directed reading
at du math
Part of the mentoring team in the math common room in the picture above. From left to right: Isis, Flor, Vlad and Jesse. (Credit: Casey Schlortt )
Welcome to the directed reading at du math webpage!
The first edition of the Directed Reading at DU program will run from January 12, 2023 until May 15, 2023.
Thanks to the support of the DU Math Department, each mentor-mentee team member will get a personal copy of the team's book.
The goal of the program is to provide opportunities and support for undergraduates interested in learning beautiful math and math-adjacent topics under the guidance of one of our graduate student mentors.
We will focus on creating an inclusive and diverse learning community for the exchange of beautiful mathematics. We will also work on presentation skills with the goal of communicating math ideas in an effective way.
THE MENTORING TEAM FOR THE 2023 EDITION OF THE DIRECTED READING:
Casey Schlortt (she/her/hers)
Isis A. Gallardo (she/her/hers)
Jesse Parrish (he/him/his)
Kempton Albee
More details about the program:
During the Winter and Spring quarters mentees will meet once a week for an hour with their mentors to discuss material related to their project.
At the end of the program, each mentee will give a 20 minute presentation on something cool that they have learned. The mentor-mentee team will work together on this presentation during the last month of the program.
We will have a few social events in which we all get together to consider relevant issues to the program such as: ways in which we can build an inclusive and diverse math community, ways in which we can improve as communicators of math ideas and ways in which we can be supportive mentors.
We are particularly interested in supporting the participation of students of color, including Latinx, Black and Indigenous students as well as the participation of LGBTQI+ students, non-binary students, trans students and/or women. If you are on the fence about applying and/or have any questions please reach out to Flor (florencia dot orosz at du dot edu).
Prerequisites to apply:
1) Be excited about at least one of the projects described below. (Please read the project descriptions at the bottom of the page to make sure that you satisfy any class specific prerequisites of the project. Please, also note that most projects have no extra prerequisites).
2) Be available to meet once a week for an hour with your mentor, plus 1.5 hours of reading/work outside of the weekly meeting during the Winter and Spring quarters.
3) Be available for a few social gatherings.
4) Be interested in presenting some of what you have learned at the end of the program with the help and support of the mentoring team.
5) Be an undergraduate at DU.
APPLICATIONS ARE OPEN FROM NOV 1ST TO NOV 15TH 2022
Read the project descriptions at the bottom of this page and
APPLY HERE!
We will be in touch with news on the mentor-mentee pairings by Jan 8 2023.
Part of the mentoring team on a zoom meeting (Jesse, Flor and Kendall clockwise from top left).
the projects:
Graph Algorithms
How does your GPS find the shortest distance between your location and where you want to go? How do airlines ensure that there are enough planes in each airport at the time they need to be there? How does Google decide which pages you see first when you search for something?
All these problems were solved using a branch of mathematics called Graph Theory. We will explore the basics of graph theory with a focus on graph algorithms such as Dijkstra’s Algorithm, the Ford-Fulkerson Algorithm, and the PageRank Algorithm (which coincidently solve each problem above respectively). With time and sufficient interest, we may also discuss how to implement these algorithms using Python.
Prerequisites: None
Mentor: Casey Schlortt (she/her/hers)
Exploring infinity
an introduction to Set Theory
Are you a believer? Is the infinity real? Can we trust infinity?
In this project we will introduce basic concepts of set theory in order to understand what infinity means in mathematics. We will explore paradoxes, contradictions and interesting implications given by infinity.
Some of the concepts we will work on are: Arithmetic of ordinals and cardinals, the construction of the natural numbers, paradoxes such as the Hilbert's hotel one and equivalences of the axiom of choice.
Prerequisites: None
Mentor: Isis A. Gallardo (she/her/hers)
Introduction to Knot Theory
Knots are common objects in our world. Aside from being used to keep shoes on one’s feet, knots also appear in many scientific areas (including biology, chemistry, and physics).
We will see how knots can be analyzed, characterized, and classified through modern mathematical techniques. As we explore the fascinating landscape of this area of math, we will keep ourselves grounded with practical examples and applications (and we will surely come up with a few knot puns along the way!)
Prerequisites: None
Mentor: Jesse Parrish (he/him/his)
An Investigation of Modal Logics
Traditionally, the propositional calculus (PC) is widely accepted. However, there are limitations in such a logic; that is, there are phenomena throughout mathematics that PC does not capture.
Modal logic was devised to help remedy this issue. In general, a modal is an expression that is used to qualify the truth of a judgement. Modal logic, roughly speaking, analyzes the deductive behavior of the resulting modals. From the flexibility of the interpretation, there is a vast range of applications.
We will review PC and we will introduce syntax and semantics for modal logics as well as completeness and soundness theorems. We will also discuss decidability and filtration and time permitting, we will study the characterization and embedding theorems for modal algebras.
Prerequisites: None
Mentor: Kempton Albee
Graph Theory-Colorings
Any 2-dimensional picture can be filled in with 4 colors so that no two adjacent regions share the same color.
While this statement is easy to test, it was very challenging for mathematicians to prove. In this project, we will learn the basic concepts of Graph Theory, the study of relationships. We will focus on colorings and planar graphs, building up to a discussion of the 4 Color Theorem and proofs of similar theorems.
Prerequisites: None
Mentor: Kendall Bonner (she/her/hers)
Reinforcement learning and Markov chains
The universe is effectively random. This means that, even if it is deterministic, our ignorance forces us to use probability to describe it.
A Markov chain is a useful and important tool to describe the evolution of a random system. One of its uses is in machine learning, specifically self-supervised reinforcement learning. Recently, AlphaGo in the game of Go, and OpenAI Five in Dota 2 have shown supremacy in skill over the best human players. We will learn some beautiful and important theorems about Markov chains, and get hands on experience by working with them on a computer. The end goal is to teach a computer to balance a match-stick on a moving platform. Time permitting, we can try teaching a computer something more complicated, like snake, tetris etc.
Cool videos with more info: Our goal, Intro to Markov Chains, Lectures, Notes
Prerequisites: Basic probability, and basic python coding.
Mentor: Vladimir V. Kovalchuk