ruth luo
Department of Mathematics
University of Illinois at Urbana-Champaign

About


Since Fall 2014, I have been a math graduate student at the University of Illinois at Urbana-Champaign.

I am currently working on my PhD. I received a MS in Mathematics from UIUC in 2016. Prior to attending UIUC, I received a BS in Mathematical Sciences from Carnegie Mellon University in 2014.

Here is a youtube video of how to pronounce my last name.



Feel free to contact me!
Email: ruthluo2 (at) illinois.edu
Office: Coble Hall B2

Research







Ibirapuera Park in São Paulo, Brazil with Anton Bernshteyn

I am mostly interested in graph theory, extremal combinatorics, and probabilistic combinatorics. My advisor is Alexandr (Sasha) Kostochka. My Erdős number is at most 2!

Recent Work
For a full list of preprints and published papers, please see my CV.

  • (with Zoltán Füredi and Alexandr Kostochka) On 2-connected hypergraphs with no long cycles.
    (Paper)
  • (with Zoltán Füredi and Alexandr Kostochka) Avoiding long Berge cycles II, exact bounds for all n.
    (Paper)
  • (with Alexandr Kostochka) On r-uniform hypergraphs with circumference less than r .
    (Paper, Talk slides)
  • (with Zoltán Füredi and Alexandr Kostochka) Avoiding long Berge cycles, Journal of Combinatorial Theory, Series B, 2018.
    (Paper, Talk slides)
  • (with Zoltán Füredi and Alexandr Kostochka) A variation of a theorem of Posa. Discrete Mathematics, 2018.
    (Paper)
  • (with Zoltán Füredi, Alexandr Kostochka, and Jacques Verstraëte) Stability in the Erdős--Gallai Theorem on cycles and paths, II. Discrete Mathematics, 2018.
    (Paper, Talk slides)
  • (with Zoltán Füredi and Alexandr Kostochka) Extensions of a theorem of Erdős on nonhamiltonian graphs. Journal of Graph Theory, 2018.
    (Paper)
  • The maximum number of cliques in graphs without long cycles. Journal of Combinatorial Theory, Series B, 2017.
    (Paper, Talk slides)


Additionally, I have served as a graduate mentor for three undergraduate research projects through the Illinois Geometry Lab: Spring 2015 - Collaboration graphs and cluster analysis under Steve Bradlow, Spring 2016 - Interactive Learning Tools for Linear Algebra under Cary Malkiewich and Jenya Sapir, Fall 2017 - The Four Color Theorem: Archival Documentation and Outreach under Jeremy Tyson.

Teaching


I have had the pleasure of teaching thousands of students during my graduate and undergraduate career. In 2018, I won the Department TA Instructional Award from the UIUC Mathematics department.

I am currently not teaching in Spring 2019.

Review material for Applied Linear Algebra

In the past I have taught the following courses.
At University of Illinois

  • Fall 2018 - 1 section of Math 181: A Mathematical World (Instructor).*
  • Spring 2018 - 5 sections of Math 415: Applied Linear Algebra (TA).**
  • Fall 2017 - 5 sections of Math 415: Applied Linear Algebra (Head TA).**
  • Spring 2017 - 5 sections of Math 415: Applied Linear Algebra (Head TA).**
  • Fall 2016 - 5 sections of Math 415: Applied Linear Algebra (TA).**
  • Spring 2016 - 4 sections of Math 415: Applied Linear Algebra (TA).**
  • Fall 2015 - 2 sections of Math 231: Calculus II (TA).**
  • Spring 2015 - 4 sections of Math 415: Applied Linear Algebra (TA).**
  • Fall 2014 - 2 sections of Math 231: Calculus II (TA).*

* = On the list of Teachers Ranked as Excellent by their students
** = * + outstanding rating (4.8+/5)

At Carnegie Mellon University

  • Spring 2014 - 1 section of 21-241: Matrices and Linear Transformations (Linear Algebra) (TA).


From Linear Algebra and Its Applications by David Lay