Instead of a monolithic PDF, some learners prefer targeted solutions. The user saz and Did (now inactive) provided definitive solutions to Williams’ most infamous problems, such as:
Ironically, the very act of hunting for the best solutions teaches you something: Williams’ exercises often have multiple valid solution paths. Comparing solutions from Wood, MathStackExchange, and GitHub reveals the creativity hidden in the problems.
The problems are not merely drills; they are extensions of the theory. Solving them is essential to truly "owning" the material. Where to Find the Best Solutions
Use the search: [probability] [martingales] Williams exercise X.Y on MathStackExchange. The best answers are those that have upvotes > 10 and a comment from the original poster confirming the solution.
David Williams’ Probability with Martingales is a staple text for second-year probability courses at Cambridge and a rite of passage for aspiring mathematicians. It is renowned for its elegance, brevity, and the author's distinct voice—often witty, sometimes cryptic, but always rigorous.
: Check with your university library’s digital repository or ask a course instructor. Some professors keep a copy for teaching assistants.
