Dane Sabo
df8f28fce3
M .sessions/nvim_config.vim M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data A Class_Work/nuce2101/exam2/2101_Exam_2_2025.pdf A "Class_Work/nuce2101/exam2/Fundamental Kinetics Ideas_Rev_17.pdf" A "Class_Work/nuce2101/exam2/Simplified Parallel Coupled Reactors Rev 8.pdf"
86 lines
3.9 KiB
TeX
86 lines
3.9 KiB
TeX
\documentclass{letter}
|
|
|
|
\signature{Dane}
|
|
\address{769 Shady Drive East \\ Apartment 303 \\ Pittsburgh, PA 15228}
|
|
|
|
\begin{document}
|
|
|
|
\begin{letter}{Brian Sabo \\ 6 Windsor Way\\ Coraopolis, PA 15108}
|
|
|
|
\opening{Hey Brian,}
|
|
|
|
I was so pleased to receive your letter. To be honest with you, I don't think I
|
|
have ever received a hand-typed letter before in the mail. It was a nice break
|
|
from the usual impersonal text messages the modern day is used to.
|
|
|
|
I actually have a great story for you about a challenging class I took, and
|
|
how it frankly changed my career path.
|
|
|
|
I was in my junior year of my mechanical engineering degree when a graduate
|
|
class called 'Linear Algebra for Machine Learning' was announced it would be
|
|
offered. It was taught by a new assistant professor in the department named Ben
|
|
Erichson. He was more of a statistics background, so I was very curious how the
|
|
class would be taught. Plus, who isn't interested in machine learning?
|
|
|
|
Let me tell you about an early hiccup in that class. Did you know that the least
|
|
squares estimate, a.k.a. a linear fit, can be written like this?
|
|
|
|
\begin{equation}
|
|
\min_{\mathbf{x}} (\mathbf{A}\mathbf{x} - \mathbf{b})^T(\mathbf{A}\mathbf{x}
|
|
- \mathbf{b})
|
|
\end{equation}
|
|
|
|
where $\mathbf{x}$ is the set of parameters, $\mathbf{A}$ is the input data, and
|
|
$\mathbf{b}$ is the measured output. Basically, you choose $\mathbf{x}$ such that you
|
|
minimize the error when you multiply it by the input and subtract the expected
|
|
output. You can get the best linear estimator by doing:
|
|
|
|
\begin{equation}
|
|
\hat{\mathbf{x}} = \left( \mathbf{A}^T \mathbf{A}\right)^{-1} \mathbf{A}^T
|
|
\mathbf{b}
|
|
\end{equation}
|
|
|
|
If you do it for a two dimensional case, you'll find you get exactly the result
|
|
a linear fit in Excel will give you.
|
|
|
|
Anyways, the derivation of this and the proofs were all in the first 60 minutes
|
|
of class. My cocky ass didn't even know you could write vectors as bold small
|
|
letters at that point. This class became the most difficult class I had taken to
|
|
that point. But, in the struggle that class presented, the learning of difficult
|
|
concepts provided me a sense of accomplishment and satisfaction that no other
|
|
class previously had. I knew at that point that I needed to find somewhere I
|
|
could keep learning and tackle hard problems. For me, that was a PhD. I don't
|
|
use the material from that class on a day to day basis, but I still think about
|
|
it a lot.
|
|
|
|
So let me answer your question. When it comes to focusing on a concentration,
|
|
taking more harder classes or taking the easy road, I say take what classes you
|
|
find \textit{interesting}. Even if those classes are "difficult", they will be
|
|
easy because you won't mind working on them. To that end, I don't think
|
|
certificates or concentrations are too important. I'd ask your dad if he cares
|
|
about a concentration when hiring someone, or would rather have someone who's
|
|
curious, versatile, and challenges themselves.
|
|
|
|
There is another important angle to consider when choosing classes. Certificates
|
|
and concentrations are attractive. But, consider that if you're choosing between
|
|
a class that'll give you a subtitle on your degree and one that you're curious
|
|
about, remember that this is the \textit{only} time you will get to choose. When
|
|
you finish school, you won't have an opportunity to take that 'interesting'
|
|
class again, or really any class. Cherish the fact that you're able to pursue
|
|
different courses now.
|
|
|
|
Workload be damned. You're a very smart guy---you'll figure it out. If you want
|
|
to do great things, they won't come easy, but they won't come at all if you
|
|
don't push yourself. It's a privilege to be able to do this difficult work.
|
|
|
|
\closing{Your cousin and friend,}
|
|
|
|
P.S. Proofread your prose. You have typos in there! Most people will only know
|
|
you through your writing, and you don't want to give a bad impression.
|
|
|
|
P.P.S. I love the Leo picture and am keeping it in the office :)
|
|
|
|
\end{letter}
|
|
|
|
\end{document}
|