From Linear Algebra to Agentic AI

I am planning to revise basics and learn a few new topics along the way. Follow along if you are interested…

The progression builds foundational math, moves into machine learning (ML), deep learning (DL), reinforcement learning (RL), and culminates in agentic AI: autonomous AI systems that can plan, reason, and act in complex environments.

Mathematical Foundations

Apply math as the base layer.

• Linear Algebra Basics: Vectors, matrices, linear transformations, eigenvalues/eigenvectors, vector spaces.
• Advanced Linear Algebra + Calculus: Singular value decomposition (SVD), matrix factorization; derivatives, integrals, multivariable calculus, gradients.
• Probability and Statistics: Probability distributions, Bayes’ theorem, hypothesis testing, regression basics.

Machine Learning Fundamentals

Apply math to supervised and unsupervised learning.

• ML Overview and Supervised Learning: Regression, classification, overfitting/underfitting.
• Algorithms Deep Dive: Decision trees, SVMs, k-NN, ensemble methods.
• Unsupervised Learning and Evaluation: Clustering (k-means), dimensionality reduction (PCA), metrics (AUC, F1-score).

Deep Learning

Shift to neural networks, which power modern AI.

• Neural Networks Basics: Perceptrons, activation functions, backpropagation, optimizers.
• Convolutional and Recurrent Networks: CNNs for images, RNNs/LSTMs for sequences.
• Advanced DL Topics: Transfer learning, GANs, attention mechanisms.

Reinforcement Learning

Learn how agents learn from interactions — key for agentic AI.

• RL Fundamentals: Markov decision processes, Q-learning, policy gradients.
• Deep RL: DQN, actor-critic methods, PPO.
• Advanced RL: Multi-agent RL, exploration strategies.

Agentic AI

Focus on autonomous agents that reason, plan, and use tools.

• AI Agents Basics: Agent architectures, planning (e.g., ReAct), tool use.
• Multi-Agent Systems: CrewAI or AutoGen frameworks, collaboration between agents.
• Advanced Agentic AI and Ethics: Scalable oversight, safety in agents, real-world applications (e.g., robotics, web agents).