# Notes: Number Theory and Modern Algebra I

I took Modern Algebra I with Professor Matthias Beck in Fall 2015. These comprehensive notes were compiled using lecture notes and the textbooks,

Disclaimer: my notes are meant to be a toolbox while doing proofs and studying/practicing the course in general. There may contain typos or mistakes. Please feel free to let me know if you find any errors!

Topics Covered:

• Integers & the Euclidean algorithm
• Complex numbers, roots of unity & Cardano’s formula
• Modular arithmetic & commutative rings
• Polynomials, power series & integral domains
• Permutations & groups

Featured Image: Dodecahedron-Icosahedron Duality
Credit: Images from Algebra: Abstract and Concrete by Frederick M. Goodman

# Website Infrastructure

The notes page is set up, next I aim to finish up organizing the precalculus resources and general non-math resources.

Now, the site contains links all my notes starting from Fall 2015, which send visitors directly to my google drive, but I wonder if that is secure/wise.

Maybe there is a better way to both host the files and allow for instant updates as I compile my LaTeX files. Right now, this blog links to individual files within my google drive which is synced to a directory on my laptop. When I compile on my computer, I work directly in that directory so that the file linked in google drive is automatically synced. I want the same functionality and convenience but I’m not sure if linking to the drive is secure, since it’s a personal account.

Time to do some non-math research~

Update: I hear that wordpress has great support, so I made a post at the forums. I wonder if there’ll be an easy solution?

Let $\mathscr{H}$ be the set of all humans.

Definition: If an element $x$ “cares for” a set $S$, it “cares for” every element in the set.

Remark: If you are a human, and you “care for” humanity, then you must “care for” yourself too.

Proof of Remark: Let $x$ denote you. $x \in \mathscr{H}; x$ “care for” $\mathscr{H} \implies x$ “care for” $x$.

# Why a Blog?

So, why start a blog when there is approximately… $1.5 \times 10^{6}$ posts created per day? (Checked @ 8 AM 1/8/17)

For me, this website is a bit more than a collection of math notes and lists of resources. I am aiming to chronicle the challenges of being a student and a teacher at the same time. On the other hand, I want to also document the most fun parts of being in an intensive graduate program!

So this blog will be part survival guide, part chicken-soup-for-the-soul, and part scrapbook.

Oh. By the way, I survived the first semester of graduate school!