The CS department is now strictly enforcing the CS 173 and CS 225 prerequisites. Students must have credit for both courses (either through taking the class, passing the proficiency exam, or transferring credit from an equivalent course taken elsewhere) before they can register for 374.
The algorithms portion of the class largely follows Jeff's Algorithms textbook, which is freely available online. The book web site also contains lots of additional lecture notes, along with homeworks, lab handouts, and exams (but no solutions) from his past theory classes.
You may also find resources from other Illinois instructors useful:
Jeff's videos from Spring 2018 are also publicly available.