Mathematics for Machine Learning and Data Science Specialization Course Syllabus

Overview: This specialization provides a beginner-friendly introduction to the mathematical foundations essential for machine learning and data science. Over approximately 3 months with a commitment of 5 hours per week, learners will build a solid understanding of linear algebra, calculus, probability, and statistics through intuitive explanations, visualizations, and hands-on Python programming exercises. The course is structured into three core modules followed by applied projects, each designed to reinforce theoretical concepts with practical implementation in real-world machine learning contexts. Lifetime access allows flexible learning at your own pace.

Module 1: Linear Algebra for Machine Learning and Data Science

Estimated time: 16 hours

• Vectors and vector operations
• Matrices and matrix properties (rank, singularity, linear independence)
• Matrix operations: dot product, inverse, determinants
• Eigenvalues and eigenvectors
• Applications in Principal Component Analysis (PCA)

Module 2: Calculus for Machine Learning and Data Science

Estimated time: 12 hours

• Derivatives and gradients
• Optimization of functions using calculus
• Visualizing differentiation and its role in models
• Gradient descent algorithms
• Activation and cost functions in neural networks

Module 3: Probability & Statistics for Machine Learning & Data Science

Estimated time: 16 hours

• Probability distributions and their properties
• Exploratory data analysis for pattern identification
• Quantifying uncertainty using confidence intervals and p-values
• Hypothesis testing
• Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP)

Module 4: Python Programming for Mathematical Applications

Estimated time: 10 hours

• Implementing linear algebra operations in Python
• Using calculus for optimization in code
• Data analysis with probability and statistics
• Interactive lab exercises with visualizations

Module 5: Mathematical Foundations Review and Integration

Estimated time: 8 hours

• Connecting linear algebra, calculus, and statistics
• Interpreting mathematical concepts in ML contexts
• Problem-solving strategies across domains

Module 6: Final Project

Estimated time: 12 hours

• Apply linear algebra in a PCA-based data reduction task
• Implement gradient descent to optimize a cost function
• Analyze a dataset using statistical inference and hypothesis testing

Prerequisites

• Familiarity with basic Python programming
• High school level mathematics background
• Basic understanding of functions and graphs

What You'll Be Able to Do After

• Understand and apply core mathematical concepts in machine learning algorithms
• Use Python to implement mathematical techniques in data science tasks
• Interpret and visualize mathematical operations behind ML models
• Analyze data using statistical methods and quantify uncertainty
• Optimize machine learning models using calculus-based techniques