Showing posts with label juggling. Show all posts
Showing posts with label juggling. Show all posts
Wednesday, May 2, 2012
Juggling 2: How do you learn new math?
How do you start on problems that require learning the basics of another mathematical field? All I know how to do is read. I read the papers I'd like to understand, I follow back through the bibliographies, I try to get back to the basics in the field. Sometimes that is not so easy, as there is no basic introduction. Talking to people seems to be a very effective way to learn the basics of another area of mathematics, but this requires finding a person who knows what you want to know and who is willing and able to explain these things. I have had particular difficulty with this when I've seen some words that make me think that the ideas from another area might help me out but I'm unable to formulate a good question. "Tell me about how combinatorics might help me with my PDE problem" is awfully vague.
Collaborators are also phenomenally useful in this regard: they are usually people who like you and respect you at least a little bit, so you can ask questions without feeling terribly stupid. I have collaborators with complementary expertise and really enjoy learning from them.
Looking forward to summer -- I have an immense pile of reading I'd like to get to.............
Friday, March 30, 2012
Juggling
Old post (written as I finished my dissertation): With apologies to mathematicians who actually juggle, I am wondering about how people maintain multiple mathematical projects. There are a lot of questions I'm interested in. While some stay in my narrow field of mathematics and are continuations of dissertation questions, others veer into related areas, with contributions from as far afield as combinatorics and PDE.
How many projects are you comfortable with at once? Given the time needed for teaching, service, and administrivia, how many problems do you like to have in active rotation? I am reaching for three. I find that I get very wrapped up in one problem at a time and have an extremely hard time pulling my head out of it to look at another, even if they are closely related. My mind always wants to go back to the one it's spent the most time on recently. I have a little file of questions and I've got six at the top, which means I am keeping my eyes open for papers that apply and people who might be able to help out. I read somewhere that Conway liked six. Maybe over time I will be able to switch more easily from one problem to another and make steady progress on several...
Do you like to have different problems in various stages? Some folks seem to like having a problem they're just starting to think about, a problem that they're making active progress on, one they're writing up. Do you aim to have a range like this? Does it work? How do you do it? I guess right now, by default, I have some things I'm wrapping up (dissertation) and some projects I'm starting.
On a related note, I am getting some advice from my advisor (if I understand correctly) that I should not be spending much time starting different things right now --- I ought to concentrate solely on finishing. If anyone has any first-hand advice they'd like to share, I'd be eager to hear it!
New commentary (after time as something approximating a real professor): These days I am fairly comfortable having three or four projects in the air at once. I only manage this because they are closely related. I really have more projects, but I am not making any progress at all on a few of them -- it seems like the ones left behind are mathematically different than the others. I also manage the projects that are progressing through collaboration. That makes it a social affair and something that must be scheduled into my daily calendar. When a student emails to ask about time to meet outside of office hours it is easy to say, "Oh, I guess I could reschedule my research time and talk to you about calculus instead"........ unless you've got a Skype date with someone across the country!
Small weekly goals and discussions help me move forward with multiple projects even if I can't devote hours a day to anything. Just keeping my head in a problem on a daily basis is pretty important. Being an overworked participant in the American liberal arts system has pushed me to learn this.
On that note.... I need to escape my office as I have a whole free hour. Time to do some research!
How many projects are you comfortable with at once? Given the time needed for teaching, service, and administrivia, how many problems do you like to have in active rotation? I am reaching for three. I find that I get very wrapped up in one problem at a time and have an extremely hard time pulling my head out of it to look at another, even if they are closely related. My mind always wants to go back to the one it's spent the most time on recently. I have a little file of questions and I've got six at the top, which means I am keeping my eyes open for papers that apply and people who might be able to help out. I read somewhere that Conway liked six. Maybe over time I will be able to switch more easily from one problem to another and make steady progress on several...
Do you like to have different problems in various stages? Some folks seem to like having a problem they're just starting to think about, a problem that they're making active progress on, one they're writing up. Do you aim to have a range like this? Does it work? How do you do it? I guess right now, by default, I have some things I'm wrapping up (dissertation) and some projects I'm starting.
On a related note, I am getting some advice from my advisor (if I understand correctly) that I should not be spending much time starting different things right now --- I ought to concentrate solely on finishing. If anyone has any first-hand advice they'd like to share, I'd be eager to hear it!
New commentary (after time as something approximating a real professor): These days I am fairly comfortable having three or four projects in the air at once. I only manage this because they are closely related. I really have more projects, but I am not making any progress at all on a few of them -- it seems like the ones left behind are mathematically different than the others. I also manage the projects that are progressing through collaboration. That makes it a social affair and something that must be scheduled into my daily calendar. When a student emails to ask about time to meet outside of office hours it is easy to say, "Oh, I guess I could reschedule my research time and talk to you about calculus instead"........ unless you've got a Skype date with someone across the country!
Small weekly goals and discussions help me move forward with multiple projects even if I can't devote hours a day to anything. Just keeping my head in a problem on a daily basis is pretty important. Being an overworked participant in the American liberal arts system has pushed me to learn this.
On that note.... I need to escape my office as I have a whole free hour. Time to do some research!
Monday, March 26, 2012
Teaching three-three
One of my motivations for blogging is that by reading the blogs of others I get a glimpse into what life might be like (for real) for people in very different situations than mine. This post, on teaching three-three, is one of those posts for other people.
Teaching: I teach every day of the week other than Saturday and Sunday. I teach calculus, of course, and another class. Two of these are MWF and one is TTh. At my school, it is expected that I learn every student's name and hopefully something about them as people. It is also expected that I teach excellently, using either lecture or more "reform"-style teaching methods.
Hours with students: It is requested/required that I have between 4 and 5 office hours a week, distributed over four different days. I do that. I also have meetings with students by appointment. Many weeks, I actually do spend up to nine hours with students outside of class. This does not count my independent study students (oh, did I mention that I'm overseeing some independent studies on topics not covered at my small college?) or my undergraduate research students.
In addition to math questions, I do have a few students who seek me out for conversation, relaxation, and life advice. Interestingly, most of them are not math majors :) This also takes some time, but is usually quite rewarding -- I think these are very interesting and talented people, and sometimes we go for coffee or ice cream rather than sitting in my office.
Research: I try to follow the advice of Robert Boice and work in small daily chunks. I have managed to maintain some research projects using this method. I also like to work with collaborators, as it is fun and they can sometimes keep a project going even if I have to stop for a week. I still don't have a lot of papers, though.
Service: Right now, the department is very busy with some administrative adventures. I attend between 2 and 4 hours a week of meetings. In general, the department does not waste much time or spend meeting time on stupid stuff. Meetings do take time though.
Grading: I have an undergraduate grader, but I do need to grade all exams. I love having an undergraduate grader.
Class prep: Fortunately, I have taught calculus for six or seven years before this. I think about how to present concepts for these classes -- these people -- but I do not have to spend much time relearning integration by parts. I spend time assigning homework problems, thinking about what students should get out of the class, thinking about how to deal with the poor preparation some students are coming in with, and figuring out pacing of the classes whether using worksheets or lecturing. I also spend time trying to come up with new examples or activities that relate directly to the interests students in these classes have. Last semester: chemists all over the place. Reaction rates. This semester: economists, dance majors, and social justice advocates. Different activities.
Service: I work on inviting speakers, scheduling and funding mathematical/cultural events, and organizing workshops on technology that the department would be interested in using. I'm also involved in some regional and national activities.
Undergraduate research: have two undergrads working on a project related to my research. Hopefully they spent all spring break revising the paper we are writing together! I have spent up to three hours a week with these students, although our arrangement is quite informal and some weeks we spend no time together at all.
I certainly did spend my 60 hours a week on this job for a long time. Now I'm not quite sure -- is it 55? Sixty certainly made me very tired, and I am not sure it's sustainable. Of course, last year was my first year, and this is only my second. I hear that some of these things get easier to do -- but then you get more responsibilities.
Teaching: I teach every day of the week other than Saturday and Sunday. I teach calculus, of course, and another class. Two of these are MWF and one is TTh. At my school, it is expected that I learn every student's name and hopefully something about them as people. It is also expected that I teach excellently, using either lecture or more "reform"-style teaching methods.
Hours with students: It is requested/required that I have between 4 and 5 office hours a week, distributed over four different days. I do that. I also have meetings with students by appointment. Many weeks, I actually do spend up to nine hours with students outside of class. This does not count my independent study students (oh, did I mention that I'm overseeing some independent studies on topics not covered at my small college?) or my undergraduate research students.
In addition to math questions, I do have a few students who seek me out for conversation, relaxation, and life advice. Interestingly, most of them are not math majors :) This also takes some time, but is usually quite rewarding -- I think these are very interesting and talented people, and sometimes we go for coffee or ice cream rather than sitting in my office.
Research: I try to follow the advice of Robert Boice and work in small daily chunks. I have managed to maintain some research projects using this method. I also like to work with collaborators, as it is fun and they can sometimes keep a project going even if I have to stop for a week. I still don't have a lot of papers, though.
Service: Right now, the department is very busy with some administrative adventures. I attend between 2 and 4 hours a week of meetings. In general, the department does not waste much time or spend meeting time on stupid stuff. Meetings do take time though.
Grading: I have an undergraduate grader, but I do need to grade all exams. I love having an undergraduate grader.
Class prep: Fortunately, I have taught calculus for six or seven years before this. I think about how to present concepts for these classes -- these people -- but I do not have to spend much time relearning integration by parts. I spend time assigning homework problems, thinking about what students should get out of the class, thinking about how to deal with the poor preparation some students are coming in with, and figuring out pacing of the classes whether using worksheets or lecturing. I also spend time trying to come up with new examples or activities that relate directly to the interests students in these classes have. Last semester: chemists all over the place. Reaction rates. This semester: economists, dance majors, and social justice advocates. Different activities.
Service: I work on inviting speakers, scheduling and funding mathematical/cultural events, and organizing workshops on technology that the department would be interested in using. I'm also involved in some regional and national activities.
Undergraduate research: have two undergrads working on a project related to my research. Hopefully they spent all spring break revising the paper we are writing together! I have spent up to three hours a week with these students, although our arrangement is quite informal and some weeks we spend no time together at all.
I certainly did spend my 60 hours a week on this job for a long time. Now I'm not quite sure -- is it 55? Sixty certainly made me very tired, and I am not sure it's sustainable. Of course, last year was my first year, and this is only my second. I hear that some of these things get easier to do -- but then you get more responsibilities.
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