The Math of Large Language Models Transformer Architectures

What you'll learn

⚡ Master the core principles of Self-Attention Mechanics.
⚡ Deconstruct the architecture and tradeoffs of Multi-Query Attention (MQA).
⚡ Analyze the design patterns governing KV Caching.
⚡ Build a deep mental model of Positional Encodings (RoPE) at scale.

Requirements

❗ No coding experience is required. We focus entirely on system design and core theoretical concepts.
❗ A basic interest in technology systems, algorithms, or computer science architecture.
❗ No special software or local development environment setup is needed.

Description

"This course contains the use of artificial intelligence."
Build a Deep Mathematical Understanding of Modern LLMs — Without Writing a Single Line of Code
Large Language Models are transforming the future of AI, but understandingwhy they work is far more valuable than simply learning how to use them. This course is designed to help you master the mathematical foundations and architectural principles behind Transformer-based models without requiring any programming experience.
Rather than focusing on coding frameworks or implementation details, you'll develop the conceptual thinking needed to understand how modern language models process information, scale efficiently, and make intelligent predictions.
Whether you're an AI professional, researcher, student, or technology leader, this course provides the theoretical foundation required to confidently understand and discuss modern LLM architectures.

What you'll learn

✨ Build a strong mathematical foundation in linear algebra, vectors, matrices, probability, optimization, and neural network fundamentals.
✨ Understand how Transformer architectures revolutionized Natural Language Processing.
✨ Master the mathematics behind Self-Attention and why it enables context-aware language understanding.
✨ Learn how Multi-Query Attention (MQA) improves inference efficiency while reducing computational costs.
✨ Explore KV Caching and understand how modern LLMs generate text efficiently.
✨ Discover Rotary Positional Embeddings (RoPE) and other positional encoding techniques.
✨ Analyze computational complexity, memory

Requirements

, and scalability trade-offs in Transformer architectures.
✨ Understand embedding spaces, token representations, and semantic relationships.
✨ Explore gradient propagation, optimization strategies, and training dynamics.
✨ Study reinforcement learning concepts that contribute to modern language model alignment.
✨ Learn Explainable AI principles, model auditing, and responsible AI governance.
✨ Identify common architectural anti-patterns and understand best practices for designing scalable AI systems.
Course Curriculum
Module 1: Mathematical Foundations
✨ Linear Algebra for Deep Learning
✨ Matrix Operations and Vector Spaces
✨ Probability and Statistics
✨ Calculus for Optimization
✨ Gradient Descent Fundamentals
Module 2: Neural Networks
✨ Artificial Neural Networks
✨ Forward and Backward Propagation
✨ Activation Functions
✨ Loss Functions
✨ Optimization Algorithms
Module 3: Transformer Architecture
✨ Evolution from RNNs to Transformers
✨ Encoder-Decoder Architecture
✨ Tokenization Concepts
✨ Embedding Representations
✨ Transformer Pipeline
Module 4: Self-Attention Mathematics
✨ Query, Key, and Value Vectors
✨ Scaled Dot-Product Attention
✨ Attention Weight Calculations
✨ Multi-Head Attention
✨ Mathematical Intuition Behind Attention
Module 5: Multi-Query Attention (MQA)
✨ Motivation Behind MQA
✨ Computational Advantages
✨ Memory Optimization
✨ Performance Trade-offs
✨ Practical Design Considerations
Module 6: KV Caching
✨ Key-Value Memory Mechanism
✨ Autoregressive Inference
✨ Cache Management
✨ Latency Optimization
✨ Real-World LLM Inference
Module 7: Positional Encoding
✨ Why Position Information Matters
✨ Sinusoidal Positional Encoding
✨ Rotary Positional Embeddings (RoPE)
✨ Relative Position Encoding
✨ Long-Context Modeling
Module 8: Architecture Trade-offs
✨ Compute vs Memory
✨ Latency vs Accuracy
✨ Model Scaling Laws
✨ Context Window Considerations
✨ Efficient Transformer Design
Module 9: NLP and Embedding Geometry
✨ Word Embeddings
✨ Semantic Vector Spaces
✨ Similarity Metrics
✨ Contextual Representations
✨ Language Understanding
Module 10: Advanced AI Concepts
✨ Reinforcement Learning Fundamentals
✨ Explainable AI
✨ Model Auditing
✨ Ethical AI Principles
✨ Future Directions of Large Language Models
Why Take This Course?
✨ No programming required
✨ Strong emphasis on mathematical intuition
✨ Clear visual and conceptual explanations
✨ Covers the core building blocks of modern LLMs
✨ Ideal preparation for advanced AI and Machine Learning studies
✨ Designed for long-term conceptual understanding rather than memorizing implementation details

Who this course is for

⭐ AI Engineers, Software Architects, Research Students

Homepage

https://www.udemy.com/course/the-math-of-large-language-models-transformer-architectures

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