Solution to Mathematical Toy Box – AQ2024 #2

Prof. Bockting Problems & Solutions

The integers 1 thru 100 are written on individual cards, and those 100 cards are mixed into a hat. Aisha draws one card at a time, without replacement, until she draws a card relatively prime to all the cards she has already collected. What is the maximum number of cards Aisha could draw in this game?

Solution: 90.  One can construct a sequence of maximal length as follows:

  • Starting with 2, include all the even numbers from 2 through 100, a total of 50.
  • Ignoring 1, now include all the odd numbers that are not primes over 50. Since there are 10 primes between 50 and 100, there are 49-10=39 of these.
  • The 90th pick will now either be a 1 or a prime over 50, all of which will be relatively prime to all those on the list.

MAT Community Tea & Coffee Hour Dates for Winter 2025

Prof. Bockting Events

Throughout the year, the MAT Department hosts a number of informal events meant to help build and sustain our mathematical sciences community here at DePaul. These events provide an opportunity to meet with fellow MAT students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.

We will have five teas during the winter quarter:

  • Friday, 1/17 at 1:30-2:45 pm
  • Friday, 1/31 at 1:30-2:45 pm
  • Friday, 2/14 at 1:30-2:45 pm
  • Friday, 2/28 at 10:30-11:45 am (note the different time)
  • Friday, 3/14 at 1:15-1:55 pm (note the different time)

These community hours will take place in the MAT Department office suite (on the 5th floor of SAC, roughly SAC 546). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.

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!