Algebra and Differential Calculus for Data Science Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview (80-120 words) describing structure and time commitment.
Module 1: Linear Algebra for Data Science
Estimated time: 12 hours
- Vector and matrix operations and properties
- Linear transformations and their applications
- Eigenvalues and eigenvectors in data contexts
- Singular Value Decomposition (SVD) for dimensionality reduction
Module 2: Differential Calculus Foundations
Estimated time: 16 hours
- Multivariable functions and partial derivatives
- Chain rule in multiple dimensions
- Gradient vectors and directional derivatives
- Visualizing gradients in high-dimensional spaces
Module 3: Optimization for Machine Learning
Estimated time: 16 hours
- Gradient descent algorithms: batch and stochastic
- Convexity and its role in loss functions
- Mathematics of backpropagation
- Convergence analysis and learning rate selection
Module 4: Mathematical Foundations of Neural Networks
Estimated time: 12 hours
- Linear algebra in neural network layers
- Activation functions and Jacobian matrices
- Weight updates using differential calculus
Module 5: Practical Applications in Data Modeling
Estimated time: 14 hours
- Implementing linear regression from scratch
- Building a basic neural network layer in Python
- Optimization case studies using real datasets
Module 6: Final Project
Estimated time: 10 hours
- Design and train a minimal neural network using first principles
- Apply SVD for feature compression in a regression task
- Document mathematical reasoning and code implementation
Prerequisites
- Familiarity with basic algebra and functions
- Basic Python programming fluency
- Understanding of fundamental data structures (arrays, lists)
What You'll Be Able to Do After
- Apply linear algebra to real-world data modeling problems
- Compute and interpret gradients for multivariable models
- Implement gradient descent and backpropagation from scratch
- Use SVD and eigen-analysis for dimensionality reduction
- Build foundational understanding for deep learning architectures