Mathematics and Machine Learning Foundations: concepts and vocabulary | Complete Generative AI: From Foundations to Production
A self-paced 26-week learning path with 15 modules: AI foundations, Python, machine learning, transformers, LLMs, prompts, APIs, embeddings, RAG, frameworks, agents, customization, multimodal AI, Spring Boot with React, and production LLMOps. Includes 15 practical assignments and three portfolio projects.
Prerequisites: Begin with basic computer skills. Programming is introduced in Weeks 2–3. Use a local Python environment for coding labs; Java and React experience helps in Weeks 21–22. Model downloads, provider accounts and deployment resources are optional learner-managed dependencies. The 26-week schedule is suggested; reading estimates exclude independent project work.
Learning goals
Vectors, matrices and dot products
Probability and statistics
Gradient descent and optimization
Supervised and unsupervised learning
Neural networks, loss functions and backpropagation
Understand the foundations
A vector is an ordered list of numbers; a matrix can represent a batch of vectors or a linear transformation. The dot product multiplies corresponding components and sums them. Probability models uncertainty, while a sample statistic estimates a property of a larger population. Classification learns labels from examples; clustering groups examples without supplied labels. Neither a high training score nor a visually tidy cluster proves that a model will generalize to new data.
Connect the ideas
Training minimizes a loss measuring mismatch between predictions and targets. Gradient descent adjusts parameters in the direction opposite the loss gradient; the learning rate controls step size. A neural network composes transformations and nonlinearities, and backpropagation applies the chain rule to obtain gradients. Keep training, validation and test purposes separate. Fit vocabulary and preprocessing only on training data. Duplicate documents across splits can make evaluation look excellent while hiding poor performance on new documents.
Checkpoint: explain these concepts in your own words, then describe one failure that the design must detect. Use synthetic or permissioned data throughout the course.
01. Introduction to Artificial Intelligence · Week 1
02. Python Programming for Gen AI · Weeks 2–3
03. Mathematics and Machine Learning Foundations · Week 4
04. Deep Learning and Transformers · Weeks 5–6
05. Large Language Models (LLMs) · Weeks 7–8
06. Prompt Engineering · Weeks 9–10
07. Generative AI APIs and Application Development · Week 11
08. Embeddings and Vector Databases · Weeks 12–13
09. Retrieval-Augmented Generation (RAG) · Weeks 14–15
10. LangChain, LlamaIndex and AI Frameworks · Week 16
11. AI Agents and Agentic AI · Weeks 17–18
12. Fine-Tuning and Model Customization · Week 19
13. Multimodal Generative AI · Week 20
14. Gen AI with Java Spring Boot and React · Weeks 21–22
15. Production Gen AI, LLMOps and Capstone · Weeks 23–26