Tom Moore's Web Page
General Information
I am a Professor of Mathematics in the
My degrees were obtained at Stonehill College and at The University of Notre Dame, both schools run by the Congregation of the Holy Cross.
For information on my current courses, office hours, etc. go here.
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Copyright (c) 2000 Scott Kim. All rights reserved.
Mathematical Interests
My research interests are in finite group theory and
number theory, as well as their connections to Recreational
Mathematics. See my publications
Pedagogical Interests
I am interested in the use of technology at all levels of the
mathematics curriculum.For example in an introductory Linear Algebra course I
have used MINimal MATlab from Joel W.
Robbin which accompanies his 1995 Matrix Algebra textbook. I have
most recently taught this course aided by MAPLE software from Waterloo Maplesoft. I am about to move
from Maple 9.5 to Maple 12 to use in various of my courses.
A great resource for software related to K-12 and collegiate level mathematics
is the Mathematics Archives WWW
Server at the
I am also interested in using recreational mathematics in my
mathematics teaching, whenever possible, especially in Abstract Algebra
courses. There, for example, I illustrate coset partitions using circular
residue designs on the subgroups of the integers mod m or on the group of units
mod m. We analyze peg-jumping games with the aid of the Klein four-group and
sliding marker games on star graphs with the aid of Lagrange's Theorem. In this same
spirit I have recently created a course and a manuscript called Mathematical
Games and Puzzles for K-12 Classrooms (MATC 560).
My graduate student, Neil Roza, is in the process of creating Java Applets for some of the games from my manuscript. At this time you can play Ducci's Game which is a subtraction game. It consists of rounds of subtraction (which the applet does for you) starting with a quadruplet of integers of your choice and with the goal being to arrive at four zeroes in the greatest number of steps. Go here to play. And use the browser's back arrow to return to this page.
Also available is the Pile Splitting Game. A natural number N is used as input. Triple click on the starting default value of 1; type your starting value of N; hit enter. The program generates the first split automatically into two summands. To change a summand just triple click on it and then type the value of your choice and hit enter. You then continue to split summands by double clicking on their folder symbols (and you can change the program's generated summands at any time with a triple click and by entering your choice). Continue splitting until you reach all 1s. For each split the applet will multiply the summands and finally it will total all these products. A surprise awaits you as you play again with the same number N and split in different ways! Go here to play, answering "open" to the request in the dialog box you'll see.
Pretty pictures and more! Make your own Residue Designs. This applet illustrates the arithmetic/algebra in the group of reduced residues modulo N. You first specify a natural number N as modulus and a multiplier which must be less than N and relatively prime to N. Do this by clicking on the change numbers button. (The slow draw button option is currently not implemented.) The applet places all the reduced residues equally spaced around a circle. Then it multiplies each residue by your choice of multiplier. If the answer to multiplying x on the circle is y (reduced mod N) on the circle, then a chord is drawn joining x and y. Images can be very intriguing. Go here to create a design, answering "open" to the request in the dialog box you'll see.
The game of SIM. Invented by Gustavus Simmons this game is from graph theory, specifically, the easiest case of Ramsey theory. But it can be played by preschoolers as well as adults! Two players take turns coloring the edges of the complete graph K6, each having a different color to use. The image of K6 we use is that of a hexagon and all its diagonals. The first to draw a triangle (with its corners on three of the hexagon's corners) is the loser. So it's a game of avoidance! Go here to play, answering "open" to the request in the dialog box you'll see. Thanks again to Neil Roza.
Mathematics Association of America
The Math and CS Department here at BSC hosted the annual
November meeting of the Mathematical Association of America-Northeastern
Section on Friday and Saturday, Nov. 16 and 17, 2001 and the theme was...Recreational
Mathematics! See what this national organization devoted to collegiate
level mathematics has to offer: MAA site.
Bill Ritchie, founder of Binary Arts (now Thinkfun), and me. November, 2001 Binary Arts/Thinkfun.
In
January, 2004, I traveled to the Joint Mathematics Meeting in Phoenix where my
colleague Tom Koshy from Framingham State College and I celebrated the
publication of his latest textbook. Here we are pointing out a small
contribution I made to this outstanding discrete mathematics text.
In January,
2006, Tom Koshy and I, and my daughter Katie, traveled to the Joint Mathematics Meetings at
San Antonio, TX, where Tom and I served as facilitators at a session on
Applications of Number Theory. The three of us also traveled in January, 2008 to the Joint Mathematics Meetings in San Diego. In January, 2009, Tom and I were co-facilitators at a session on
The Power and Beauty of Number Theory again at the Joint Mathematics Meetings, this time in Washington, D.C. Speakers included Ken Ono, Carl Pomerance, Kirstin Eisentrager and George Andrews.
A
note on the distribution of primes in arithmetic progressions.
The Journal of Recreational Mathematics, 1972, 5(4), p. 253.
Cayley's Color Group.
The Mathematics Teacher, 1973, 66(7), pp. 615-618.
Order as a subgroup-lattice homomorphism (with H. D'Alarcao).
American Mathematical Society Notices, 1973, 20(2), A-253.
Lagrange's Theorem Revisited (with H. D'Alarcao).
American Mathematical Monthly, 1975, 2(3), pp. 270-273.
Complete residue systems in the sequence of primes (with R. F. Sutherland).
Journal of Undergraduate Mathematics, 1975, 7(1), pp. 49-50.
Euler's formula and a game of Conway's (with H. D'Alarcao).
Journal of Recreational Mathematics, 1976, 9(4), pp. 249-251.
Isomorphisms between groups of rational numbers.
Mathematical Gazette: the Journal of the British Mathematical Association, 1980, 64, pp. 286-287.
An aspect of group theory in residue designs .
Two-Year College Mathematics Readings, Warren Page, editor, The Mathematical Association of America, 1981, pp. 254-257.
What hath Rubik wrought?.
Bridgewater Review, 1984, 2(2), pp. 25-26.
SIM on a microcomputer.
Journal of Recreational Mathematics, 1987, 19(1), pp. 25-29.
Counting bit strings with a single occurence of 00.
Pi Mu Epsilon Journal, 1988, 8(9), pp. 572-575.
Euclid's algorithm and Lame's theorem on a microcomputer.
The Fibonacci Quarterly, 1989, 27(4), pp. 290-295.
On the least absolute remainder Euclidean algorithm.
The Fibonacci Quarterly, 1992, 30(2), pp. 161-165.
Triangle Trek.
Bridgewater Magazine, 1992, 2(4), pp. 12-14.
Was Gauss Smart?
Math Horizons, November, 1999, p. 24.
This article has appeared in a book collection
The Edge of the Universe:
Celebrating Ten Years of Math Horizons
Deanna Haunsperger and Stephen Kennedy, Editors, pub. by the Mathematical Association of America, 2006.
Original Problems Published in Mathematics Journals
(7) Problem 926
Pi Mu Epsilon Journal, 1997, 10(7), pp. 579-580.
(10) The number 99
Pi Mu Epsilon Journal, 2008, 12(8), p. 494
(12) Magic squares of abundant numbers, submitted to the Pi Mu Epsilon Journal
(13) In what bases are 121, 232 and 343 perfect squares? , submitted to Crux Mathematicorum, Spring 2009
Department
of Mathematics and Computer Science
Hart Hall
Bridgewater State College
Bridgewater,MA 02325
U.S.A.
Telephone:
(508) 531-2328
Fax: (508) 697-1361
e-mail: moore@bridgew.edu