Leading an Academic "Book Club" Short form: How should one lead a collaborative "book study group" amongst one's peers, particularly when the leader does not have deep prior knowledge of the book?

Long form: I'm an undergraduate CS student&dagger; (rising junior).  In the remaining time before I graduate, I thought it would be a fun idea to read a volume of Knuth's Art of Computer Programming each semester and work some of the problems.  Since I know others in the department might be interested in studying this work, I decided I would organize a "book club" where we read ~40-50 pages a week and then meet up to discuss what we read and/or solutions to exercises that we have solved.

So, my biggest question is: Besides solutions to exercises in the book or clarifications on what we read, what else should or could be discussed during our weekly meetings?

There are plenty of resources online about "how to lead a book club," but they all primarily focus on literature/story analysis, etc., not something suited for scientific writing.  Many book clubs will have a time where they read a chapter aloud, which also is not applicable to Knuth's work.  I feel as though I'm searching for the wrong term when I use the phrase "book club."  Is there a standard term for this form of study group that I could use in searches?  

Furthermore, I have not read AoCP before.  Thus, I don't have a strong basis of knowledge upon which I could draw to guide discussion.  Obviously, a great solution would be to get a professor or grad student who has read AoCP to act as a mentor for the group; however, I do not know if any have done so--assume for sake of this question that such a mentor is not available.



&dagger;I know that issues facing undergraduates are generally off-topic here.  However, I believe this situation could also be faced by a grad student or a postdoc--the primary difference would be the difficulty of the source material they are studying.  I simply mention my background so readers may understand where I'm coming from.
I ran one of these a few years back. Here's what we did:

Start by publicizing the idea with your friends/colleagues and setting up an initial meeting. You'll get a sense prior to the meeting whether there's interest. The more advertising you do here the higher chance you'll actually have a showing at the first meet.

At the first meet, re-state the purpose—group of people working through the ideas in the book—and decide the meeting cadence (weekly, biweekly, monthly). This is important; reading through books like this take time, and for the group to work it's critical that people actually read the content and come prepared to discuss questions. You need to give enough time to let them read, and not so much that they'll forget what they read.
On this note, we also split the book up by chapter (we were reading [Elements of Statistical Learning](http://statweb.stanford.edu/~tibs/ElemStatLearn/, chapter splits made sense there). You may decide to split by topic or whatever else. The main idea is to ensure that everyone's on the same page, and comes to the next meet prepared to discuss the same content.

During the break, read up on content. As the group leader/organizer you may want to take notes on what you read to prompt discussion (itemize points covered, questions you thought of, points for discussion). Send out one or two emails reminding them about it.

At the first meet, come with discussion points and be prepared to lead a discussion, as it's likely no one else will take the lead. You don't have to be an expert, you just have to lead the conversation and bring up talking points. If you're not comfortable in this role, find someone who is and make sure they come to the meeting.
I recommend you keep the meeting at 60 minutes or less. If the first one is a success the rest then just wash, rinse, repeat.