AI basics syllabus: from the fundamentals to language models and agents

A map of every article in the series — maths, search, machine learning, signal processing, neural networks, LSTM, transformers, generative models and AI agents.

8 minutes Matěj Žalmánek 2026-10-15

This is the plan for the whole AI basics series: everything we want to explain, ordered from the fundamentals to the details. Finished articles are links; we are writing the rest one by one. The syllabus is a map, not a mandatory route — every article can be read on its own, and at its start you will find what is useful to know beforehand.

The modules build on each other as the graph shows. First the map and the maths, then the two big families of AI — the one that searches and the one that learns. Machine learning and signal processing grow into neural networks, those grow into language models and generative AI, and in the end everything comes together in AI agents. The number under a module’s name shows how many of its articles have already been published.

• beginner no prior knowledge needed
• intermediate builds on the fundamentals from earlier modules
• in depth for those who want to know how it works inside

1. Introduction and map

Where to start: what artificial intelligence is, where it came from and the basic vocabulary.

1. 1.1
   Map of artificial intelligence What AI, machine learning, deep learning and language models are and how they fit together.
   beginner
2. 1.2
   A brief history of AI From the Turing test through the AI winters to language models.
   beginner
3. 1.3
   Data, model, training, inference The basic terms you will need throughout the rest of the series.
   beginner

2. Mathematical foundations

First the language of mathematics — notation, sets, relations, functions, logic and graphs — which lets you read every definition in the series. Then only as much maths as you need, always with an example from AI. Gradient descent is the heart of almost everything that learns.

1. 2.1
   How to read mathematical notation Symbols, subscripts, sums and quantifiers — a glossary that lets you read every definition in the series.
   beginner
2. 2.2
   Sets and relations Elements, subsets, the Cartesian product and relations — the building blocks of states, data and graphs.
   beginner
3. 2.3
   Functions and mappings Domain, codomain and composition — what exactly the notation f : X → Y means.
   beginner
4. 2.4
   Logic and proofs Connectives, implication, the quantifiers ∀ and ∃, and how a mathematical proof works.
   beginner
5. 2.5
   Graphs and trees Vertices, edges, paths and trees — the structure that both search and neural networks are built on.
   beginner
6. 2.6
   Linear algebra for machine learning Vectors, matrices and the dot product — the language every model speaks.
   beginner
7. 2.7
   Derivatives, gradients and the chain rule How to find out which way to turn the model's knobs.
   beginner
8. 2.8
   Gradient descent: how a model learns Gradient descent, SGD, momentum and Adam, animated across the loss landscape.
   intermediate

3. Probability and statistics

Machine learning is largely statistics. From a precise definition of probability through random variables, the cumulative distribution function and density to distributions, estimation and entropy.

1. 3.1
   What probability is Random experiments, events and the Kolmogorov axioms — a precise definition instead of “the ratio of favorable outcomes”.
   beginner
2. 3.2
   Conditional probability and Bayes' theorem How to update your estimate when you learn something new — the basis of spam filters and medical diagnosis.
   beginner
3. 3.3
   Random variables and the cumulative distribution function Discrete and continuous variables, and the function that tells you everything about the distribution of each.
   beginner
4. 3.4
   Probability density and probability mass functions Why a continuous variable has probability zero at any single point — and what the density shows instead.
   intermediate
5. 3.5
   Expected value, variance and covariance Where a distribution lies, how wide it is and how two variables relate to each other.
   beginner
6. 3.6
   An overview of probability distributions Bernoulli, binomial, Poisson, uniform, normal and exponential — when to use which.
   beginner
7. 3.7
   The law of large numbers and the central limit theorem Why averages behave so predictably and why the normal distribution is everywhere.
   intermediate
8. 3.8
   Statistics and parameter estimation Samples, estimators, maximum likelihood and confidence intervals.
   intermediate
9. 3.9
   Information theory Entropy, cross-entropy and KL divergence — where loss functions come from.
   intermediate

4. Classical AI: search, games and logic

AI that learns nothing but thinks: it searches through options, calculates moves ahead and reasons from rules.

1. 4.1
   State-space search BFS, DFS, UCS, greedy search and A* on a single maze.
   beginner
2. 4.2
   Games and adversaries Minimax, alpha-beta pruning and Monte Carlo tree search.
   intermediate
3. 4.3
   Constraint satisfaction Sudoku, timetables and backtracking with constraint propagation.
   intermediate
4. 4.4
   Logic and knowledge-based systems Knowledge written as rules, automated reasoning and expert systems.
   intermediate
5. 4.5
   Planning How AI puts together a sequence of actions to reach a goal — from STRIPS to today's agents.
   intermediate

5. Nature-inspired algorithms

When there are so many options that you cannot go through them all, it helps to borrow from nature: evolution, ants, flocks of birds and cooling metal.

1. 5.1
   Local search and simulated annealing A hill climber that gets stuck on a hill — and how the physics of cooling metal helps it.
   beginner
2. 5.2
   Genetic algorithms A population of solutions, crossover, mutation and natural selection in code.
   beginner
3. 5.3
   Evolution strategies and genetic programming Evolving numeric parameters and whole programs.
   intermediate
4. 5.4
   Ant colony optimization How pheromone trails find a short path — even for the travelling salesman problem.
   intermediate
5. 5.5
   Particle swarm optimization A swarm that shares the best place found so far, and why it works.
   intermediate
6. 5.6
   Neuroevolution Evolving both the weights and the architecture of neural networks — NEAT and its successors.
   in depth

6. Fuzzy logic and fuzzy systems

The world is not black and white, and fuzzy logic takes that into account: instead of “yes or no” it asks “to what degree”. From rules a person can understand, it builds controllers and models.

1. 6.1
   Fuzzy sets and membership functions When an element belongs to a set neither fully nor not at all — how to write down “somewhat warm”.
   beginner
2. 6.2
   Fuzzy logic and probability Why “it is somewhat warm” does not mean the same as “it is probably warm”.
   beginner
3. 6.3
   Fuzzy logic: operations and rules Fuzzy intersection and union, t-norms and IF–THEN rules.
   intermediate
4. 6.4
   Fuzzy control: Mamdani and Sugeno Fuzzification, inference and defuzzification — how a fuzzy controller runs a washing machine or an air conditioner.
   intermediate
5. 6.5
   Fuzzy clustering The fuzzy c-means algorithm: a point can belong to several clusters at once.
   intermediate
6. 6.6
   Neuro-fuzzy systems (ANFIS) Fuzzy rules whose parameters are learned like a neural network.
   in depth

7. Probabilistic models and sequences

How to reason under uncertainty and about what happens over time — from Markov chains to the Kalman filter.

1. 7.1
   Markov chains Memoryless random processes, the transition matrix and the stationary distribution.
   intermediate
2. 7.2
   Hidden Markov models What happens when we cannot see the state — and the Viterbi algorithm.
   intermediate
3. 7.3
   Bayesian networks A graph of dependencies between random variables and how to draw inferences from it.
   intermediate
4. 7.4
   The Kalman filter Estimating the true state from noisy measurements, step by step.
   in depth

8. Machine learning

The general framework: what kinds of learning there are, why a model fails on new data and how to tell that it has learned well.

1. 8.1
   Types of machine learning Supervised, unsupervised, semi-supervised, self-supervised and reinforcement learning.
   beginner
2. 8.2
   Overfitting and regularization Why a model that knows its training data by heart fails — and what to do about it.
   intermediate coming soon
3. 8.3
   Evaluating a model Training and test data, cross-validation, accuracy, F1 and ROC.
   intermediate coming soon
4. 8.4
   Clustering and dimensionality reduction k-means, PCA and t-SNE — how to see structure in hundreds of dimensions.
   intermediate coming soon

9. Classification and regression

The two most common machine learning tasks — which box does it belong in, and how much will it be — and the models that solve them: from a straight line through trees to SVM.

1. 9.1
   Classification and regression: two supervised learning tasks When a model answers with a class and when with a number — and how that changes the way error is measured.
   beginner coming soon
2. 9.2
   Linear regression Least squares, geometrically and with matrices, and what R² means.
   beginner coming soon
3. 9.3
   Polynomial and nonlinear regression How to bend a straight line — and why a curve bent too far predicts worse.
   intermediate coming soon
4. 9.4
   Logistic regression Classification with the sigmoid, the decision boundary and cross-entropy.
   beginner coming soon
5. 9.5
   Multiclass classification and softmax From two classes to many: one-vs-rest and the softmax function.
   intermediate coming soon
6. 9.6
   Naive Bayes classifier Bayes' theorem in practice: a fast text classifier that works better than it should.
   intermediate coming soon
7. 9.7
   Loss functions MSE, MAE, Huber loss, cross-entropy and hinge — what exactly the model minimizes.
   intermediate coming soon
8. 9.8
   Decision trees and k-nearest neighbors Two models you can explain without a single formula.
   intermediate coming soon
9. 9.9
   Ensembles: random forests and gradient boosting Why a hundred weak models beat one strong one.
   intermediate coming soon
10. 9.10
    SVMs and the kernel trick The widest possible margin between classes and how to bend it.
    in depth coming soon

10. Signal processing

Sound, images and measurements are signals. Before a model gets them, they have to be turned into numbers — and convolution carries over from here straight into neural networks.

1. 10.1
   Signals and sampling What a signal is, how to turn it into numbers and why the Nyquist theorem holds.
   beginner coming soon
2. 10.2
   The Fourier transform Breaking a signal down into frequencies and what the spectrum tells us.
   intermediate coming soon
3. 10.3
   Filters and convolution Smoothing, edge enhancement and noise removal — and why convolution is everywhere.
   intermediate coming soon
4. 10.4
   Sound and speech Spectrograms, the mel scale and MFCC — how audio is prepared for a model.
   in depth coming soon
5. 10.5
   Images as signals Pixels, colors, 2D convolution and edge detection.
   intermediate coming soon

11. Neural networks and deep learning

From a single neuron to networks for images and sequences — including recurrent networks, LSTM and GRU.

1. 11.1
   The perceptron and the artificial neuron The simplest neural network and what it cannot do.
   beginner coming soon
2. 11.2
   A neural network from scratch A multilayer network and backpropagation, by hand and step by step.
   intermediate coming soon
3. 11.3
   Activations, initialization and normalization The small details that decide whether a deep network learns at all.
   intermediate coming soon
4. 11.4
   Convolutional networks (CNN) How a network recognizes images — layer by layer.
   intermediate coming soon
5. 11.5
   Recurrent networks (RNN) Networks with memory for sequences, and the vanishing gradient problem.
   intermediate coming soon
6. 11.6
   LSTM and GRU Gates that decide what the network remembers and what it forgets.
   in depth coming soon
7. 11.7
   Autoencoders and representations A network that learns to compress data and unpack it again.
   intermediate coming soon
8. 11.8
   Embeddings and word2vec How a word becomes a vector you can calculate with.
   intermediate coming soon

12. Transformers and language models

Attention, the transformer and everything that turns a language model into an assistant.

1. 12.1
   The attention mechanism How a model learns what to look at in a text.
   intermediate coming soon
2. 12.2
   Transformers and large language models The transformer architecture step by step and how it becomes an LLM.
   in depth coming soon
3. 12.3
   Tokenization How text is chopped into the pieces a model works with.
   intermediate coming soon
4. 12.4
   Pretraining and scaling Why a bigger model and more data work — and where that stops being true.
   in depth coming soon
5. 12.5
   Fine-tuning and RLHF How a model that completes text becomes an assistant.
   in depth coming soon
6. 12.6
   Prompts, context and RAG How to give a model the right information at the right time.
   intermediate

13. Generative models

Models that don’t sort data but create it — images, sound and even new molecules.

1. 13.1
   Variational autoencoders (VAE) Generating new data from a continuous latent space.
   in depth
2. 13.2
   Generative adversarial networks (GAN) Two networks trying to outwit each other.
   in depth
3. 13.3
   Diffusion models How pure noise gradually turns into an image.
   in depth

14. Reinforcement learning

How to learn to act from rewards and penalties alone — from the Bellman equations to the algorithm behind RLHF.

1. 14.1
   Markov decision processes States, actions, rewards and the Bellman equations.
   intermediate
2. 14.2
   Q-learning and DQN Learning the value of actions — from a table to a deep network.
   intermediate
3. 14.3
   Policy gradient and PPO Learning the policy directly — the algorithm that is also behind RLHF.
   in depth

15. AI agents in practice

Where it all comes together: a language model that plans, uses tools and works for you.

1. 15.1
   How an AI agent works A language model in a loop: tools, planning and memory.
   intermediate
2. 15.2
   Programming with AI agents How to hand work to an agent, check it and keep track of it.
   beginner
3. 15.3
   Evaluation and safety of AI systems How to measure what AI can do and how to stop it from doing what it shouldn't.
   intermediate

Is something missing from the syllabus that you would like explained? Write to us — the order of the upcoming articles also depends on what people are interested in.

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