{"id":1032,"date":"2015-03-02T08:30:23","date_gmt":"2015-03-02T14:30:23","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1032"},"modified":"2015-03-02T09:53:48","modified_gmt":"2015-03-02T15:53:48","slug":"topology-teaching-blogs","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2015\/03\/02\/topology-teaching-blogs\/","title":{"rendered":"Topology Teaching Blogs"},"content":{"rendered":"
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Stereographic projection of a Clifford torus making a rotation through the xz plane in 4-space. Image: Jason Hise, via Wikimedia Commons.<\/p><\/div>\n

I\u2019m teaching topology for the first time this semester, so\u00a0I\u2019ve been poking around the blogosphere for ideas of different ways to explain some of the ideas\u00a0in this class to my students.<\/p>\n

Luckily, right before I started the semester, I ran across this post on College Math Teaching<\/a>: Bad notation drove me nuts\u2026.(and still does)<\/a>. Quick, what\u2019s the area of a circle? \u03c0r2<\/sup>. What\u2019s the fundamental group of the circle? \u2124. Those aren\u2019t the same circles. The circle with fundamental group \u2124 has area 0. It\u2019s the boundary<\/i> of the circle with area \u03c0r2<\/sup>. Unlike the author of College Math Teaching, I wasn\u2019t confused about the circle when I first saw it in topology, and it never occurred to me that that particular example of\u00a0sloppy nomenclature could be a stumbling block for my students. I think that reading that post has helped me be more thoughtful and careful about notation and terminology when I\u2019m teaching this class.<\/p>\n

Another post that has shaped my thinking about teaching upper-level undergraduate classes is a guest post on the AMS math education blog: Mathematics professors and mathematics majors’ expectations of lectures in advanced mathematics<\/a>. The short version: those expectations are different. For example, I (and apparently many other\u00a0math teachers) think that leaving some details of proofs to students can be a good way for them to solidify their understanding of a proof in class. After reading that post, I’ve decided to include more of those details in classes if I think they’re important, and if\u00a0I want students to fill in details on their own, I am having them do it in class or on homework.<\/p>\n

I\u2019m teaching algebraic topology, and the author of College Math Teaching is teaching point-set topology, so there aren\u2019t a lot of posts directly about the material I\u2019m teaching, but I\u2019m enjoying a feeling of camaraderie when I read their posts about their class this semester. My students are fairly experienced proof writers at this point, but the author\u2019s students are not<\/a>. I can\u2019t imagine trying to teach some of these concepts at the same time as teaching proofs writing! On a companion blog, there are course notes for the author\u2019s class. I could probably use some brushing up on the separation axioms<\/a>. I\u2019ve been interested in counterexamples in topology recently because I wrote about <\/a>the \u03c0-Base<\/a>, an online version of the classic Steen and Seebach book. College Math Teaching has nice posts about two interesting counterexamples, the Alexandroff Square<\/a> and the Topologists\u2019 Sine Curve<\/a>.<\/p>\n

I\u2019ve also found Math \u2229 Programming<\/a>, Jeremy Kun\u2019s blog, to be valuable for my teaching. I read over his post about the fundamental group<\/a> at the beginning of the semester when I was starting to teach it. I\u2019m doing a lot of my teaching from Munkres, which can be a bit too formal at the expense of intuition, so seeing an explanation that is a little more idea-focused is helpful. Kun is a very good math writer, and I\u2019m sure his primers<\/a> would be useful for students and teachers of other subjects as well. There\u2019s plenty more to enjoy in his blog, and I can\u2019t help but point you to his guest post <\/a>on Baking and Math. After all, torus knot baklava is much tastier than programming. (Sorry, programmers. I\u2019m never going to be as interested in programming as I am in pastry.)<\/p>\n

I recently ran across The Geometric Viewpoint<\/a>, a blog about geometry and topology aimed at undergraduates and written by Colby College faculty and students. I thought about having some writing assignments in my topology class and ultimately decided against it, but maybe reading the student posts will make me think about it more for next time.<\/p>\n

There are a few defunct or rarely updated blogs I\u2019ve found useful. Sketches of Topology<\/a> has some interesting\u00a0topology constructions with great illustrations. Dan Ma\u2019s Topology Blog<\/a> has accessible posts about point-set topology. I haven’t seen much about undergraduate algebraic topology in the blogosphere, though.<\/p>\n

Any other recommendations for topology blogs that focus on undergraduate topology?<\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

I\u2019m teaching topology for the first time this semester, so\u00a0I\u2019ve been poking around the blogosphere for ideas of different ways to explain some of the ideas\u00a0in this class to my students. Luckily, right before I started the semester, I ran … Continue reading →<\/span><\/a><\/p>\n

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