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MATH 101: Linear Algebra for Machine Learning
Course Code MATH 101
Course Name Linear Algebra for Machine Learning
Department Mathematics
Semester Offered Odd (Term 1)
Tuition Hours 30 hours
Course Level Foundational
Pre-requisite -
Co-requisite MATH 102: Calculus for Machine Learning
Course Objective Linear Algebra is the operating system of modern AI. Every model your students will build this term, whether it's a recommendation engine, chatbot, or autonomous agent, runs on vector representations and matrix operations under the hood.

This course is not about solving textbook problems for the sake of it. It is about understanding what your model is actually doing when it “learns.” When a neural network adjusts weights, it is transforming space. When embeddings are created, they are positioning meaning in high dimensions.

The goal is simple: they should be able to reason about data geometrically, debug models intelligently, and avoid treating machine learning as a black box.
Course Philosophy This course emphasizes
  • Geometry before formulas
  • Intuition before notation
  • Application before abstraction
We do not chase mathematical completeness. We focus on what actually shows up when you build AI products. If a concept does not help you ship or debug something in Term 1, it does not belong here.
Course Learning Outcomes Upon successful completion of this course, students will be able to:
  • Represent real-world data as vectors and understand feature spaces.
  • Work with matrices as transformations, not just tables of numbers.
  • Understand dot products, similarity, and distance, and apply them in search, ranking, and recommendations.
  • Interpret eigenvalues and eigenvectors in the context of dimensionality reduction and embeddings.
  • Reason about what happens inside a neural network layer, at least at a conceptual geometric level.
  • Debug simple ML models using linear algebra intuition, instead of trial-and-error coding.
Course Author Sagar Udasi
MSc Statistics and Data Science with Computational Finance from The University of Edinburgh.
Contact: sagar.l.udasi@gmail.com
Course Organiser TBD
No. Lecture Title Concepts Covered Lecture Objective
01 Why Everything You Build Starts As A Vector Vectors, feature representation, high-dimensional data Students understand that every input (text, image, user behavior) must be converted into vectors before AI can use it. Direct link to their Term 1 product inputs.
02 The Geometry of Similarity Dot product, cosine similarity, norms Teaches how systems measure similarity. Critical for search, recommendations, and ranking in their AI microbusiness.
03 Matrices Are Functions, Not Tables Matrix multiplication, linear transformations Students see matrices as transformations of space, which directly maps to neural network layers.
04 What Actually Happens Inside One Neural Layer Weighted sums, affine transformations Connects linear algebra directly to forward pass in neural networks. Removes black-box thinking.
05 When Data Lives in 1000 Dimensions High-dimensional spaces, curse of dimensionality Helps students reason about embeddings and why intuition from 2D fails in ML systems.
06 Projection: Extracting What Matters Vector projection, subspaces Teaches how models focus on relevant features. Useful in feature selection and embeddings.
07 Orthogonality: The Idea of Independence Orthogonal vectors, independence Connects to uncorrelated features and clean representations in ML models.
08 The Magic Behind Dimensionality Reduction Eigenvalues, eigenvectors, PCA intuition Students learn how systems compress information. Useful for building efficient AI systems.
09 When Your Model Is Learning… What Is Actually Changing? Basis change, transformations, parameter updates Helps students interpret training as movement in vector space, not just loss minimization.
10 When Linear Algebra Breaks (And Why It Still Works) Limits of linearity, non-linearity intuition Prepares students to understand why neural networks stack linear layers with activations.
11 Embeddings: Turning Meaning Into Coordinates Embedding spaces, semantic similarity Direct application to LLMs, search, and AI agents they will build.
12 Building a Simple Recommendation Engine Vector similarity in practice Students implement a small system using similarity measures. Immediate product relevance.
13 Debugging Models With Geometry Visualizing errors, vector intuition Moves students away from blind tuning toward structured debugging.
14 Speed Matters: Efficient Matrix Computation Sparse matrices, computational tricks Helps students build systems that actually scale within constraints.
15 From Equations to Code Translating math to NumPy/Python Bridges gap between theory and implementation for their projects.
16 Case Study: How Your AI Agent Uses Linear Algebra Real-world system breakdown Shows how all concepts tie into their Term 1 AI agent.
17 Lab: Fixing a Broken Model Applied debugging session Students apply concepts to fix an intentionally flawed model.
18 Lab: Improving Recommendations Optimization using similarity tweaks Iteration mindset applied to a working system.
19 Project Integration Review Applying concepts to student projects Ensures students are actually using linear algebra in their product.
20 Final Synthesis: Thinking in Vectors Conceptual integration Students leave with a mental model, not a bag of formulas.
Component Weightage
Written Examination (2 hours) 50%
Practical Assignments (2 total) 30%
Project Integration (Applied to Term 1 AI Product) 20%
Type Resource Provider
Lecture MIT 18.06 Linear Algebra Prof. Gilbert Strang
Lecture Essence of Linear Algebra 3Blue1Brown (Grant Sanderson)
Reading Linear Algebra and Its Applications Gilbert Strang
Practical NumPy Linear Algebra Documentation NumPy
Practical CS231n: Linear Algebra Review Stanford University