Concentration inequalities

People join this course to build a strong theoretical foundation in probability that is essential for advanced studies and research in data science, machine learning, artificial intelligence, and applied mathematics. It is particularly valuable for students preparing for research-oriented careers, higher education, or competitive exams, as concentration inequalities are frequently used in analyzing algorithms and large-scale data behavior. Learners also benefit from understanding how uncertainty and randomness are controlled in real-world systems

1. Review of probability theory and random variables

2. Markov and Chebyshev inequalities

3. Hoeffding’s inequality

4. Chernoff and Bernstein bounds

5. Azuma–Hoeffding inequality and martingales

6. McDiarmid’s inequality

7. Sub-Gaussian and sub-exponential random variables

8. Applications in machine learning and randomized algorithms

9. High-dimensional probability concepts