The William Lowell Putnam Mathematical Competition takes place every year during the first Saturday of December all around the United States, Canada and other countries around the globe. Every undergraduate student is welcome to participate, the prizes are high and there is nothing to loose.

The official MAA Putnam competition website.

Putnam 2020+:

Students should self-register at the MAA website

Putnam 2019:

This year's Putnam at USC will take place on Saturday December 7, 2019, morning session 8am-11am, afternoon session 1pm-4pm, lunch provided in the 11am-1pm break.

Location: KAP 414.

Time: 8am-4pm (with 2 hour break).

Registration: NO prior registration required, forms will be filled out on the spot. Just come at 8am to KAP 414.

Resources:

The USC Math 395 course

The Putnam archive by Kiran Kedlaya

Art of Problem Solving's Olympiad Books list (be sure to check out their forums too)