The textbook for this class is Algorithm Design, by Jon Kleinberg and Éva Tardos.
Your grade in the course will be determined by your performance on two in-class midterm exams (20% each), a takehome final exam (20%), and homework (40%).
Working with your classmates is generally a good thing. Sharing insights can be fun, and can enhance everybody's learning. The main danger of collaborating on course work is in allowing your collaborator to do all the work, and thus all the learning. You may work with others on assignments for this class, but each of you should write up solutions separately. If you get ideas from other people or on-line or off-line resources, cite your sources clearly.