The 2017 Northern Illinois University Mathematics Contest took place on March 1. The first prize of $150, the second year in a row, was taken by Rebecca Dziubla, a senior mathematical sciences major from Roselle, IL. Jeremy Simonson, a senior electrical engineering major from DeKalb, IL, was second and won $100. The third place, with the prize of $75, was won by Matthew Swed, a sophomore mathematical sciences major from Paw Paw, IL. The winners will be recognized at the Department of Mathematical Sciences’ Award Ceremony and Reception on Sunday, April 23.
The annual Northern Illinois University Mathematics Contest has a format where freshmen and sophomores have a fair chance to compete with juniors and seniors. The underclassmen have fewer restrictions on their choice of problems to attempt. The contest is open to all full-time undergraduates at NIU. Each contestant turns in solutions to a choice of six out of eleven problems. Topics this year ranged from logic puzzles, algebra and geometry through calculus, differential equations and linear algebra. Professors Michael Geline, Y. C. Kwong and Gleb Sirotkin supervised the competition.
The following geometric problem was a popular choice among the contestants:
Without using any knowledge about the decimal expansion of the number Pi, show that 3<Pi< 4 holds. You can use geometric ways to introduce Pi for this problem.
Here is a linear algebra problem from the contest:
Suppose A and B are 3×3 matrices such that det A = 2016, det B = 2017 and the matrix products are equal AB = BA. Show that there exists a 3×3 matrix C such that CAB = I – the identity matrix. Moreover, for every 3×3 matrix D, we will have an equation of matrix products C(BAD) = ABCD.
For more information on the annual Math Contest, contact Gleb Sirotkin 815-753-6734 or by email at [email protected].