Informal Description of the Course
This class is quite likely very different than other math classes you may have taken. Given this, it's important to know what to expect, so you know what you're getting in to.
- This class is an introductory math class. I will review topics as necessary and there will be ample opportunity to get help from me and math tutors outside of class. However, if math is a subject you really, really struggle with, this might not be the course for you. If you were ok at math in high school, but didn't like it and/or have forgotten most of it, then this is probably an ok course for you. On the other hand, if you had significant difficulty with algebra, and feel like it's something you've never understood, this course might be frustrating for you.
- This course is somewhat difficult to describe. I think the most important pre-requisite is to approach the material with an open mind and a sense of exploration and adventure. With a little intellectual initiative I think you will find many opportunities to make connections between the material of this course and other interests of yours.
- This is the fourteenth time I've taught this class. So I have a pretty sense of the general contours of the course. However, every year is different, as more than any other class I teach, this course depends on the contributions of the students.
- If you have taken calculus before, I strongly recommend that you not take this class.
- Falling behind in this course is not a good idea. If you're confused about something, it's very important that you seek help sooner rather than later. There are many people around who can offer help. However, we can't offer assistance if we don't know who needs it when. You need to take responsibility to seek help if you need it. On a related note ...
- I do not expect all of the homework assignments to be easy; I don't expect you to be able to sit down and do them right away. Don't let yourself get frustrated -- I strongly suggest working with others and seeking help if you need it.
- You will be writing papers for this course. These papers will be short response papers and can be entirely non-technical. I have found that most students enjoy the chance to reflect upon the ideas in the class; a few students, however, find writing about math and science to be uncomfortable and/or difficult.
- In many traditional math classes the instructor shows you how to do a bunch of problems, you go home and obediently practice the stuff your instructor showed you, and then you take a test. This class will not be like that—there will be some traditional-style homework, but there will be many other exercises too.
- Some of the homework assignments are more like laboratory exercises. That is, rather than doing a quick problem and getting a simple answer, I'll ask you to explore some stuff, make observations, and look for patterns. Frequently these assignments will have open-ended questions. You will enjoy these assignments more (and do better on them) if you approach them as you would a good laboratory exercise in a science class.
- This class is not a systematic review of algebra or trigonometry; it is not explicitly designed to prepare you for further math classes. Nevertheless, you will review and strengthen your understanding of algebra and functions by taking this course.
- The exact syllabus for this is quite flexible; feedback is encouraged, and will help make the class better.
- There is a list of errata for my book here. If you find any errors or typos in my book that aren't already on the list, please let me know.
- The material we'll be reading about in Gleick's book, and the work we'll do in my book and in class will shift in and out of phase with each other. The two books don't cover the same topics in the same order. In the past this hasn't been a problem; it's just something to be aware of.
- In terms of the math stuff we'll be doing, it will take a few weeks to get to the chaos material. Before we do, what we're doing might seem odd. The initial exercises we do might seem boring or irrelevant, but this phase of the course is essential groundwork for what's to follow.
We will do a lot of different things during class meetings, including discussing readings. These discussions are chance for us to explore some of the philosophical, conceptual, historical, and social aspects of chaos and fractals. The readings we do will range widely in content, style, and difficulty. There are several goals and motivations I have for discussions:
- The discussions are a chance to figure out some things together. We will be doing some readings that are sometimes difficult and subtle and, I hope, interesting. Working together we can solidify and deepen our understanding.
- In some of the discussions it will be particularly valuable to hear a diversity of opinions. I expect there will be a range of reactions and responses to some of what we read, and I think that there is tremendous value to listening to and engaging with a diversity of thought.
- Discussion meetings are also a chance to demonstrate to me that you are engaged with the material. More on this below.
Expectations for class discussions:
- Prepare. Do the reading and think about it. Expect to spend an hour or two preparing, although obviously this will vary a lot from reading to reading. Take notes, write down questions, and prepare responses to any questions I might have posed.
- Work with a hard copy of the reading. I think it is easier to engage with a text via a physical copy, and I don't want us to have laptops open when we meet.
- Be present. Listen to others, respond, and contribute your own ideas and questions.
We should all work to create an inviting atmosphere and ensure that there is opportunity for all to contribute. At the same time, there is no need for everybody to contribute equally. It is natural for some people to talk more than others, and I think this is normal and good. Also, I expect that students will engage and contribute at different levels, depending on prior coursework. I see this diversity of backgrounds as a strength and not a weakness; there are roles for everyone to play. Asking good questions is as important as providing answers.
Finally, it goes without saying, but I'll say it anyway: the point of discussions is not to figure out who is right and who is wrong, but to help all of us get to a deeper, and not necessarily uniform, understanding.
As much as possible, I'd like to minimize the use of laptops, tablets, and phones during our class meetings. There is good evidence that these wonderful devices can harm the learning environment, even for those who are not using their own devices and are merely exposed to the devices of others. An excellent, reasoned discussion of this is Why I Just Asked My Students To Put Their Laptops Away by Clay Shirky. I highly recommend giving his essay a read.
There is no need to ban laptops entirely—that just seems silly to me. There will be times in class when we will do exercises that require computers, and there will also be moments when we might want to grab a device and look up the meaning of a word or a historical tidbit or something. So let's use common sense and keep devices holstered except when they're needed, at which point we should use them proudly and without apology.