Patrick Dugan

Patrick Dugan

he/him

Undergrad at University of Pennsylvania

Posts by Tags

Algebra

Complex Image Mapping

1 minute read

Published:

In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.

Dirichlet Convolutions

less than 1 minute read

Published:

This is a blog post where I, in an effort to myself better grasp the concept, discuss/introduce Dirichlet Convolutions.

Fields

less than 1 minute read

Published:

This post is the third in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Some Results with Kernels

less than 1 minute read

Published:

This post is the first in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Algorithms

Maximum Subarray Sum

less than 1 minute read

Published:

In this post I will be going over an algorithms problem and explaining the optimal solution.

Calculus

Derivative Rules

less than 1 minute read

Published:

As a freshmen in Highschool I would spend time trying to re derive basic calculus rules. These blog posts written a long time ago are writeup of these attempts. As I was very early on in my mathematical education and doing things on my own away from the help of the internet one can see a lot different minor mistakes. These write ups are quite important to me as they were my first experience with derivation/proofs and began to teach me by doing what constitutes a proof and how to go about solving such questions.

Proving e is irrational

less than 1 minute read

Published:

This post is me using alternating series to show that e is irrational.

Complex Numbers

Complex Image Mapping

1 minute read

Published:

In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.

Computer Science

Complex Image Mapping

1 minute read

Published:

In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.

Maximum Subarray Sum

less than 1 minute read

Published:

In this post I will be going over an algorithms problem and explaining the optimal solution.

Field Theory

Fields

less than 1 minute read

Published:

This post is the third in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Group Theory

Fields

less than 1 minute read

Published:

This post is the third in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Some Results with Kernels

less than 1 minute read

Published:

This post is the first in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Math

Complex Image Mapping

1 minute read

Published:

In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.

Dirichlet Convolutions

less than 1 minute read

Published:

This is a blog post where I, in an effort to myself better grasp the concept, discuss/introduce Dirichlet Convolutions.

Fields

less than 1 minute read

Published:

This post is the third in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Some Results with Kernels

less than 1 minute read

Published:

This post is the first in a sequence of 3 posts leading up to proving a famous result about Z/pZ * being cyclic.

Derivative Rules

less than 1 minute read

Published:

As a freshmen in Highschool I would spend time trying to re derive basic calculus rules. These blog posts written a long time ago are writeup of these attempts. As I was very early on in my mathematical education and doing things on my own away from the help of the internet one can see a lot different minor mistakes. These write ups are quite important to me as they were my first experience with derivation/proofs and began to teach me by doing what constitutes a proof and how to go about solving such questions.

Proving e is irrational

less than 1 minute read

Published:

This post is me using alternating series to show that e is irrational.

Number Theory

Dirichlet Convolutions

less than 1 minute read

Published:

This is a blog post where I, in an effort to myself better grasp the concept, discuss/introduce Dirichlet Convolutions.

Proving e is irrational

less than 1 minute read

Published:

This post is me using alternating series to show that e is irrational.

Prefix Sums

Maximum Subarray Sum

less than 1 minute read

Published:

In this post I will be going over an algorithms problem and explaining the optimal solution.