Each student will have to do a presentation in class this semester. But the presentation will only last for about 20 minutes and will be fairly minor. It will work as follows.
Each of you should pick out an interesting theorem/result/example, or an interesting non-trivial (and non-assigned!) problem, related to the class material (e.g. from Sections 25 to 35 of the Billingsley textbook). If you have trouble picking a good topic, or trouble preparing your presentation, then you may talk to me about it. As soon as you have chosen your item you should let me know, and we will choose a time slot (during class time) for your presentation.
At your scheduled time, you will present the item at the blackboard. You will be judged on the clarity and quality of your presentation, and on your apparent understanding of the topic.
Note that 20 minutes is not very long so you should choose a simple, concrete item which can be explained easily. Consider your timing carefully; most things take longer to present than you might think, and AFTER ABOUT 30 MINUTES YOU WILL BE CUT OFF! Also, your presentation should not consist of merely recopying what is in the book, but rather should show that you have fully understood the topic (and why it is interesting) in your own way. After each presentation, there will be a brief opportunity for questions. In addition, all other students will fill out a "feedback" form giving their impressions of the presentation.
One final note: the presentations will be done at the appropriate time as we progress through the book, so if you would prefer to do your presentation EARLY you should choose an item from the earlier sections, while if you would prefer to do your presentation LATER you should choose an item from the later sections. I will try to be flexible about scheduling; tell me about your needs.