Week 2 Done!

I'm officially exhausted. Teaching 4 days a week is rough. We're definitely making movement in the course, and I'm starting to feel the pressure of fitting an entire linear algebra course in just 5 weeks. I am covering 2 sections of text every day, which amounts to covering 2 chapters a week. Next week is their midterm, and that puts me at the next challenge. I do have the added experience of being an exam writing for a program run through the department, which I've done for the last 2 years. And I was also a worksheet writer during the past two semesters for a program which gave calculus students the opportunity to discuss harder calculus problems than we would cover within the course, so I have some idea of how I should be doing phrasings and even slightly on timing as well. It's just very hard to come up with clever ways to present problems that cover knowledge of the material in a way such that those that know the material will be able to do the problems without much difficulty but those that did not put the work will have a fair amount of difficulty. But then again, it's simply impossible for the students to have a full working knowledge and mastery of the subject material after these quick lectures and limited homework.

I guess we will see. For now, it is the weekend. The midterm exam is written, and I will tackle writing up lectures for Monday-Wednesday another day.

Week 1 Down

The first week of the summer linear algebra course is over and appears to have gone quite well. With the exception of maybe 3 or 4 students (out of approximately 20), the dynamic has gotten quieter and quieter. I haven't caught anyone full out sleeping yet though, so that's a good sign I suppose. We've completely covered the first 2 chapters of the text we are using, and I've already gotten a number of comments that I should do a few more examples. Hopefully I will have the time to do this as we get to the more difficult material. There's just only so many examples you can do of determining whether a transformation is linear or not, or determining the geometric interpretation of a 2x2 matrix!

Next week we start covering chapter 3, which deals with subspaces and their dimensions. It seems that I should be able to do a bit more example wise with this material. We'll see.

Lecture #1

Talk about a whirlwind!!! Turns out I had EXACTLY enough material to cover the full 2 and a half hours of my course today. Granted, it was the whole first chapter, but I think it went well!!!

It's a different experience lecturing, as opposed to leading a recitation. I'm used to the students interacting with me. Today, all 20 of them just sat there. With one or two questions thrown in. It was bizarre.

It was definitely a roller coaster though. I thought I was going to run out of material at the beginning when it only took me 10 minutes to go over the entire course in general. Then in the middle I thought I wouldn't finish, so I sped up a bit. Then back up to not having enough material. I guess I planned it out just right though! I had to have enough material to get me til 3:30, and I finished at 3:28. Not too shabby for a first timer!

As for my actual lecturing, I need to tighten things up. There were a few minor slip ups, but my students were actually paying attention and got the words out for me, so that was nice. I hope that means they were really thinking about the material while I was covering it! I get to do it again tomorrow. I'm exhausted after just one day!!

Planning Lectures

Calling all teachers of mathematics!! I'm teaching a course this summer (starting in a little over a week) on Linear Algebra. The course will run for 5 weeks with 4 classes a week except for the first, where there will be three (due to the US holiday). I've got the material all planned out, and when homeworks/quizzes will be due and what they will all be. I'm at the stage where I need to start planning out the lectures. Any tips for a newbie on motivating especially the first lecture? Each lecture is 2 and a half hours long, so I need to keep them in tune with what's going on at the board - easier said than done, I know. Any advice would be greatly appreciated!

Recognition!!

Finally, some solid real recognition from my department! Two pieces really. First, was a very nice goodbye from my advisor, who said something to the effect that I would have been successful in the PHD program if I had been allowed to stay, and then gave me some pointers on where to go next in my reading to keep me motivated on the Algebraic Topology route. The next text up? McCleary's A User's Guide to Spectral Sequences, since ... those who are comfortable with spectral sequences have a large advantage over those who don't. This should be interesting enough, since most if not all of my questions this semester have been about spectral sequences! A User's Guide would be nice.

The second form of recognition meant a GREAT deal to me. There are 2 teaching awards that are given out each year. One given out purely by the department (of which 2 are given out), and one given out by a family member of a previous member of the department. Well, I got one of the ones given out by the department!! What a way to go, right? :-) It's wonderful to be recognized for my hard work in my teaching. Thankfully, my students recognized it, since they are the ones who nominated me. But, this is what I want to do with my degree. I want to teach.

Now, let's hope I come through for them again, and give them the tools to get decent grades on their final exam!!

Question

Hello All,

This post is actually a question. I realized throughout my course at JHU that I had failed to learn a good chunk of advanced undergraduate concepts (for example, Jordan Blocks and Diagonalization in Linear Algebra, and I have completely forgotten most common examples/methods in Calculus from Series in Calculus II into the entirety of Calculus III with the exception of basic operations of vectors (adding, cross product, dot product,etc.) and I never even learned Stokes and Green's Theorems. Now, here's my question. I just finished going through (reading and doing all exercises) in a Linear Algebra textbook. So, I've filled in those gaps as far as Jordan Blocks, Diagonalization, Projections, Orthogonality, etc. But, I don't know what the next step is. I'm tempted to go back to Calculus and really nail down all of that, but fear it will take too long, and it should be stuff that I can pick up as I need it by reading a few sections in a standard calculus textbook. It's only really methods and basic tools that I've lost, but upon reading it I should be able to get it back fairly easily. I taught Differential Equations last summer, so I'm fairly comfortable with that material, and the next logical thing would be to move towards an Abstract Algebra textbook (at least for me). I know that I did not pass the analysis qualifying exam, but I'm comfortable with undergraduate analysis (a lot due to the fact that I did most of an undergraduate textbook last summer, while studying for my analysis exam, thinking that I had missed something in undergrad, but I didn't). Now, if that is the next step, I'm not sure which book I should use. I have 3 or 4 at my disposal:

Lay's A First Course in Abstract Algebra
Hungerford's Abstract Algebra: An Introduction
Nicholson's Introduction to Abstract Algebra
Lanski's Concepts in Abstract Algebra

It is my knowledge that Lay's is the most elementary of the 4, and it is the one I used as an undergraduate. At Hopkins, we used Lang's Algebra, so you can see that there was quite a gap. I have heard that Hungerford is good, and JHU is using Nicholson for their undergraduate course right now. Wesleyan will use Dummit and Foote, which I also semi have access to, but not fully, so I would like to avoid using that one at the current moment.

My question ... Help! Which book do I use!? And is this even the right direction to go? Maybe I should go back to Calculus? Or, since I may be studying moving to study Graph Theory at Wesleyan, do I do my Graph Theory text?

Thanks all!

Next Chapter!

Hello All!! I've officially accepted an offer at Wesleyan University. I am extremely excited to start classes and such this fall.

I still am finishing up classes at JHU this semester. And I'm teaching Linear Algebra (solo) this summer through JHU. Then I'll be heading home for a month or so, and then I'm getting married, moving to CT and starting at Wesleyan. It's a very very exciting time, and I'm confident that it will work out better this time. I'll be closer to family and friends, and closer to my undergrad where I still have a great relationship in tact. Yay for new beginnings!