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.

Fall 2008 Courses

All course materials can be accessed through the Angel system. To find Angel, first login at my.scranton.edu . To login, 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). If you have trouble logging in then you will have to contact the Technology Support Center at (570) 941-4357.

Once you are successfully logged in at my.scranton.edu, click on the University tab near the top of the window. On this new page you will find the link to Angel as the first listed in the Academic Links box in the lower middle of the screen.

Once you have successfully logged in to Angel, you will see your course name listed in the box on the left. After choosing your course name from the menu you will find the syllabus among other information on the course page. Other course documents, including the text homework problems and quizzes, can be found by clicking the Lessons tab near the top of the screen.

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 2008-2009 academic year are as follows:

President - Danny Marx ( marxd2@scranton.edu)

Vice President/Service Activities Coordinator - Samantha Baietti ( baiettis2@scranton.edu)

Treasurer - Sarah Kelly ( kellys7@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.)