• Problems 1 highlights a crucial difference between connections and preconnections.
• Problem 2 is an exercise in unravelling notation.
• Problems 3 and 4 concern a specific connection on $TS^n$.
• Problem 5 asks you to show that any bundle over an interval is trivial.
• Problem 6 shows that Proposition 29.9 can be improved when working with a connection on a vector bundle.