Mathematics is the study of shape and form, of numbers and patterns, of concrete examples and abstract generalizations. As a discipline mathematics is not easy to categorize. It is an art: there is great beauty in its execution and exposition. It is a science: it is extremely rigorous and it has an experimental aspect. It is pure: within mathematics one can create a whole universe and explore its properties. It is applied: many of the best ideas of mathematics arise from attempts at solving everyday problems, and some of its most pure concepts have surprisingly practical applications. It is a philosophy: mathematics is grounded in ideas. Most of all, mathematics is alive. Although mathematics has engaged human thought for millennia it is still today a vibrant and growing area of human endeavor with new and important discoveries. It is the goal of the Department of Mathematics not only to provide students with a firm foundation in the concepts and skills of mathematics, but to instill in them an appreciation for the beauty and power of the subject.
The Department of Mathematics offers a Bachelor of Science in mathematics, a Bachelor of Arts in mathematics and a Bachelor of Science in applied mathematical economics (in collaboration with the Department of Economics and Finance). We also offer a Master of Science in applied mathematics.
Alumnus earns top honors
Donation honors professor emeritus
University of Dayton faculty aren't always aware of their lasting impact on students' lives. But Harry Mushenheim, mathematics professor emeritus, learned of his influence on former student Dr. Pieter Wiersema '74 when the latter donated $10,000 to the department of mathematics in Mushenheim's honor.Read More
Problem of the fortnight
20 February, 2017
A tribute to Raymond Smullyan
(This puzzle is from Raymond Smullyan's book "The Lady or the Tiger? and Other Logic Puzzles." Raymond Smullyan died earlier this month at the age of 97. He was a mathematician, well-known for his logic puzzles (and books). See https://www.nytimes.com/2017/02/11/us/raymond-smullyan-dead-puzzle-creator.html?_r=0 for a wonderful remembrance of Dr. Smullyan.)
The king of a certain land had read "The Lady or the Tiger?" a story by Frank Stockton. The king decided to try his prisoners by a similar scheme: making the prisoner choose between two rooms, one of which (the one with the lady) brings freedom, while the other room (with the tiger) keeps the prisoner imprisoned. The king would post signs on the rooms, and would tell the prisoner certain facts about the signs. If the prisoner were clever ... and logical, the prisoner would go free.
In the first trial, the king explains to the prisoner that each of the two rooms contained either a lady or a tiger, but it is possible that there tigers in both rooms, or ladies in both rooms, or maybe one room contained a lady and the other room a tiger.
The sign on the door of Room I said, "In this room there is a lady, and in the other room there is a tiger." The sign on the door of Room II said, "In one of these rooms there is a lady, and in one of these rooms there is a tiger." Further, the king tells the prisoner that one of the signs is true while the other is false.
If you were the prisoner, which room would you select, assuming that you prefer freedom?
Solutions are due by noon on February 27. Remember, full explanations are needed!
The intent of this activity is simply to have fun thinking about mathematical problems. Anyone may submit a solution. You need not be a mathematics major to submit a solution.