Essential Linear Algebra for Data Science Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview: This course provides a practical, hands-on introduction to linear algebra as it applies to data science, designed for learners with basic Python knowledge. Over approximately 12-18 weeks of flexible study, students will progress from foundational concepts to real-world applications, including PCA, NLP, and image processing. Each module blends theory with Python implementation using NumPy, emphasizing computational efficiency and practical problem-solving in data contexts.
Module 1: Foundations of Linear Algebra
Estimated time: 12 hours
- Vectors, matrices, and tensor fundamentals
- Matrix multiplication and inversion
- Solving systems of linear equations
- Computational complexity considerations
Module 2: Matrix Decompositions
Estimated time: 16 hours
- LU and QR decompositions
- Eigendecomposition theory and applications
- Singular Value Decomposition (SVD) deep dive
- Practical implementations in Python
Module 3: Applications in Data Science
Estimated time: 20 hours
- PCA for dimensionality reduction
- Linear regression through matrix formulations
- Word embeddings and latent semantic analysis
- Image processing with matrix transformations
Module 4: Advanced Topics
Estimated time: 10 hours
- Tensors for deep learning
- Graph theory adjacency matrices
- Sparse matrix optimizations
Module 5: Real-World Case Studies
Estimated time: 8 hours
- Implementing SVD for recommendation systems
- Image compression using PCA and SVD
- NLP embeddings with linear algebra
Module 6: Final Project
Estimated time: 10 hours
- Apply PCA to a real dataset for dimensionality reduction
- Implement SVD for collaborative filtering or image compression
- Submit a Jupyter notebook with analysis and visualizations
Prerequisites
- Basic Python proficiency
- Familiarity with Jupyter notebooks
- High school level algebra
What You'll Be Able to Do After
- Master matrix operations and their computational efficiency in data tasks
- Understand vector spaces and transformations for dimensionality reduction
- Apply eigenvalues and eigenvectors to principal component analysis (PCA)
- Learn singular value decomposition (SVD) for recommendation systems
- Implement linear algebra concepts in Python using NumPy