Derive it yourself
Researcher track
Full derivations, proofs, theoretical framing and the papers behind each idea. Assumes you want the ELBO derived rather than quoted.
Best if: Preparing for GATE DA, postgraduate study or research work.
- 01
Linear Algebra
Vector spaces through SVD. The language every model in this curriculum is written in, built from first principles with worked numeric examples.
19 of 20 lessons on this track
- Vectors and Vector Spaces
- Subspaces, Span and Basis
- Linear Independence, Rank and Nullity
- Matrices and Their Operations
- Special Matrices
- Systems of Linear Equations
+13 more
- 02
Calculus and Optimisation
Single- and multi-variable calculus, convexity, Lagrange multipliers and KKT — the machinery behind every training loop.
17 of 17 lessons on this track
- Functions, Limits and Continuity
- Differentiability and Rules of Differentiation
- Rolle's and the Mean Value Theorems
- Taylor and Maclaurin Series
- Maxima and Minima of One Variable
- Optimisation in One Variable
+11 more
- 03
Probability
Counting through Markov chains: the complete probability syllabus, with every distribution derived and applied to worked numeric problems.
28 of 28 lessons on this track
- Counting, Permutations and Combinationsready
- Inclusion–Exclusion and Pigeonholeready
- Sample Spaces and the Axioms of Probabilityready
- Events, Independence and Mutual Exclusivityready
- Joint, Marginal and Conditional Probabilityready
- The Law of Total Probabilityready
+22 more
- 04
Statistics and Inference
From descriptive summaries to hypothesis tests, estimation theory, experiment design and causal reasoning.
22 of 23 lessons on this track
- Descriptive Statistics
- Skewness and Kurtosis
- Populations, Samples and Sampling Methods
- Sampling Distributions and Standard Error
- Point Estimation and Estimator Properties
- Maximum Likelihood Estimation
+16 more
- 05
Optimisation Algorithms
Linear and integer programming, duality, first-order and interior-point methods, metaheuristics and Bayesian optimisation.
26 of 27 lessons on this track
- The Optimisation Landscape
- Formulating an Optimisation Problem
- Linear Programming
- The Simplex Method
- Linear Programming Duality
- Sensitivity and Post-Optimality Analysis
+20 more
- 06
Game Theory
Strategic interaction from Nash equilibrium to mechanism design, Shapley values and the games hidden inside GANs and multi-agent systems.
24 of 25 lessons on this track
- What Game Theory Studies
- Normal-Form Games
- Dominance and Best Response
- Nash Equilibrium
- Mixed Strategies
- Nash's Existence Theorem
+18 more
- 07
Logic
Propositional through higher-order logic, proof systems, decidability, and the modal, temporal, description and non-classical families.
30 of 30 lessons on this track
- What Logic Is
- Propositional Logic
- Logical Equivalence and Laws
- Normal Forms: NNF, CNF and DNF
- Validity, Satisfiability and Entailment
- Natural Deduction
+24 more
- 08
Classical Artificial Intelligence
Search, adversarial games, planning, knowledge representation, and exact and approximate inference in Bayesian networks.
19 of 19 lessons on this track
- Agents and Environments
- Problem Formulation and State Spaces
- Uninformed Search
- Informed Search and A*
- Heuristics, Admissibility and Consistency
- Local Search and Metaheuristics
+13 more
- 09
Machine Learning Foundations
The concepts every algorithm shares: risk minimisation, generalisation, the bias–variance trade-off, validation and metrics.
16 of 20 lessons on this track
- What Machine Learning Actually Isready
- Formulating a Learning Problemready
- Empirical Risk Minimisationready
- Generalisation, Overfitting and Underfittingready
- The Bias–Variance Trade-offready
- The No Free Lunch Theoremready
+10 more
- 10
Supervised Learning
Every supervised algorithm on the syllabus, each derived from its objective, traced on small numeric data, then coded from scratch.
24 of 25 lessons on this track
- Simple Linear Regression
- Multiple Linear Regression
- Regression Assumptions and Diagnostics
- Polynomial and Basis Expansion Regression
- Ridge Regression
- Lasso and Elastic Net
+18 more
- 11
Unsupervised Learning
Clustering, dimensionality reduction, association rules and anomaly detection, each traced numerically and derived where it matters.
26 of 26 lessons on this track
- The Unsupervised Landscape
- Distance and Similarity Measures
- k-Means Clustering
- Initialisation and Choosing k
- k-Medoids and PAM
- Agglomerative Hierarchical Clustering
+20 more
- 12
Reinforcement Learning
Bandits and MDPs through to PPO: the full progression from tabular dynamic programming to deep policy-gradient methods.
26 of 26 lessons on this track
- The Reinforcement Learning Problem
- Multi-Armed Bandits
- Exploration Strategies
- Markov Decision Processes
- Returns, Policies and Value Functions
- The Bellman Equations
+20 more
- 13
Neural Networks and Deep Learning
Backpropagation derived and computed by hand, then optimisers, CNNs, RNNs, autoencoders, VAEs, GANs and diffusion models.
33 of 38 lessons on this track
- From Perceptron to Deep Networks
- The Universal Approximation Theorem
- Forward Propagation
- Backpropagation
- Backpropagation: A Complete Numeric Example
- Activation Functions
+27 more
- 14
Natural Language Processing
Tokenisation and n-grams through embeddings, attention and the complete transformer, with shapes traced end to end.
29 of 32 lessons on this track
- The NLP Pipeline
- Text Normalisation
- Stemming and Lemmatisation
- n-Gram Language Models
- Smoothing
- Perplexity
+23 more
- 15
Large Language Models
How modern LLMs are built, aligned, decoded, evaluated, served and turned into agents — with the mechanics, not the hype.
31 of 32 lessons on this track
- What an LLM Actually Is
- Decoder-Only Architecture in Detail
- Pretraining Objectives
- Pretraining Data Pipelines
- Scaling Laws
- Compute and Token Economics
+25 more
- 16
Graph Machine Learning
Spectral graph theory, PageRank and node embeddings through to GCN, GraphSAGE, GAT and graph transformers.
25 of 26 lessons on this track
- Graph Theory Refresher
- Representing Graphs for Learning
- The Graph Laplacian
- Spectral Graph Theory
- Centrality Measures
- PageRank
+19 more
- 17
Practice Vault
Formula sheets, banks of fully solved problems, GATE-DA style question sets and interview preparation.
9 of 11 lessons on this track
- Formula Sheets
- Solved Problems: Probability
- Solved Problems: Linear Algebra
- Solved Problems: Statistics
- Solved Problems: Machine Learning
- Solved Problems: Deep Learning
+3 more