In the diagram below, the radius of each of the smaller circles is r. What is the radius of the larger circle?
Author: Prof. Bockting
Solution to Toy Box – Fall 2023
Problem: If all possible (distinguishably different) arrangements of the letters A, C, C, L, L, S, U, and U are put in alphabetical order, in what position is the word “CALCULUS”?
Solution: The total number of distinguishably different arrangements of the letters A, C, C, L, L, S, U, and U is given by
To find the appearance of “CALCULUS,” we first, we need to “clear” all the arrangements that begin with A, of which there are
Those arrangements that begin with “CAC” will appear next on the list and need to be cleared as well. There are
of these, the number of distinguishable arrangements of the remaining letters L, L, S, U, and U.
The next several entries on the list will begin with “CALC,” followed by the letters L, S, U, and U. We can first clear the arrangements that start with “CALCL,” numbering
and then those that begin “CALCS,” which also number
Then the next arrangement on the list is “CALCULSU,” followed immediately by “CALCULUS.” Hence, “CALCULUS” appears in position number
630 + 30 + 3 + 3 + 1 + 1 = 668.
MAT Community Tea & Coffee Hour on F 2/2
Throughout the year, the Math 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.
Our next event will take place on Friday, 2/2 at 10:30-11:45 am in the MAT Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.
MAT Community Tea & Coffee Hour on 1/19
Throughout the year, the Math 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.
Our next event will take place this Friday, 1/19 at 1:30-2:45 pm in the MAT Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.
MAT Community Tea & Coffee Hour on Th 11/9
Throughout the year, the Department of Mathematical Sciences 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.
Our next event will take place this Thursday, 11/9 at 2:45-4:00 pm in the MAT Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.
DePaul Math Club
The DePaul Math Club meets Fridays at 12:00 in Arts and Letters 410. It’s a great time filled with pizza, beverages, great people, a relaxed environment, and some fascinating mathematics—math that’s both niche and underdiscussed and the hottest topics leading the math world today. We are usually joined by student researchers, graduate students, or professors—some from DePaul and some from other institutions—to share the math they work with. No math background required. We’re excited to see you there!
MAT Scholarships – Applications due 11/19
For those of you who are earning a degree from the Mathematical Sciences department, there are some scholarships that you are likely eligible for. We would like to encourage you to apply. The application process is very quick. Be sure that you upload your transcript on the application form. The scholarships can be found here: https://depaul.academicworks.com/users/sign_in
The deadline for applications is Sunday, 11/19.
21st Annual DePaul Undergraduate STEM Research Showcase on F 11/3
We invite you to mark your calendar and reserve the date for an exciting upcoming event: the 21st Annual Undergraduate STEM Research Showcase, taking place on November 3, 2023, at McGowan South (1st and 2nd floors).
Join us as students from our diverse science and health disciplines come together to present their cutting-edge research through engaging oral presentations and captivating poster displays. Additionally, the planning committee has secured several wonderful alumni speakers to grace us with their insights, adding a valuable perspective to this exceptional event.
More information, including a schedule of the day’s events can be found here: 21st Annual DePaul Undergraduate STEM Research Showcase
MAT Community Tea & Coffee Hour on F 10/27
Throughout the year, the Math 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 math students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.
Our next event will take place this Friday, 10/27 at 10:15-11:45 am in the Math Department office suite (on the 5th floor of SAC). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.
Math Events Calendar
Curious about what’s happening in the MAT department? Check out our Events Calendar.