Syllabus for our LAC on Chaos and Fractals

Course purpose

This course is Math 178 - A Liberal Arts Colloquium on Fractals and Chaos. It is a Mathematics class, though one without specific pre-requisites. The course description also makes it clear that there will be some work on the computer. Thus, this class is relatively technical amongst our First Year Colloquia. If you're curious or concerned, I've set up a page outlining the specific skills that should be useful in this class.

On the other hand, according to the Liberal Arts First-Year Colloquia website,

Although each FYC has its own specific academic content, each is also designed to introduce students to higher education within a Liberal Arts environment, particularly by integrating information and intellectual approaches from different disciplines to address the multidisciplinary nature of liberal studies. They may also introduce students to the cultural events and special opportunities specific to our campus, ...

Considering this, we will strive to make this course broadly applicable to your college experience. While the content might seem at times fairly specialized, many of the skills we develop and the tools we use will be useful throughout your academic work, particularly for those of you who major in technical disciplines.

Taking all of this into account, we will focus on developing skills in the following areas:

Writing: All Liberal Arts Colloquia involve a fair amount of writing and this one is no exception. Writing in the technical disciplines has much in common with writing in the softer disciplines but also has it's own style and expectations. This course will prepare you well for that type of experience.
Applications: What could be more multi-disciplinary than mathematics? It's literally the language of the natural sciences. As such, we'll take a look at scientific applications as diverse as meteorology and biology. We'll also expand out of the natural sciences and into the social sciences. The current fairly chaotic election will provide a nice context for this.
History: The sciences of Chaos and Fractals developed mostly over the last half of the 20th century. We'll delve into some of that history and the colorful characters involve.
Technology: We'll use several cutting edge technologies to communicate with one another, to automate some computation, and to produce images to illustrate our writing. Many of these tools could be useful throughout your academic career.
Mathematics: Did you know that Mathematics is a liberal art?! Indeed, arithmetic and geometry form half the quadrivium which, together with the trivium form the seven liberal arts of antiquity. More immediately, mathematics is the language of natural science and, as such, will be applicable throughout many of your college careers. Again, mathematics is part of this class. It's gentle, but it's there.
General growth: I am your academic advisor and, as such, we have things to talk about beyond this class. Your academic path is your own but I am happy to talk with you about it and things affecting it.

Materials

Texts: We don't have any particular text that is required for purchase. I'm preparing a text of my own that covers the technical details that I will make available to you. We will also use a considerable number of online resources. The historical material will be based partly on a small part of James Gleick's Chaos, which is on reserve in the library. There's also a very short, but fairly nice, summary of that text on Harvard's climatology page.
Technology: My anticipation is that you have good access to computers - ideally, a good laptop that you can bring to class. We won't need computers in the classroom every day but we will have in class computer projects that we work on together at times. Some of the specific technological tools that we'll use include:
- Discourse: Discourse is an online discussion platform that makes it easy to communicate technical ideas with prose, code, images, and beautifully typeset mathematics. It is similar in capabilities to the StackExchange network of sites (like math.stackexchange.com) but it's open source making it easy to deploy our own private forum.
- LaTeX: Your papers will be prepared with LaTeX - the tool of choice for preparing technical documents. While this has a steeper learning curve than a basic word processor, the results are spectacular. Furthermore, you'll get a gentle introduction to typesetting mathematical snippets with LaTeX via Discourse and there's a very nice online interface to LaTeX called Overleaf.
- Python, Javascript, and web applications: You will not do much actual computer programming in this class but you will need to write just a few lines of code for a couple of assignments. For your more involved experiments, you will use web applications.
- Mathematica: The most powerful interactive computational tool for mathematics today is certainly Mathematica. Unlike all the tools mentioned to this point, Mathematica is not free but actually quite pricey. UNCA, however, has an excellent site license allowing UNCA students free access. You may register and download a copy from the Wolfram User Portal using your UNCA email.

Evaluation

Papers: You will type two papers during the term in the 5-7 page range. Each will be worth 60-80 points. The first will be a comparison/contrast type paper involving the first two technical subjects we discuss that we write in late September. The second will be something of a summary of some topic near the end of the semester.
Typed HW: A couple of weeks before we start each paper, you'll type a shorter description of a rather specific mathematical problem. These will be worth about 20 points each.
Discourse: Our online discussion has three trust levels and you can earn 15 points per trust level to earn 45 points. In addition, there will be a few specific discussions that everyone earns points on. That's probably about another 30 points.
Exams: There will be two exams during the term worth about 80 points each. Tentative dates for these exams are:
- Friday, September 23
- Monday, November 21 (just before Thanksgiving)
There is also a final exam worth around 120 points scheduled for Wednesday, December 14 at 8:00 AM.
Quizzes: There will be two quizzes - each, about two weeks ahead of an exam:
- Friday, September 9
- Friday, November 4
There will also be the occasional 10 point reading quiz. I believe the first one is coming Friday.
Late work: In general, I don't accept late work.
Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for the class.

Resources

Here are a few resources you should be aware of to help you succeed in this class.

Me: I like to talk to people about mathematics and related topics! That's why I chose this profession. My schedule is posted on my webpage, including office hours, but I'm around much more regularly on MWF. Please feel free to approach me any time you have questions.
Your classmates: Most people learn best by talking things through with others. You will find that you can both learn from and help your fellow classmates. In particular, if your classmate is explaining a fine point to you, then you are helping them!
The Math Lab: The Math Lab rocks! It's open long hours and is located right across the hall from my office. You will be welcome there and will definitely find people to talk to about mathematics.
The Writing Center: The UNCA Writing Center is a great resource to hone your writing skills. You should definitely have them read your papers over during the writing process.
Office of Academic Accessibility: UNCA is committed to making courses, programs and activities accessible to persons with documented disabilities. Students requesting accommodations and/or academic adjustments may do so through the Office of Academic Accessibility.