Maureen T. Carroll

Associate Professor

Department of Mathematics

157 St. Thomas Hall

University of Scranton

Scranton, PA 18510

570-941-6346

This Week in Mathematics

Links to a new puzzler, biographies, and cool mathematics sites updated weekly.

Spring 2008 Courses

All course materials can be accessed through either the Blackboard system or the Angel system. Links to both systems can be found under the University links tab after logging in to my.scranton.edu . To access this page, be sure to use your standard University of Scranton username (typically your lastname followed by your first initial followed by a number) and password (Your password is either Royal ID plus two-digit day of birth OR Social Security Number plus two-digit day of birth).

Blackboard: For those of you using Blackboard for the first time, you may find the extra instructions at the Blackboard Login Instructions web page helpful. If you are not a new Blackboard user then you can just click on the link for your course below. Once you have successfully logged in, you will see your course name listed. After choosing your course name from the menu you will find, for example, the syllabus and text homework problem sheet in the Course Documents section.

Math 222 Analysis III

Math 142 Discrete Structures

Angel: For those of you accessing the Angel website, course information can be found under the Lessons tab.

Career Information for Mathematics Majors

Check out the web site www.mathclassifieds.org that pairs bachelor, master, and Ph.D. level graduates
in the mathematical sciences with potential employers.

Have you ever wondered what mathematics majors do with their degrees?
Mathematics majors have many job opportunities. Some you may have never
imagined. In fact, here's what some University of Scranton alumni mathematics majors
have done with their degrees.

Mathematics Club

carrollm1@scranton.edu

The officers for the 2007-2008 academic year are as follows:

President - Matt Prudente ( prudentem2@scranton.edu)

Vice President/Service Activities Coordinator - Erin Gilmartin ( gilmartinm2@scranton.edu)

Treasurer - Natalie Kottke ( kottken2@scranton.edu)

Activities

We typically sponsor several trips to local professional mathematics meetings every year. We also send students to undergraduate student conferences, actuarial fairs, and career fairs. We sent two teams to compete in the Garden State Undergraduate Mathematics Contest at Rutgers University in April 2004. One team (Ken Monks, Maria Monks, Steve Tizzoni) came in first place and the other (Jackie Carrigg, Michelle McGowan, Jeff Wojcik) came in eighth.

The Mathematics Club sponsors an annual event during Mathematics Awareness Month (see below) to bring faculty and students together in an informal setting. Typically, several faculty members explain one of their current scholarly interests. This is followed by a reception for faculty and students. Look for the club to sponsor an event during next year's Mathematics Awareness Month.

The Club also sponsors a Bi-Weekly Puzzle which appears every Wednesday. Solutions are posted the following week.

Some Papers

Tic-Tac-Toe on a Finite Plane
Everyone knows how to play tic-tac-toe. On an n x n board, if a player is able to place their marks "n in a row" either horizontally, vertically, or diagonally then they have won the game. What if we keep the rules of the game the same but increase the number of possible lines to include some that would not fit our standard description of "in a row"? We have done this in a systematic way by including only those lines prescribed by a finite affine plane, creating an interesting, geometrically motivated game. We discuss Latin squares and affine planes and the relationship between them in order to describe how the game is played on an affine plane. We also discuss projective planes, showing them as a natural extension of affine planes. Sample tic-tac-toe games on these finite planes are given and the existence of winning and drawing strategies for both players is discussed. (Appears in Mathematics Magazine, 77 (2004).)

Play tic-tac-toe on the affine plane of order 4 by clicking the board below.

The Wallet Paradox Revisited
In Martin Gardner's "Wallet Game", two players agree to wager the contents of their wallets. The player carrying the lesser amount of money wins the other player's amount. Assuming infinitely repeated trials, we view this game probabilistically and ask if an optimal strategy exists when the distribution of the players' amounts are required to have the same mean. In this paper, we show that no such strategy exists in both the discrete and nonatomic cases. We also consider the analogous restriction on the median. (Appears in Mathematics Magazine, 74 (1999) 378-383.)

Stuck in Traffic in Chicago: A World Wide Web Project
You are caught in bumper-to-bumper traffic heading south to downtown Chicago on Lake Shore Drive. Tuning your radio to the traffic station, you grit your teeth as you hear that the normal fifteen minute commute time from Montrose Street to Randolph Street has been replaced by forty minutes of torture. With all the time on your hands, you start wondering: "How do they calculate traffic times in Chicago?" (This web-based project for calculus students appears in MAA Online: Innovative Teaching Exchange, (2000) at http://www.maa.org/t_and_l/exchange/exchange.html.)

Invariance of the Wilansky Property
In 1991, A. K. Snyder and G. Stoudt identified the Wilansky property as a basis property for a Banach space. In my paper, this property is shown to be invariant with respect to the closed span of the coefficient functionals associated with a basis. (Appears in Analysis, 19 (1999) 327-340.)