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Senior Projects
Oct. 29th, 2004 10:10 pmEvery undergraduate student at this university has to finish his/her career with a "capstone project" of some kind, displaying mastery of GenEd skills and of major-specific skills. In our department, it takes the form of a paper on some mathematical or statistical topic, to be presented before a committee of faculty. During the student's next-to-last semester, s/he takes a course preparing them for this; late in the term, s/he submits a proposal for the topic of the project, and during the last semester writes and delivers it.
So, this past week I've had a couple of students come by asking me to supervise their projects. I usually handle such requests by asking if they have any ideas; if not (they usually don't, although the guy I'm supervising this term did - and he's doing original research!), I ask which advanced classes they've taken, which they did well in, and which they enjoyed. The first one said that her favorite course was my history of math class, and that she wanted to do something which would tie in with her future career as a schoolteacher. So I thought for a minute, and came up with the idea of a paper on George Peacock. He's largely forgotten now, but he was a transitional figure in the shift from the relatively "concrete" algebra of the seventeenth and eighteenth centuries to the highly abstract algebra of the late nineteenth century. In his day - ca. 1830 - there was still considerable resistance to the idea of negative numbers - let alone complex numbers - and Peacock's Treatise on Algebra was an effort to make the new numbers make more sense. In the process, he clarified the role of the commutative, associative, and distributive laws, emphasized that the shift to including negative and complex numbers was a process of generalization, and raised the possibility of using different laws for different purposes. (He didn't actually carry out that last, but it was soon afterwards that W. R. Hamilton developed the first non-commutative algebra.) I suggested that she read the Treatise on Algebra, summarize it in modern terms, and discuss ways in which his insights might be used by a high school teacher - e.g., in persuading high school students that negative numbers actually do make sense! She seemed enthused by the possibility, and has been able to order a copy through Interlibrary Loan. (I've never read Peacock myself, so I'll be interested to see what she can come up with.)
The other student came in this afternoon, and when I asked her what advanced courses she'd taken, she hemmed and hawed; it turns out that she's currently taking Calculus III (a sophomore-level course) and my junior-level abstract algebra course, and that's as far as she's gotten. She's not expecting to graduate until Spring '06! Why her adviser put her in the project-prep class, I have no idea. We went and talked to the guy teaching that class, and he agreed to give her an incomplete. Next fall, after she's got a few more courses under her belt, she'll come back and talk to me (or whoever she wants as her project supervisor) and to him and submit her proposal. Sheesh. Poor kid. She was really kind of distraught about it.
So, this past week I've had a couple of students come by asking me to supervise their projects. I usually handle such requests by asking if they have any ideas; if not (they usually don't, although the guy I'm supervising this term did - and he's doing original research!), I ask which advanced classes they've taken, which they did well in, and which they enjoyed. The first one said that her favorite course was my history of math class, and that she wanted to do something which would tie in with her future career as a schoolteacher. So I thought for a minute, and came up with the idea of a paper on George Peacock. He's largely forgotten now, but he was a transitional figure in the shift from the relatively "concrete" algebra of the seventeenth and eighteenth centuries to the highly abstract algebra of the late nineteenth century. In his day - ca. 1830 - there was still considerable resistance to the idea of negative numbers - let alone complex numbers - and Peacock's Treatise on Algebra was an effort to make the new numbers make more sense. In the process, he clarified the role of the commutative, associative, and distributive laws, emphasized that the shift to including negative and complex numbers was a process of generalization, and raised the possibility of using different laws for different purposes. (He didn't actually carry out that last, but it was soon afterwards that W. R. Hamilton developed the first non-commutative algebra.) I suggested that she read the Treatise on Algebra, summarize it in modern terms, and discuss ways in which his insights might be used by a high school teacher - e.g., in persuading high school students that negative numbers actually do make sense! She seemed enthused by the possibility, and has been able to order a copy through Interlibrary Loan. (I've never read Peacock myself, so I'll be interested to see what she can come up with.)
The other student came in this afternoon, and when I asked her what advanced courses she'd taken, she hemmed and hawed; it turns out that she's currently taking Calculus III (a sophomore-level course) and my junior-level abstract algebra course, and that's as far as she's gotten. She's not expecting to graduate until Spring '06! Why her adviser put her in the project-prep class, I have no idea. We went and talked to the guy teaching that class, and he agreed to give her an incomplete. Next fall, after she's got a few more courses under her belt, she'll come back and talk to me (or whoever she wants as her project supervisor) and to him and submit her proposal. Sheesh. Poor kid. She was really kind of distraught about it.
