When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?

– Enrico Bombieri

# Golden Power Series!

As you probably know, I wear my heart on my sleeve:

Well, I took the golden opportunity (ha!) to bring the golden ratio $\Phi = \frac{1+\sqrt{5}}{2}$ into Calc 2 this week, using it (and its little pal $\Psi = \frac{1-\sqrt{5}}{2}$) to find a closed formula for the $n$-th term of the Fibonacci sequence.

The ubiquitous Fibonacci sequence! It’s something you may have encountered out in the wild. You know, it goes a little like this:

$F_0 = 1, \, \, F_1 = 1, \, \, F_n = F_{n-1} + F_{n-2},$
so $F_2 = 2, \, \, F_3 = 3, \, \, F_4 = 5, \, \, F_5 = 8, \, \, F_6 = 13, \, \, F_7 = 21 \, \, \ldots.$

And let’s say for some reason, you need to cook up $F_{108}$. I hope you have some time on your hands if you’re planning to add all the way up to that. Instead, wouldn’t it be nice if we had a simple formula that we could use — i.e., a formula that was not recursive — to figure out the $n$-th Fibonacci number?

Luckily, such a formula exists, and there are lots of ways to find it. In this post, we’ll find it using power series. Read on, brave blogosphere traveler.

# Dealing with stress: my pet rock

As you might imagine, starting a “real” job entails a certain amount of stress. Suddenly, your support network of graduate student friends is dispersed across the country, and you’re one of a handful of junior faculty across a smattering of disciplines. So, you have to find new outlets for your stress. Aside from climbing at the rock wall a few times a week, I’ve found that it’s incredibly helpful to have a creative outlet. This brings me to…

…Henry.

Henry is my pet rock.  Over Christmas, I saw this little chair that my sister had gotten my mom for her iphone, and I thought, that’s about pet-rock sized.  And then my world changed forever.

# The end of the first semester is almost here…

You know, in my first semester of graduate school, I celebrated the end of every week. “I made it one more week!” was the refrain for all the new grad students.

My first semester as faculty? By the end of every week I was too tired to even form a coherent sentence. Maybe it’s because there isn’t exactly a whole class of newbie professors who see each other everyday, or maybe it’s because there’s always a full weekend’s worth of work to do, but I just didn’t work up the energy for celebrating on Fridays. But now that the end of the semester is almost here, I am starting to feel like it’s time to congratulate myself for making it through without any seriously huge screw-ups. (For those keeping score at home, there were at least 4 moderate screw-ups.)

One of the things that’s surprised me the most about this semester is that I have a pretty good idea of who my students are as people. In grad school, my students didn’t come to office hours, and they didn’t make a special effort to get to know me or let me get to know them. It’s the opposite story here. I see my students a lot. They participate in class. They’re funny and clever and quirky and curious and invested. The biggest surprise, to me, is that I have the emotional wherewithal to really care about 60 students. This was not something I was expecting to learn about myself! I was expecting to learn things like, “I’m not good at coming up with examples on the fly,” or, “I can draw a pretty convincing circle.”

The last week will be sad. Although some of my Calc 1 students will take Calc 2 with me, I won’t see my Linear Algebra students next semester. There are some who might never take another class with me! I’ll miss these people that I’ve come to know.

Mathematics is no more computation than typing is literature.
—John Allen Paulos

# One month gone

I had this grand plan that I would begin my days by leisurely blogging. Ha.

The semester is flying by! I am barely on top of the things I absolutely need to do everyday, and even then, I occasionally find myself with half a lecture prepared and twenty minutes to finish the other half. Fortunately, I work well under pressure. Unfortunately, I don’t do anything else well under pressure.

My job here is intense; the students are smart, motivated, committed, and genuinely kind and thoughtful. I’m used to having to exert great force to get students to come to office hours, visit a tutor, or take advantage of opportunities to help them learn. Here, many students don’t even need my intervention. Those that I have nudged to seek a little help have been willing and thorough. I really, really love this atmosphere!

The most difficult part of the job right now is figuring out how long things will take and then scheduling enough time. This weekend, for example, I would like to get my portion of midterm grading done. I also have a stack of writing assignments from my writing intensive linear algebra class to finish grading (we teach proof writing alongside linear algebra).

Next weekend, I’m going to the AMS sectional meeting in Louisville; I have to write that talk, and I should probably get my lectures for the beginning of the week prepared, too.

I’ve been managing to do some fun stuff, too. There’s a pub trivia night on Tuesdays here at the Little Pub on campus. I’ve joined a faculty team (“No Extra Credit”) and we’re doing pretty well. I go to the climbing wall a few times a week, which is really good for my mental health. Tonight I’m going to a jazz performance, and tomorrow there’s a “Fallcoming” picnic for the math department where majors, faculty, and alumni get together.

Today a student asked me to mentor his senior project.

I’m slowly starting to feel like I fit in here.

# Creative dissertation binding

My friends are really the coolest people you could hope to meet. Thanks, Melanie!

# It was awful, but I’m pretty sure this is a dream.

I had my first pre-semester stress dream. I was teaching my first day of calc 1, and I had this really cool activity planned that would get students out of their seats and talking to one another, but it totally flopped. Not only that, but I couldn’t get the document projector to display the syllabus (which I had to borrow from a prepared student because I didn’t even have a copy of the syllabus), I barely managed to get the students to pay attention, and I forgot to assign the first homework assignment.

I went back to my office, and someone came by and asked how my first day went.

“Well, it was awful. But that’s okay. I’m pretty sure this is a dream. I’m supposed to teach Linear Algebra in an hour and I don’t even have the book. Also, this isn’t my office.” (It wasn’t. My dream office was in a hard-to-find turret attached to the math building. I shared this office with several of my coauthors and former office mates and a person-sized bat.)

There’s something to be said for being a mathematician, even while sleeping. I deduced the heck out of that one. Usually there a few little snags in the dream-logic that clue me in, even in sleep mode. (Take that, smart phone. There’s something you can’t do!)

Do you have stress dreams, and are you able to rationalize your way to the understanding that you’re in a dream?

# How to get a job, Part I: your materials

Or: Gearing up for the job market; thank God it’s not me this time.

Hey friends!  Now that I’ve been on the market once, I’m qualified to give you advice.  Here’s the first part in an n-part series.

Your materials!  They’re how you let the job market know who you are and what you have to offer.  But you knew that already.  My first piece of advice is get a working draft of your teaching and research statements by the end of next week.  Why?  Because they’re hard to write, and it only gets harder once the semester starts.  Once you have a draft, you’ve done the hard work of thinking about your teaching and research, and you can relax and edit those puppies while grading stacks of exams.