Solution to Mathematical Toy Box – AQ2024 #1

Prof. Bockting Problems & Solutions

The coefficients of the quadratic function f(x)=ax2+bx+c are chosen from the numbers 1 through 6 by three independent rolls of a fair die. What is the probability that the parabolic graph of  y=f(x) has its vertex on the x-axis?

Solution:  5/216 . There are  63=216 possible outcomes for the ordered triple of coefficients (a, b, c). The vertex of the graph will lie on the x-axis if and only if the discriminant b2-4ac=0. Since b must therefore be even, the possibilities can be narrowed down quickly to these five:

(1, 2, 1), (2, 4, 2), (1, 4, 4), (4, 4, 1), and (3, 6, 3).

Alumni Panel on PhD Programs

Prof. Bockting Events, Outreach

We invite you to attend a panel discussion with recent DePaul alumni on their experiences in PhD programs!

Who: Anyone who is curious about PhD programs in science and math

What: A panel discussion in which recent DePaul alumni discuss their experiences applying for and taking part in PhD programs in pure and applied math.

When: November 7 at 4:30 PM

Where: in Arts & Letters Hall, Room 308 and on Zoom at https://depaul.zoom.us/j/95804448725

We hope to see you there!

Combinatorics of Coxeter Groups (WQ class)

Prof. Bockting Uncategorized

Looking for an interesting class to fill out your winter schedule? Check out Dr. Petersen’s course on the combinatorics of Coxeter groups! In the class, you will use combinatorial thinking to understand the structure of Coxeter groups. The primary example is how combinatorics of permutations connect to properties of the symmetric group.  A PDF of the flyer can be found here.

Math Research Opportunities for Summer 2025

Prof. Bockting Student Opportunities

Already thinking of all the cool math you’re hoping to do next summer?  Then take a look at this page!

https://sites.google.com/view/mathreu

It contains a listing of the Research Experience for Undergraduates (REUs) aimed at mathematics students that will plan to run in the summer of 2025.

Interested in doing research closer to Chicago?  Then you might consider applying to the CSH Undergraduate Summer Research Program (URSP).  Not sure where to start?  Reach out to the math department’s undergraduate research coordinator, Dr. Emily Barnard, at e.barnard@depaul.edu!

EDGE Summer Program

Prof. Bockting Student Opportunities

Applications for the EDGE Summer Program are now open! Apply today.

The EDGE Summer Program is a four-week, residential session designed to prepare a cohort of gender nonconforming individuals to thrive in their PhD programs in the mathematical sciences. The 2025 EDGE Summer Program will be held June 1 – June 28, 2025 at the University of Tennessee, Knoxville.

Program activities include:

  • Four core workshops in courses such as algebra, analysis, measure theory, and machine learning.
  • Daily collaborative problem sessions with advanced graduate student mentors.
  • Regular office hours and highly personalized feedback from facilitators.
  • Weekly colloquium on a variety of research topics.
  • Special discussions on equity and identity in mathematics, teaching practices, and other professional development skills.

 

The EDGE Foundation will cover all travel, room, and board expenses related to the Summer Program. Program participants will also receive a modest stipend.

Applicants to the program should be women or gender nonconforming individuals who: 1) are applying to PhD programs in the mathematical sciences or 2) just completed their first year in a PhD program in the mathematical sciences. Students from underrepresented minority groups are especially encouraged to apply.

Applications for the 2025 EDGE Summer Program are now available at https://www.mathprograms.org/db/programs/1338. Applications are due February 14, 2025. For more information, visit https://www.edgeforwomen.org/summer-session/. Please send any questions to edgestaff@edgeforwomen.org.

 

Printable flyer available here.

MAT gives back

Prof. Bockting Outreach

Shortly before the start of autumn classes, eighteen faculty and staff from Mathematical Sciences joined together and spent the day volunteering with Nourishing Hope, one of the largest and longest-operating hunger relief organizations in Chicago. Volunteers spent the day packing groceries, sorting food, and assisting in other important tasks.

 

 

Photos from the warehouse!

2024 Summer Undergraduate Research

Prof. Bockting Events, Math Talks, Student Opportunities

Several students from the DePaul mathematics community spent their summers engaging in full-time mathematical research. Some students conducted research with DePaul faculty as part of the Undergraduate Summer Research Program, while others conducted research at external institutions.  Regardless of location, students learned to ask and answer their own questions, and even proved things that had never been proven before! So cool!

At the end of the summer, the following students came together and presented their work at the 2024 Mathematical Sciences Summer Research Showcase:

  • Rose Bittle, Modifications to the Spiral Array
  • Clara Campos, Optimal Transportation on Histograms (Research mentor: Dr. Enrico Au-Yeung)
  • Erik Dahlen, The Imbalance of a vector in a d-dimensional hypercube and the Eulerian numbers (Research mentor: Dr. T. Kyle Petersen)
  • Joosung Lee, Imbalance and Eulerian numbers (Research mentor: Dr. T. Kyle Petersen)
  • Owen Levens, Bijection, Collaboration, and Perseverance in Global Pattern Avoidance (Research mentor: Dr. Bridget Tenner)
  • Blair Johnson, Odd-Even Transposition Sort (Research mentor: Dr. T. Kyle Petersen)
  • Nicholas Oses Frola, Finding Frobenius Symmetry for Four Element Sets (Research mentor: Dr. David Sher)
  • Olivia Medina, 2D Conical Radon Transform used in Medical Imaging (Research mentor: Dr. Enrico Au-Yeung)

Abstracts for the student talks can be found here: 2024 Summer Research Showcase Abstracts

Interested in learning more about these students’ experiences? Keep an eye out for upcoming DePaul Math Club talks! 

Are you interested in conducting mathematical research? (Great!) You can start by talking to the faculty members you know or by reaching out to the MAT department’s undergraduate research coordinator, Dr. Emily Barnard (e.barnard@depaul.edu).

Nebraska Conference for Undergraduate Women in Mathematics (NCUWM)

Prof. Bockting Events, Student Opportunities

The Nebraska Conference for Undergraduate Women in Mathematics (NCUWM) will be accepting applications for participants between October 1 and October 18. This conference is open to all undergraduates and provides most of the local funding as well as some travel support. Students may present research talks or posters, or they can attend without presenting. The conference is helpful for all students, whether they know they want to go to graduate school in math or whether they like math and are unsure what to do with it. Please consider applying!

 

The conference will take place January 31 – February 2, 2025.  More information can be found here: NCUWM