Inquiry based learning (IBL) is a teaching method that replaces lectures with student inquiry and exploration. It is especially suited to courses like this one, in which the focus is on developing a facility with proof based mathematics, rather than learning a list of theorems. Since I will essentially be helping you teach yourselves, class participation will be greatly valued, and weighted accordingly in the grading scheme. I understand, though, that many students are generally reluctant to participate in class. (I was the same way in college.) While I will try to draw out those of you who do not participate on your own accord, the hope is that the classroom atmosphere will be friendly enough, and participation will be so common, that eventually all of you will feel comfortable contributing. Participation can be a comment on someone's proof, or even just something like I didn't understand that. Can you say it again? Typically, the class should feel more like a group discussion than a lecture, and everyone certainly has the ability to get a 100% participation grade.

Why you should take this course. There is no better way to internalize proof based mathematics than to develop it yourself. While lecture based courses can also be effective, in an IBL class you will likely understand more deeply what a correct proof is, and eventually be able to recognize and produce them more quickly. Sometimes, it can be difficult to cover as much material in an IBL course as in a lecture-based course, but coverage is not really the focus of 2216. The whole point is to get you to think deeply about the structure of a proof, so that you will have the language and facility needed to take proof based 300 and 400 level courses. As such, IBL fits 2216 perfectly.

A typical day. The previous day, you will be assigned a few exercises to think through. You will be asked to write up solutions to a couple of these exercises, and you should bring these solutions to class. At the beginning of class, a couple of you will be selected to put your written solutions up on the board. You will then take the class through your solutions. The class is encouraged to ask questions and debate the validity of the argument. During this process, the rest of the students should correct their solutions in red ink. After this, the solutions will be handed in, to be graded on a `completed vs. not completed' scale. After this, we may have people write solutions to other (possibly unwritten) problems on the board, to be again debated. Or we may break into small groups, after which the group work may be presented to the rest of the class.

Note that lecture is not an integral part of this course, although if it seems expedient to give a mini lecture on something at some point, I may do so. The way that you will learn the material is by working through the given problems. For the most part, the problems will be organized into scripts, sheets of exercises designed to lead you step-by-step through a given topic. You will be able to find these sheets above.

Topics to be covered. Sets, functions, relations, number theory, combinatorics, graph theory.

Midterm Exams. There will be two in-class written midterms, dates TBA.

Homework. There will be two types of homework in this class. First, there will be the daily homework described under `a typical day' above. You will receive full credit for this if you complete it. Every week, you will also have a weekly homework. This will be graded in a more familiar way, with each problem assigned 3 points. The grading will be strict: unclear solutions or sloppy grammar/logic will never get full credit.

Late homework will not be accepted under any circumstances, but I will omit your lowest homework grade from the final tabulation. You are encouraged to collaborate on homework, but solutions must be written up individually.

Grading. 5% daily homework, 15% weekly homework, 15% each midterm, 20% participation, 30% final exam.

Final exam. The final exam will be held on Wed, Dec 14 at 9 AM. It cannot be rescheduled.

Academic integrity. The work you do on homework and on the exams is expected to be your own, although as mentioned above, collaborating with your classmates is encouraged on homework. Dishonest representation of the source of your solutions is taken very seriously, following BC’s policies.

Students with disabilities. If you have a disability and would like accommodation in this course, please contact either

    • Kathy Duggan, (617) 552-8093,, or
    • Paulette Durrett, (617) 552-3470,

Kathy Duggan is at the Connors Family Learning Center and specializes in learning disabilities and ADHD, while Paulette Durrett is in the Disability Services Office and handles all other types of disabilities, including temporary disabilities. Their offices do require advance notice and documentation.

Syllabus. A pdf containing the information on this page can be found here.