If the goal is to help others understand the value and ubiquity of mathematics, we must ourselves become adept at perceiving math in the world around us and understanding its significance.
Hence, the first major assignment of the semester is to write a blog post highlighting mathematics in our natural or built environments. Your post should stem from, and be focused around, one or more pictures and/or videos that you personally (or one of you, if you work with a partner) have taken.
The post should of course describe generally where and when the image(s) were taken and what they depict. It should then go on to describe in depth what mathematical idea or structure is either explicitly or implicitly present in the image(s). It should discuss how that underlying mathematics interacts with/enables/enriches/or even detracts from the non-mathematical aspects of what's shown in the image(s).
After this, the post should pose one specific nontrivial (i.e., not just arithmetic) mathematical problem or question inspired by the mathematics seen in the image(s). The connection with the images may be loose, but it should be explained. And then your post should conclude with an exposition of the solution of that problem. The solution may be something you come up with, or read about, but the exposition must be your own. It's also possible that the problem you pose is an unsolved problem -- that's totally fine; in this case, your exposition should discuss what is known about this problem, what remains to be solved, and if possible, who's working on it and/or what approaches are being used.
Remember, as a blog post, your putative (and perhaps actual, see mechanics below) audience is the entire readership of the internet. Therefore, your post should strive to convey the mathematical ideas in as accessible a fashion as possible, without trivializing. Minimize the amount of mathematical jargon you use, and carefully explain, in a common-sense fashion, the terms you decide are key to employ to capture the mathematical ideas you want to convey.
An account has been created for you at studioinfinity.org. To access your account, go to the login page and click "Lost your password?" Enter your email address (the one you're identified by on this course's roster) and click "Get new password." You'll receive an email with your user id and a link to set your password. Once you've done that, you can log in normally. You can also get to the login page by just going to studioinfinity.org, clicking on "About" at the top of the page, and looking for the login link at the bottom right.
Once you are logged in, you will be on the "Dashboard". There's a lot of information there about existing posts and such, but the main thing you need to get started is the "+New" button at the top. You want to create a "Post," not a "Page" or "Media". When you click on that, you'll be able to enter your post's title, its text, upload pictures and/or videos, and arrange everything how you like.
Optionally, if you would like practice with the site, you are welcome to make one post introducing yourself. Say who you are, what you're interested in, why you're appearing as a guest blogger on studioinfinity.org, and include at least one picture -- it could be of yourself but does not have to be; it could be something else interesting to you, and if so, describe what it is and why it's interesting. Your intro post will not be graded, but if you make one and want general feedback on it, just send me the link by email to email@example.com.
While you are working on a post, you can "Save Draft"s, and I recommend you do so. When you have finished a post, you should set the visibility either to "Public" or "Private." The former will mean that anyone on the internet can see your post, the latter will mean that only logged-in users (me and members of the class and any other guest bloggers on the site) will be able to read your post. You're welcome and encouraged to make your post public, but not required to do so for this class, and your grade will not be affected by which you designate. Then hit "Publish" and your post is live. (You can edit it after you've published it, and are welcome to do so, but not after the due date. Note I can see a log of all edits.)
When the post is complete, you should also submit a link to it on Canvas, along with your statement of acknowledgments and sources (including any you explicitly reference in the post), and if you worked with a partner, your collaboration statement (see the Syllabus). The Canvas submission (and the post itself) must be complete by the due date, Oct 3 at review session time.
I will give a fairly detailed case study of creating a blog post for this assignment in class this Friday, Sep 21. In addition, you may want to look at some of the entries in the following blogs for similar types of posts that can help to serve as inspiration/guidance in your writing. Note that very few of these contain the element of an associated math problem, so remember you need to include that if you are following one of these examples as a sort of template. Also remember that not every post in every one of these blogs is in the format described above, although if you browse through the history of these blogs, you will find many such examples.
- The Mathematical Tourist by Ivars Peterson (note that the last couple years are mainly pictures without explanation, but that older posts have a great deal more expository text).
Found Math at the Mathematical Association of America (MAA).
Roots of Unity by Evelyn Lamb for Scientific American.
Math Mondays by the National Museum of Mathematics.
Devlin's Angle by Keith Devlin for the MAA.
This post at Mathematical Enchantments by Jim Propp (his blog may have other relevant posts, too).
When you feel you have some image(s) and topic ideas that would make a good post, you should make an appointment with me to bounce your idea off of me and get feedback, plus it will be a good opportunity to say hello and talk briefly about the course individually. Available times are on the course calendar; you have to click on the "Find an appointment" button to see them and schedule one.