It is your job this semester to take on the mantle of mathematician, and help your classmates to do the same. This is simple, like cooking an omelette, but that’s not to say there’s no technique. I’ll try to sum it up:
- Curiosity — The desire to understand is paramount. This is a form of caring, mentioned more below.
- Patience/Persistence — Math is not about getting something right the first time, it’s about not giving up when answers are hard to come by.
- Active thinking — A little hard to describe, but reading with a pen and paper is a good sign. You cannot learn without doing.
The other requirement is not one mathematicians are widely known for, but is absolutely essential:
- Communication — though the ‘aha’ moment is a personal one, this class is a joint quest. Individual progress is not enough.
General
- Be curious and take initiative in satisfying your curiosity
- Get others excited about the ideas you find fascinating, and help them to stick with tough concepts
- Bring your A game to class sessions
- Pick up new skills as needed.
Writing
- Keep an online reading journal: keep track of content, ideas, themes, people, etc.; ask questions; work through problems; try out your own ideas.
- Revise and extend 3 works to submit as a portfolio
- Contribute to a shared annotated bibliography for each research project.
The content of your writing will fall into many categories. The basic idea is to use our readings as a chance to generate topics and questions, and then to follow up on a subset of these. The following list represents several possible categories of writing relevant to this material. In each module, I will suggest several possible topics, problems, research questions, etc. You are free to take on these or come up with your own.
- Problem — you know this one. Each problem is designed to make you think about something. The answer itself is not important. The existence of an answer though helps one focus on what the problem is trying to get you to think about.
- Practice — the kind of problem you usually get in lower level math classes. There is no hard thinking here, just a method you are familiar with. Practice helps it become part of how you think.
- Warm up — something to get the creative juices flowing in class.
- Recall — essentially a pop quiz, this keeps you on your toes with the reading.
- Research — a question or problem which you will need to do some outside reading to consider. The goal is not to arrive at a single answer, but to gain some broad, supported understanding and report back something specific and interesting.
- Follow up — like research, but on a smaller scale.
- Try it — A chance to get your hands dirty with something physical beyond pen and paper.
- Reflection/Discussion — often not specifically mathematical in nature, somewhat similar to research but specifically allowing you to produce a supported opinion, not simply report the facts.
Learning to write in a course like this—writing in and about math—entails confronting psychological and technological barriers. More on those here.
Performances
Twice in person, lead the class to introduce/understand/practice/dig deeper into a topic. This will be done in small groups.
Reading
All of the important work we do will begin with reading. We will read a few things together, and try to wring meaning out of these good books. We will see that there is such a thing as a good math book, and learn how to read them. This will lead to more reading, and sometimes watching. But what, how, and why we are reading is enough for its own page.
