The Directed Reading Program (DRP) at UIC is a program in which undergraduate students are paired with graduate student mentors and pursue independent reading projects. The presentation session for the Spring 2024 iteration of the DRP will be held on Friday, April 26 from 11AM to 2PM in SEO 636. The schedule for the presentation session is as follows:
Undergraduate students are not expected to propose their own project, but they are welcome to if they so desire. A list of texts to consider, compiled by the DRP at The University of Texas at Austin, can be found here.
Undergraduate students interested in a first experience with mathematics outside the classroom, as well as undergraduate students who may have undergone challenges throughout their journey with mathematics as a result of their identity or life circumstances, are highly encouraged to apply.
The timeline for fall and spring iterations of the DRP is as follows:
Using Causal Inference To Study the Spread of COVID-19
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We demonstrate a use case of causal inference to learning a Bayesian network modeling the spread of COVID-19 across the USA. We describe the methods used as well as challenges faced. We also interpret the model learned and discuss additional methods to potentially improve its accuracy.
Sheaves and Cohomology: An Introduction
Max Nguyen, mentored by Vignesh Jagathese
Abstract: This presentation will introduce the notion of a sheaf, a useful tool to study properties of spaces. Despite this, sheaves still have some shortcomings. By studying these shortcomings one can derive a powerful invariant in the form of cohomology.
Convergence Theorem for Finite Markov Chains
Sebastian Tous, mentored by Nick Christo
Abstract: When does a finite Markov chain converge? At what rate does convergence occur? In this presentation, I will discuss the prerequisite conditions for convergence and give a full proof of the Convergence Theorem for Finite Markov Chains.
Representations and Lie Groups
Mustafa Nawaz, mentored by Jennifer Vaccaro
Abstract: Abstract: In this talk, we will define Lie groups, Lie algebras, and representations. We will discuss properties, and present Schur’s Lemma.
The Mathematics of Pricing Assets
Raghav Bhutani, mentored by Kevin Zhou
Abstract: This presentation introduces essential financial tools, focusing specifically on derivatives. We will explore the fundamental mechanics of derivatives, including detailed visual representations through payoff diagrams. The core of the discussion will center on the pricing of these assets, particularly through the lens of the Black-Scholes formula. Attendees will gain an understanding of what the Black-Scholes formula represents, its significance in financial markets, and its practical applications in asset pricing.
Introduction to Ideals and Varieties
Emma Todd, mentored by Emily Cairncross
Abstract: The discussion will define and cover some examples of affine varieties. Then we will define general ideals and radical ideals and explore their connection to varieties.
Models of Random Graphs
Juan Jose Rosendo, mentored by Katie Kruzan
Abstract: There are various models of random graphs that have different purposes. The different models and the Preferential Attachment Model. Each model will be defined, accompanied with an that will be introduced are the Erdos-Renyi graph, Generalized Random Graphs, Configuration Model, example. Last, a brief description behind the motivation of each model will be given.
Foundations of of Machine Learning: Learning Guarantees and Dimensionality Reduction
Markus Perez, mentored by Duan Tu
Abstract: When designing machine learning systems, fundamental questions from “What can be learned?” to “Can we design accurate and efficient learning algorithms?” arise. This presentation will provide an introduction to the PAC-Learning Framework, which allows us to analyze learnability, and the related concepts of Rademacher Complexity and VC-Dimension. Additionally, the basics of Dimensionality Reduction will be covered.
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We demonstrate a use case of causal inference to learning a Bayesian network modeling the spread of COVID-19 across the USA. We describe the methods used as well as challenges faced. We also interpret the model learned and discuss additional methods to potentially improve its accuracy.
Sheaves and Cohomology: An Introduction
Max Nguyen, mentored by Vignesh Jagathese
Abstract: This presentation will introduce the notion of a sheaf, a useful tool to study properties of spaces. Despite this, sheaves still have some shortcomings. By studying these shortcomings one can derive a powerful invariant in the form of cohomology.
Convergence Theorem for Finite Markov Chains
Sebastian Tous, mentored by Nick Christo
Abstract: When does a finite Markov chain converge? At what rate does convergence occur? In this presentation, I will discuss the prerequisite conditions for convergence and give a full proof of the Convergence Theorem for Finite Markov Chains.
Representations and Lie Groups
Mustafa Nawaz, mentored by Jennifer Vaccaro
Abstract: Abstract: In this talk, we will define Lie groups, Lie algebras, and representations. We will discuss properties, and present Schur’s Lemma.
The Mathematics of Pricing Assets
Raghav Bhutani, mentored by Kevin Zhou
Abstract: This presentation introduces essential financial tools, focusing specifically on derivatives. We will explore the fundamental mechanics of derivatives, including detailed visual representations through payoff diagrams. The core of the discussion will center on the pricing of these assets, particularly through the lens of the Black-Scholes formula. Attendees will gain an understanding of what the Black-Scholes formula represents, its significance in financial markets, and its practical applications in asset pricing.
Introduction to Ideals and Varieties
Emma Todd, mentored by Emily Cairncross
Abstract: The discussion will define and cover some examples of affine varieties. Then we will define general ideals and radical ideals and explore their connection to varieties.
Models of Random Graphs
Juan Jose Rosendo, mentored by Katie Kruzan
Abstract: There are various models of random graphs that have different purposes. The different models and the Preferential Attachment Model. Each model will be defined, accompanied with an that will be introduced are the Erdos-Renyi graph, Generalized Random Graphs, Configuration Model, example. Last, a brief description behind the motivation of each model will be given.
Foundations of of Machine Learning: Learning Guarantees and Dimensionality Reduction
Markus Perez, mentored by Duan Tu
Abstract: When designing machine learning systems, fundamental questions from “What can be learned?” to “Can we design accurate and efficient learning algorithms?” arise. This presentation will provide an introduction to the PAC-Learning Framework, which allows us to analyze learnability, and the related concepts of Rademacher Complexity and VC-Dimension. Additionally, the basics of Dimensionality Reduction will be covered.
Undergraduate students are not expected to propose their own project, but they are welcome to if they so desire. A list of texts to consider, compiled by the DRP at The University of Texas at Austin, can be found here.
Undergraduate students interested in a first experience with mathematics outside the classroom, as well as undergraduate students who may have undergone challenges throughout their journey with mathematics as a result of their identity or life circumstances, are highly encouraged to apply.
The timeline for fall and spring iterations of the DRP is as follows:
- Week 3, Monday: Program begins, students are paired with mentors
- Week 4, Monday: Project proposals due
- Week 9, Friday: Project updates due
- Week 13, Friday: Titles and abstracts due
- Week 16, Friday: Presentations
There will be a limited Summer 2024 iteration of the DRP. The deadline for applying is May 3. To learn more, email Michael Gintz at mgintz2@uic.edu.
The current list of mentors for the DRP is as follows:
Darius Alizadeh
Julian Benali
Emily Cairncross
Lisa Cenek
Nick Christo
Karoline Dubin
Michael Gintz
Vignesh Jagathese
Shin Wook Kim
Katie Kruzan
Zhehao Li
Jake Maranzatto
Clay Mizgerd
Chirag Singhal
Duan Tu
Jennifer Vaccaro
Kevin Zhou
The Fall 2023 DRP at UIC Presentation Session was held on December 1, 2023. There were four presentations:
This program is hosted by the UIC student organization Symbols of Inclusion and co-organized by Nick Christo and Michael Gintz. Questions regarding the program can be directed to Michael Gintz at mgintz2@uic.edu.
The current list of mentors for the DRP is as follows:
Darius Alizadeh
Darius Alizadeh is a 4th year PhD student who studies groups through their actions on geometric objects, aka geometric group theory. Any topic where you can draw pictures and think in shapes is a good fit for him, including manifolds, algebraic topology, and more. He would love to explore some interesting topic outside the standard curriculum. Math is a big world to explore!
Julian Benali
Julian Benali is a PhD student studying commutative algebra, though he also has interests in logic, number theory, and category theory. Julian is looking to work with an undergraduate on a reading project in pure math. The direction is up to the student, but potential topics could include p-adic numbers, intuitionist logic, or commutative algebra.
Emily Cairncross
Emily Cairncross is a 3rd-year PhD student studying Extremal Combinatorics. While her passion is combinatorics, she also loves algorithms, other CS+Math topics, and sometimes analysis. She is most interested in reading papers or surveys with undergraduate students on topics related to their interest. Understanding a math paper fully is a difficult and rewarding adventure!
Lisa Cenek
Lisa Cenek is a 1st year PhD student. During undergrad, she focused on graph theory, especially combinatorial optimization problems. Graph theory is an exciting area of math with lots of pretty drawings and interesting topics to read about. Lisa is open to working with students coming from any level of mathematics background (no prior experience with graph theory required). She also enjoys other computer science adjacent areas of math such as algorithms and logic, and she is looking forward to getting to work with a student on a topic they are interested in learning about.
Nick Christo
Nick Christo is a 4th-year PhD candidate studying probability, combinatorics, and statistical physics. I have in mind reading through a few chapters of a textbook, reading through papers is also an option on any MCS related topic. Reading independently can be a challenging experience that one has to almost learn how to do and would be happy to help make that an easier experience.
Karoline Dubin
Karoline Dubin is a 4th-year PhD student interested in probability theory, statistical physics, and computer science. She is interested in topics of math with physical motivation and algorithmic applications, and is excited to explore such topics with undergrads.
Michael Gintz
Michael Gintz is a second-year PhD student studying algebraic geometry and commutative algebra. He'd be happy to introduce students to any number of topics related in whole or in part to either of these fields, and would be most interested to go through a textbook at the student's level to introduce them to a topic.
Vignesh Jagathese
Vignesh Jagathese is a 3rd year PhD student studying Commutative Algebra and Algebraic Geometry. Vignesh likes to use algebraic formalism to encode and understand singularities, or how "bad" a given point or region in a space is, and would thoroughly enjoy working with a UIC undergraduate on such topics. Algebra is widely applied in many fields of mathematics, so there are a lot of different topics to study! Vignesh, for instance, also likes thinking about other applications of commutative algebra such as number theory, arithmetic geometry, or just algebra for its own sake. Ultimately, though, he is happy to mentor undergraduate students and guide them towards papers covering topics that they have interest in.
Shin Wook Kim
Shin Kim is a 3rd-year PhD student studying Complex Geometry. He is interested in reading with undergraduate students on any topic that they are interested in.
Katie Kruzan
Katie Kruzan is a 2nd year PhD student studying Mathematical Computer Science with particular interest in Algorithms and Graph Theory. She is interested in reading papers//texts with undergraduate students on topics related to their interest, and also help them learn the skills around getting the most bang-for-the-buck around reading academic texts.
Zhehao Li
Zhehao Li is a 5th-year PhD student. His research is about understanding number theory using algebra and geometry.
Jake Maranzatto
Thomas (Jake) Maranzatto is a 4th year PhD student working on problems at the intersections of graph theory, information theory, and learning algorithms. He enjoys topics with a range of applications, from sensor networks to recommendation systems to social science. He believes that the best way to understand CS theory results is to implement their algorithms and run experiments. He is interested in reading through recent papers from ML theory and algorithms conferences.
Clay Mizgerd
Clay Mizgerd is a 2nd-year PhD student working in probability and combinatorics. In addition to these fields, he especially enjoys number theory, and has a broad background in analysis and algebra. He is happy to read on any field of pure math, and looking forward to learning some new math together.
Chirag Singhal
Chirag Singhal is a second year Mathematics PhD student at UIC. His research interests lie in Number Theory and in particular, Arithmetic Geometry. He also has some side interests, which include Theoretical Computer Science and Combinatorics.
Duan Tu
Duan Tu is a 4th year PhD student studying Mathematical Computer Science. Her current research focuses on machine learning theory, but her interests also involve probability and discrete math in general. Through the Directed Reading Program, she wants to help undergraduate students break the seemingly steep barrier to advanced math and math research. She is excited to learn something new together with the student!
Jennifer Vaccaro
Jennifer Vaccaro is a 4th-year PhD student studying hyperbolic geometry, specifically representations of hyperbolic triangle reflection groups. However, she comes from an engineering background, and would love to work with either a math major or a non-math major on a geometry/topology reading project. Possible texts include "The Knot Book" or "Office Hours with a Geometric Group Theorist."
Kevin Zhou
Kevin Zhou is a 6th-year PhD student working in the intersection of mathematical logic, combinatorics, and theoretical machine learning. Outside of these areas, he also enjoys learning about CS theory as well as how mathematical logic can be applied to problems in algebra. Most broadly, he is excited by finding ways that seeming disparate areas of math and computer science come together and hold insight into each other.
The Fall 2023 DRP at UIC Presentation Session was held on December 1, 2023. There were four presentations:
Towards counting lines on a smooth cubic
Leila Dahlia, mentored by Sixuan Lou
Abstract: We will introduce modern machinery to count numbers of lines lying on a given surface.
Algebraic Topology and The Fundamental Theorem of Algebra
Mustafa Nawaz, mentored by Michael Gintz
Abstract: We will talk about the notion of homology and how it can be used to give an invariant of a circle. Then, using this we can prove the fundamental theorem of algebra.
Markov Chains: Introduction and Applications
Zahra Vasi, mentored by Clay Mizgerd
Abstract: Markov chains serve as useful mathematical models for studying movements among elements in a set. These chains have unique properties that allow mathematicians to understand and predict their long-term behavior. This presentation discusses some essential definitions and properties associated with Markov chains and several examples of useful and interesting applications.
Computational Learning Theory and Probabilistic Models
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We examine the framework of PAC learning and provide examples of problems that are PAC learnable as well problems that are not. We then investigate this framework applied to learning Bayesian Networks. We address the limitations of this framework, and provide a concrete example of learning a Bayesian network given real-world medical data.
Leila Dahlia, mentored by Sixuan Lou
Abstract: We will introduce modern machinery to count numbers of lines lying on a given surface.
Algebraic Topology and The Fundamental Theorem of Algebra
Mustafa Nawaz, mentored by Michael Gintz
Abstract: We will talk about the notion of homology and how it can be used to give an invariant of a circle. Then, using this we can prove the fundamental theorem of algebra.
Markov Chains: Introduction and Applications
Zahra Vasi, mentored by Clay Mizgerd
Abstract: Markov chains serve as useful mathematical models for studying movements among elements in a set. These chains have unique properties that allow mathematicians to understand and predict their long-term behavior. This presentation discusses some essential definitions and properties associated with Markov chains and several examples of useful and interesting applications.
Computational Learning Theory and Probabilistic Models
Zach Alzubi, mentored by Abhijeet Mulgund
Abstract: We examine the framework of PAC learning and provide examples of problems that are PAC learnable as well problems that are not. We then investigate this framework applied to learning Bayesian Networks. We address the limitations of this framework, and provide a concrete example of learning a Bayesian network given real-world medical data.
This program is hosted by the UIC student organization Symbols of Inclusion and co-organized by Nick Christo and Michael Gintz. Questions regarding the program can be directed to Michael Gintz at mgintz2@uic.edu.