Learning Paths

Build the linear algebra, statistics, probability, and calculus intuition every ML algorithm assumes. You start with vectors and matrix products and finish by computing Jacobians and Hessians by hand. This is the path to take if you want the math to stop feeling like magic.

Implement the classic machine learning toolkit with nothing but Python lists and loops. You will build regression, k-NN, k-means, decision trees, naive Bayes, PCA, and boosting, plus the metrics that tell you whether they work. Ideal for anyone who has called fit() and predict() but never written them.

Activations, forward passes, and backprop, built one function at a time. You will go from ReLU and dense layers up through batch norm, attention, and a full transformer encoder block, with a little tokenization to feed the models. Perfect before you touch a framework, because you will recognize what every layer is doing.

How models actually learn: gradients, momentum, adaptive methods, and the schedules that decide whether training converges. You will implement gradient descent, Adam, and learning rate policies, then reach the quasi-Newton methods used in serious solvers. Take it after ML From Scratch or Deep Learning Essentials.

A complete tour of the matrix machinery behind ML, from dot products to spectral decompositions. You will implement row reduction, LU, Cholesky, Gram-Schmidt, power iteration, and PageRank steps from scratch. Suited to learners who want to reason about rank, conditioning, and eigenvalues fluently.

Derivatives, gradients, Jacobians, and Hessians, all computed numerically so you can verify any formula by hand. You will build finite differences, Newton and RK methods, Lagrange multipliers, and convolution integrals. Designed for learners who want optimization and backprop to rest on real calculus rather than hand-waving.

The language of uncertainty, from counting and expectation to Markov chains and concentration bounds. You will implement Bayes rule, classic distributions, inclusion-exclusion, gambler's ruin, and a CLT simulation. A good fit for interviews and for anyone starting probabilistic ML.

Turn data into decisions: descriptive statistics, sampling distributions, hypothesis tests, and robust methods. You will implement t-tests, confidence intervals, bootstrap resampling, rank correlations, and multiple-comparison corrections. Best for aspiring data scientists and analysts who need to defend their conclusions.

Text into numbers, from tokenization and n-grams to TF-IDF, edit distance, and attention. You will build the preprocessing pipeline behind search engines and language models with plain Python. Start here if you want to understand what happens before a model sees a sentence.

Images as grids of numbers, then as features a model can use. You will implement grayscale conversion, padding, convolution, pooling, Gaussian blur, edge detection, and Otsu thresholding from scratch. A hands-on introduction for anyone curious how CNNs see.

The highest-yield coding interview patterns in one sequence: two pointers, sliding windows, dynamic programming, heaps, and graph search. You will solve the canonical problems that show up in FAANG screens, implemented in pure Python. Built for interview season, not for casual browsing.

The containers that make algorithms fast, implemented by hand. You will build stacks, queues, linked lists, heaps, tries, BSTs, union-find, and caches, then wire them into classic problems. Essential for interviews and for anyone who wants to know what a library really does.

Agents that learn by acting: MDPs, value iteration, Q-learning, and policy gradients. You will begin with policy evaluation and bandits, then implement TD updates, SARSA, and REINFORCE from scratch. A gentle on-ramp before tackling deep RL.

Data that moves through time, modeled from first principles. You will build differencing, smoothing, autocorrelation, AR/MA simulation, Holt-Winters, and Yule-Walker solvers without a single library. Suited to analysts and ML engineers working with metrics, demand, or finance.

Networks traversed properly: BFS, DFS, shortest paths, MSTs, PageRank, and max flow. You will implement Dijkstra, Kruskal, Kosaraju-style components, centrality measures, and matching from scratch. Great preparation for both interviews and data-centric engineering work.

How much does a message tell you? Build entropy and mutual information from scratch, compress with real source codes, and finish with KL divergence, channel capacity, and the limits of processing. You will implement Huffman and Shannon codes, Kraft's inequality, arithmetic coding, and the data-processing gap. Perfect for the mathematically curious.

Beyond the basics: modern activations, normalization variants, efficient attention, and quantization. You will implement GELU, group norm, multi-query attention, int8 quantization, and BPTT by hand, then compute the memory and FLOPs budgets of real models. Take it once you are comfortable with backprop.

The production-minded sequence: solid fundamentals, training dynamics, evaluation, and the systems math behind serving models. You will move from standard scalers and loss functions to backprop, model diagnostics, and memory accounting. Built for engineers who ship models, not just notebooks.

From summary statistics to causal inference, the full analyst toolkit. You will compute robust descriptives, build and evaluate regression and classification baselines, measure relationships and run hypothesis tests, then finish with causal estimators and ranking curves. The right path if your job is turning messy data into defensible decisions.

Probability brainteasers, statistics, and fast algorithms, sequenced the way trading interviews ask them. You will drill counting, Bayes, and distributions, then algorithmic classics, then gambler's ruin and the limit theorems, until they are automatic. Timed practice recommended once you finish.

A month-long sampler that touches nearly every category on the platform, roughly one sitting per day. You will meet vectors, derivatives, distributions, regressions, neural nets, algorithms, graphs, and information theory in a single sweep. Ideal if you are new and want to discover which track to commit to next.

The shortest route to a working mental model of ML: eighteen problems that cover what the rest of the platform builds on. In a single evening you will implement scaling, matrix products, a derivative, expectation, linear regression, softmax, gradient descent, and one backprop pass. Perfect for a first taste of DeepForge.

How models create text and images: start with language-model sampling and alignment, then diffusion, then VAEs, and finish with GANs and sample-quality metrics. You will implement reconstruction and KL losses, diffusion noise schedules, classifier-free guidance, and preference-optimization objectives. Best for learners who already know backprop and want the generative frontier.

Search relevance and recommender systems, built from the retrieval stage to the ranking metrics. You will implement TF-IDF, inverted indexes, BM25, collaborative filtering, and NDCG from scratch. A strong fit for ML engineers working on feeds, search, or personalization.

Build and operate language models end to end: tokenization, embeddings, transformer internals, decoding and serving, then retrieval-augmented generation and evaluation. Every stage is implemented in pure Python, from byte-level BPE counts to KV-cache sizing and nDCG. Take it after Deep Learning Essentials and NLP Starter.

A single sequence for the mathematics ML actually uses: linear algebra first, then probability and statistics, then calculus, then eigen-decomposition. You implement every operation by hand, from dot products to Jacobians and t-statistics. Start here if you want one path that covers the whole mathematical toolkit.

The applied forecasting workflow, from raw timestamps to monitored production forecasts. You will engineer lag and rolling features, establish baselines, fit smoothing and seasonal models, then validate with rolling-origin backtests and decay monitoring. Complements Time Series Forecasting with a stronger machine-learning and ops flavour.

Representation learning on graphs: message passing, pooling, and normalized adjacency first, then centrality and similarity for link prediction, then embeddings with random walks, LINE, and WL kernels. Finish by training GNN-style layers and finding communities spectrally. Take it after Graph Algorithms and Deep Learning Essentials.

The deep-learning side of vision, from convolution arithmetic to ViTs and depth. You will count the FLOPs and parameters of modern conv blocks, fold batch norm, schedule augmentations, match anchors, score detections and segmentations, and patchify images for transformers. Take it after the vision starter and the deep-learning essentials.

Everything between a trained model and a live endpoint: training-system budgets, quantization, batching, KV-cache capacity, and drift monitoring. You will estimate throughput and memory, quantize weights and caches, size continuous batching, and decide when to retrain. Take it after the ML engineer track or the deep-learning essentials.

Turn raw tables and event streams into trustworthy model inputs. You will construct interactions, bins, and crossings, build lag and rolling features, split honestly without leakage, detect drift and duplicates, and sketch streams with HyperLogLog, Space-Saving, t-digest, and reservoir sampling. Take it after ML From Scratch and Statistics Mastery.

The capstone: assemble a working transformer from first principles, one component at a time. Tokenization and embeddings feed scaled attention, attention assembles into a block, masks and a stable loss train it, and caches plus FLOPs let you decode and measure it. Several problems intentionally revisit Deep Learning Essentials and LLM Engineering; that repetition is spaced review, not filler, and it is how the pieces finally lock together. Take it after Deep Learning Essentials.

Go beyond correlation to what actually changes outcomes. You will estimate propensity scores, weight and trim samples for average treatment effects, adjust with causal forests and quasi-experiments, build uplift models with trusted calibration, and test time-aware causality with Granger and cointegration tools. Take it after Statistics Mastery.