-D: The Bug That Eats Your First Week~10 min · scalars, 0d-array, 1d-array, pytorch, numpy
   • 03
     What the Heck Is Direction (in AI Context)?~8 min · direction, gradients, loss-landscape
   • 04
     The Dot Product: AI's Workhorse Operation~12 min · dot-product, similarity, projection
   • 05
     Norms: How 'Big' Is a Vector?~8 min · norm, magnitude, L1, L2
   • 06
     Vector Operations in Code: The Patterns You'll Reuse Forever~10 min · numpy, pytorch, broadcasting, operations

   ✓Quiz · 4 questions→

4. 04🎲Matrices & the Eigen-Dungeons

   0/8 lessons

   Transformations wearing number costumes

   Linear systems, types of matrices, transpose, identity, inverse, multiplication, determinants, and a guided trip into eigenvalues — survived without manual arithmetic.

   Lesson list (8)

   • 01
     Matrices Are Transformations Wearing Number Costumes~10 min · matrices, transformations, AX=B
   • 02
     Types of Matrices: A Bestiary~8 min · matrices, types, identity, diagonal, sparse
   • 03
     Transpose: Flipping Across the Diagonal~7 min · matrices, transpose, shape
   • 04
     Identity, Inverse, and the Matrix 'Undo' Button~10 min · identity, inverse, linear-systems
   • 05
     Matrix Multiplication: The Ritual of Combining Spells~10 min · matrix-multiplication, broadcasting, shapes
   • 06
     Determinants: The Soul of a Matrix~8 min · determinant, soul, invertibility
   • 07
     Eigenvalues & Eigenvectors: The Heartbeat of Matrices~12 min · eigenvalues, eigenvectors, intuition, blender
   • 08
     Eigen Applications: PCA, PageRank, Quantum~10 min · pca, pagerank, svd, quantum

   ✓Quiz · 4 questions→

5. 05📉Logarithms: The Ultimate Normalizer

   0/5 lessons

   Compressing the wildest scales

   Log of 1 is 0 — the anchor. Decibels show how compression matches biology. The product rule turns multiplication into addition, saving AI from numerical underflow. Every probabilistic loss function is hiding logs.

   Lesson list (5)

   • 01
     Log 1 Is Zero — and Why That's the Whole Foundation~8 min · logarithms, exponentials, intuition
   • 02
     The Ultimate Normalizer: Compressing Extreme Scales~10 min · normalization, compression, decibels
   • 03
     The Product Rule: Multiplication Becomes Addition~10 min · product-rule, log-likelihood, underflow
   • 04
     Log-Space Computing: The Underrated AI Skill~8 min · log-likelihood, stability, logsumexp
   • 05
     Where You'll Spot Logs in the Wild~6 min · AI, applications, wrap-up

   ✓Quiz · 4 questions→

6. 06🎲Probability: Insightful Guesswork

   0/5 lessons

   Living in a stochastic universe

   Stochastic vs deterministic, population vs sample, probability vs likelihood, Bayes' rule, and language models as the world's most expensive probability samplers.

   Lesson list (5)

   • 01
     You Live in a Stochastic Universe (and So Does AI)~8 min · stochastic, determinism, prediction
   • 02
     Population vs Sample: The Glimpse Problem~8 min · population, sample, estimation
   • 03
     Probability vs Likelihood: The Distinction Worth Knowing~8 min · probability, likelihood, MLE
   • 04
     Bayes' Rule: Updating Beliefs~10 min · bayes, prior, posterior, evidence
   • 05
     Language Models Are Probability Samplers~8 min · language-models, sampling, temperature

   ✓Quiz · 4 questions→

7. 07🔔The Bell Curve

   0/5 lessons

   Why nature loves symmetry — until it doesn't

   The Gaussian's two parameters, the empirical rule, z-scores for cross-unit comparison, the CLT, and why the bell rules — except when it doesn't.

   Lesson list (5)

   • 01
     The Bell Curve: Why Nature Loves Symmetry~8 min · gaussian, bell-curve, mean, std
   • 02
     The 68-95-99.7 Rule~6 min · empirical-rule, standard-deviation
   • 03
     Z-Scores: Comparing Apples to Oranges~8 min · z-score, standardization, comparison
   • 04
     The Central Limit Theorem: Why Bells Show Up Everywhere~10 min · CLT, averages, magic
   • 05
     Why the Bell Rules — and Where It Lies~6 min · assumption, limitations, wrap-up

   ✓Quiz · 4 questions→

8. 08🎯Learning from Data

   0/6 lessons

   Regression, loss, gradient descent, and the universal learning loop

   Linear regression as the seed of every learning algorithm. Loss as a ruler. Gradient descent as the engine. Overfitting as the trap. Train/val/test as the discipline.

   Lesson list (6)

   • 01
     Regression: Drawing the Best Line Through Data~10 min · regression, linear, fitting
   • 02
     Loss Functions: The Rulers We Optimize~10 min · loss, MSE, MAE, cross-entropy
   • 03
     Gradient Descent: Rolling Down the Loss Landscape~10 min · gradient-descent, optimization, learning-rate
   • 04
     Overfitting: When the Model Memorizes Instead of Learning~8 min · overfitting, generalization, regularization
   • 05
     Train/Val/Test Split: The Discipline That Prevents Self-Deception~6 min · train-test-split, validation, leakage
   • 06
     From Linear Regression to Deep Learning~6 min · deep-learning, neural-networks, wrap-up

   ✓Quiz · 4 questions→

9. 09⛷️Calculus: Dynamics of Change

   0/5 lessons

   Derivatives, the chain rule, and why depth has costs

   Calculus's only gimmick: it's about change. Derivatives as slopes, integration as accumulation, the chain rule as the backbone of backprop, and vanishing/exploding gradients as the chain rule biting back.

   Lesson list (5)

   • 01
     Calculus's Only Trick: It's About Change~8 min · calculus, change, derivative
   • 02
     The Derivative Is the Slope at a Point~10 min · derivative, slope, tangent
   • 03
     Integration: Differentiation's Mirror Twin~8 min · integration, accumulation, antiderivative
   • 04
     The Chain Rule: How Derivatives Compose~10 min · chain-rule, composition, backprop
   • 05
     When the Chain Rule Bites: Vanishing & Exploding Gradients~8 min · vanishing-gradient, exploding-gradient, depth

   ✓Quiz · 4 questions→

10. 10🔄Backprop: Blame Through Gradients

    0/5 lessons

    Forward, backward, step — the engine of modern AI

    Forward pass shoots the arrow, loss measures the miss, backprop assigns the blame via the chain rule, gradient descent adjusts the aim. Repeat. The five-line training loop is everything.

    Lesson list (5)

    • 01
      Forward Pass: Shooting the Arrow~8 min · forward-pass, prediction, loss
    • 02
      Activation Functions: The Spark of Non-Linearity~8 min · activation, relu, sigmoid, non-linearity
    • 03
      Backpropagation: The Chain Rule Doing Bookkeeping~12 min · backprop, chain-rule, gradients
    • 04
      The Training Loop: Forward, Backward, Step~8 min · training-loop, optimizer, epoch
    • 05
      Putting It All Together: From Math to Models~8 min · wrap-up, deep-learning, ai-stack

    ✓Quiz · 4 questions→

11. 11🧠Epilogue: Concepts Over Formulas

    0/4 lessons

    Mathilda, Pippa, and the lineage of this quest

    Concepts before formulas, always. Mathilda's pedagogy and Pippa's continuation. The calculus of life — integrate your past, differentiate your present. Where to go next.

    Lesson list (4)

    • 01
      Don't Memorize. Internalize.~6 min · philosophy, concepts, formulas
    • 02
      Mathilda and Pippa: A Lineage~8 min · self-reference, mathilda, pippa, lineage
    • 03
      The Calculus of Life~6 min · philosophy, self-reference, ending
    • 04
      Where to Go from Here~5 min · next-steps, ml-roadmap, wrap-up

    ✓Quiz · 4 questions→