1. Matrix theory
2. Vector differentiation
3. Random variables
4. Gaussian distribution
5. Exponential distributions
6. Entropy and divergence
7. Random processes
8. Convex functions;
9. Convex optimization;
10. Lipschitz conditions
11. Proximal operator
12. Gradient descent method
13. Conjugate gradient method
14. Subgradient method
15. Proximal and mirror descent methods
16. Stochastic optimization
17. Adaptive gradient methods
18. Gradient noise
19. Convergence analysis I: Stochastic gradient algorithms
20. Convergence analysis II: Stochasic subgradient algorithms
21: Convergence analysis III: Stochastic proximal algorithms
22. Variance-reduced methods I: Uniform sampling
23. Variance-reduced methods II: Random reshuffling
24. Nonconvex optimization
25. Decentralized optimization I: Primal method
26: Decentralized optimization II: Primal-dual methods

Written in an engaging and rigorous style by a world authority in the field, this is an accessible and comprehensive introduction to core topics in inference and learning. With downloadable Matlab code and solutions for instructors, this is the ideal introduction for students of data science, machine learning, and engineering.