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


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

Prior to attending UIUC, I received a Bachelor of Science 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)
Office: Coble Hall B2


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!


  • (with Zoltán Füredi, Alexandr Kostochka, and Jacques Verstraëte) Stability in the Erdős--Gallai Theorem on cycles and paths, II. Submitted.
  • (with Zoltán Füredi and Alexandr Kostochka) Extensions of a theorem of Erdős on nonhamiltonian graphs. Submitted.
  • The maximum number of cliques in graphs without long cycles. Journal of Combinatorial Theory, Series B, 2017.
    (Paper, Talk slides)
  • (with Zoltán Füredi and Alexandr Kostochka) A stability version for a theorem of Erdős on nonhamiltonian graphs.Discrete Mathematics, 2016.
    (Paper, Talk slides, Poster)
  • (with Zhanar Berikkyzy, Steve Butler, Jay Cummings, Kristin Heysse, Paul Horn, and Brent Moran) A forest building process on simple graphs. Submitted.
  • (with Xingqin Qi, Edgar Fuller, Rong Luo, and Cun-Quan Zhang) Signed quasi-clique merger: a new clustering method for signed networks with positive and negative edges. International Journal of Pattern Recognition and Artificial Intelligence, 2015.

Additionally, I have served as a graduate mentor for two 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.


For Fall 2017, I am teaching 5 sections of Math 415: Applied Linear Algebra.

Some review material.

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

At Carnegie Mellon University

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

From Linear Algebra and Its Applications by David Lay