I have added a page on the menu bar called Works. It simply lists some of the mathematical works I have done, and I intend to keep it as an updated math portfolio. The primary addition is my paper on the Riemann zeta function that I wrote last Spring for a complex analysis course, and also its corresponding presentation.

# Tag Archives: Math

# Analytic Number Theory and Other Updates

Over the winter break I self-studied Tom Apostol’s *Introduction to Analytic Number Theory* book and completed the first three chapters, as well as the majority of the fourth. I posted the solutions, in pdf format this time, to the Solutions page. I chose this subject because Cornell currently does not have any course on analytic number theory, though it does have a graduate course in **algebraic** number theory, which I am taking this semester. More of that information is in a post on my main blog.

As stated in that post, I am now a double major in mathematics and computer science. This semester I am also planning to take all my notes in real-time LaTeX, aka *LiveTeXing*, as someone pointed out. The notes I have uploaded to Scribd, as it is more organized there and easier to view at a glance. They should be uploaded by the end of the same day of each lecture. I may upload them directly to this blog as well for centralization.

Courses that I am LiveTeXing: CS 4820, CS 4850, Math 4340, Math 7370.

I am also taking CS 3410, but the professor is posting all the powerpoints online, so it would be redundant to LiveTeX it.

# #5: The Cantor Set and the Cantor Function

The **Cantor set** is a fractal that is obtained by repeatedly removing the middle third of a segment. Start with the closed interval . Remove the open interval to obtain , i.e. two disjoint closed segments. Remove the middle thirds of those two segments, and you end up with four disjoint segments. After infinitely many steps, the result is called the **Cantor set**. The diagram below is only an approximation after a finite number of steps.

# #3: Rings

The point of this post is to provide examples and non-examples for the following ring classes:

**Ring****Commutative Ring****Integral Domain****Integrally Closed Domain****Unique Factorization Domain (UFD)****Principal Ideal Domain (PID)****Euclidean Domain****Field**

# #2: Epic Morphisms

Given that the name of this site is **Epic Math**, I felt I should write about a topic where the word **epic** is a technical term! It is hardly surprising that such a term exists, as many otherwise non-mathematical words such as **almost**, **simple**, **open**, **connected**, **regular**, **normal**, **field**, **ring**, **onto**, **map**, **twin**, **lucky**, and even **sexy** have technical definitions.

**Category Theory**

The term **epic** is found in **category theory**, which is an extremely abstract branch of mathematics that formally deals with many other fields of math. It is so strange that some mathematicians have labeled it “abstract nonsense.”