A practical and mathematical guide to instruction fine-tuning, multi-task learning, catastrophic forgetting, PEFT, LoRA, soft prompts, and QLoRA.

A complete path from pretraining objectives and memory accounting to mixed precision, DDP, ZeRO, FSDP, compute-optimal scaling, and BloombergGPT as a domain-model case study.

A unified guide from next-token decoding and testable prompts to tools, lexical and dense retrieval, HNSW, reranking, evidence-grounded generation, and RAG debugging.

From sentence probabilities and n-grams to neural language models, learned word embeddings, GloVe, and the geometry behind semantic similarity and analogies.

Why linear classifiers fail on XOR, how multilayer perceptrons learn nonlinear features, what activation functions contribute, and what universal approximation does—and does not—guarantee.

A practical path from two-sided markets and contract mechanics to payoff engineering, put-call parity, volatility, Greeks, and the dynamic hedging loop used to manage an options book.

A practical competition guide to selecting problems, building a reliable toolchain, learning from strong papers, reproducing visual evidence, extending algorithms, and using AI without surrendering judgment.

From contextual word embeddings and attention to Transformer blocks, sparse experts, BERT, GPT-3, and LLaMA—with the equations, tensor shapes, and design choices explained.

A practical bridge from entity-relationship diagrams and cardinality constraints to keys, relational algebra, set semantics, joins, and optimizer freedom.

Derive LP, QP, and SOCP models from decisions, solve them geometrically and algebraically, and audit a real CUMCM crop-planning case.