PATRICK J. COSTELLO

            M.S. Ohio State University, 1978            Major Area: Mathematics

            B.S. Harvey Mudd College, 1975            Major Area: Mathematics

            Thirty quarter-hours of graduate computer science courses at OSU.

            Professor, EKU 2003-present

            Associate Professor, EKU 1987-2003

            Assistant Professor, EKU 1982-1987

            Teacher, Kentucky Governor's Scholars Program 1984, 1986, 2001-2005

            Interim Chair of the Department of Math & Stat, 2001-2004

            Mathematical Association of America (25 year membership)

            American Mathematical Society

            Kappa Mu Epsilon

SELECTED PRESENTATIONS:

"Mathematics and Mingling: The Undergraduate Math Club," Project NExT workshop at Mathfest 2006, Knoxville, August 2006.

"Notable Numbers," Morehead State University, April 2006.

"Factoring and the Number Field Sieve," Kentucky Meeting of the MAA, Morehead, 2005.

"Large Smith Numbers," Kentucky Meeting of the MAA, Georgetown, 2002.

"Be Careful with RSA," Western Kentucky University, Bowling Green, 2001.

"Jordan Canonical Forms and DERIVE," Kentucky Meeting of the MAA, Louisville, 1992.

"Amicable Pairs of the Form(i,l)," Kentucky Academy of Science, Lexington, 1989.

"Mathematics, Puzzles, Games and Productive Thinking," Greater Louisville Council of Teachers of Mathematics annual meeting, 1986.

"Counting Problems," Conference on Computers in the Content Areas, Louisville, 1986.

"Even, Unimodular 12-Dimensional Quadratic Forms over Q(sqrt5)," AMS Summer Research
Conference on Computational Number Theory, California, 1985.

"Large Smith Numbers," West Coast Number Theory Conference, California, 1984.

"Number Theory and Public-Key Cryptosystems," Kentucky Meeting of the MAA, Louisville, 1983.

"A Little Amicable Number Theory," Miami University's Fifth Annual Math and Statistics Conference, Oxford, 1977.

PUBLICATIONS:

"Periodicity of the Parity of a Partition Function Related to Making Change," Mathematics of Computation, vol  77, no 263, (2008), pp. 1749-1754.

"More Palindromic Niven Numbers," Journal of Recreational Mathematics, vol 33, no. 1, (2005), pp. 18-21.

"New Amicable Pairs of type (2,2) and (3,2)," Mathematics of Computation, vol 72, no 241, (2003), pp. 489-497.

"A New Largest Smith Number," The Fibonacci Quarterly, vol 40.4, (2002), pp. 369-371.

"Lots of Smiths," Mathematics Magazine, vol 75, no 3, (2002), pp. 223-226.  Joint paper with Kathy Lewis.

"Titanic Primes," EKU Mathematical Sciences Magazine, Spring 1999, pp. 13-16.

"Computing Jordan Canonical Forms," The College Mathematics Journal, vol 25, no 3, (1994), pp.231-234.

"Factoring with the Arithmeticulator and UBASIC," Collegiate Microcomputer, vol 10, no 4, (1992), pp. 217-227.

"Semiperfect and Integer-Perfect Numbers," Mathematics and Computer Education, vol 25, no 2, (1991), pp. 150-157.

"Amicable Pairs of the Form (i,l)," Mathematics of Computation, vol 56, no 194, (1991), pp. 859-865.

"Analysis of a Recursive Algorithm for Computing Binomial Coefficients," Computer Science Education, vol 1, no 4, (1990), pp. 317-329.

"Even Unimodular 12-Dimensional Quadratic Forms over Q(sqrt 5)," Advances in Mathematics, vol 64, no 3, (1987),  pp.241-278. Joint paper with John Hsia.

"Some Properties of Pascal's Triangle," EKU Mathematical Sciences Magazine, vol 9, no 2, (1987), pp. 10-13.

"A Program in BASIC: Decimal to Binary Conversion," EKU Mathematical Sciences Magazine, vol 6, no 3, (1985), pp. 1-3.

"Public-Key Cryptography," Math Matrix, vol 1, no 1, (1984), p. 4. (Math Matrix is an OSU publication.)

"Public-Key Cryptography," EKU Mathematical Sciences Magazine, vol 5, no 1, (1983), pp.16-19.

"Density Problems Involving p_r(n)," Mathematics of Computation, vol 38, no 158, (1982), pp.633-637.

"Amicable Pairs of Euler's First Form," Journal of Recreational Mathematics, vol 10, no3, (1978), pp.183-189

"Amicable Numbers Via the Computer," Interface, vol 3, no 1, (1975), pp.43-50. (Interface is a Harvey Mudd College publication.)

PROBLEMS PUBLISHED:

    In The Pentagon: Problem 586 (Spring 2005)

    In The Pentagon: Problem 582 (Fall 2004)

    In The Pentagon: Problem 575 (Spring 2004)

    In The Pentagon: Problem 573 (Fall 2003)

    In The Pentagon: Problem 562 (Fall 2002)

    In The Pentagon: Problem 557 (Spring 2002)

    In The Pentagon: Problem 525 (Spring 1999)

RECENT PROBLEMS SOLVED:

Problems 4435 (Dec 1993), 4532 (Oct 1995), 4628 (Nov 1997), 4678 (Oct 1998), 4694 (Jan 1999), 4701 (Feb 1999), 4722 (Nov 1999), 4728 (April 2002), 4738 (Oct 2002), 4746 (Nov 2002), 4777 (April 2003) from School Science and Mathematics.

Problems 464 (Fall 1993), 513 (Fall 1997), 541 (Fall 2000), 552 (Fall 2001), 563 (Fall 2002), 564 (Fall 2002) from The Pentagon.

Problems 831 (Spring 1994), 959 (Spring 1999), 978 (Fall 1999), 1043 (Fall 2002), 1056 (Spring 2003), 1061 (Spring 2003) from The Pi Mu Epsilon Journal.

Problem 153 in the February 2002 issue of Math Horizons.

Problems 734 (Sept 2002), 746 (March 2003) from The College Mathematics Journal.

Problems 10947 (May 2002), 11109 (October 2004) [my solution published] from The American Mathematical Monthly.

AMICABLE PAIRS:

Discoverer of over 92000 amicable pairs including one pair with 1121 digits.

(See http://amicable.homepage.dk/apstat.htm for list of discoverers.)

Discoverer of a majority of the (2,2) amicable pairs including a pair of 233-digit numbers.

(See http://amicable.adsl.dk/aliquot/apstat/apreg22.txt for the list of all (2,2) amicable pairs.)

BOOK REVIEWS:

N. Robbins, Beginning Number Theory, Jones and Bartlett, 2004.

P. Schumer, Introduction to Number Theory, Boston: PWS-Kent, 1995.

J. Strayer, Elementary Number Theory, Boston: PWS-Kent, 1994.

G. Ehrlich, Fundamental Concepts of Abstract Algebra, Boston: PWS-Kent, 1991.

J. Gilbert and L. Gilbert, Elements of Modern Algebra (2^nd Edition), Boston: PWS-Kent, 1988.

J. Kaufmann, College Algebra, Boston: PWS, 1987.

ARTICLE REVIEWS:

"Harmonic Encryption" for The Pi Mu Epsilon Journal, 2004.

"The Tau, Sigma, Rho Functions and Some Related Numbers" for The Pi Mu Epsilon Journal, 2003.

"Further Developments Towards a Resolution of the Goldbach Conjecture" for The Pi Mu Epsilon Journal, 2003.

"Product Formula and Multiplicative Perfect Numbers" for The Pi Mu Epsilon Journal, 2002.

"When is Rank Additive?" for The College Mathematics Journal, 1997.

"A Computational Introduction to Eigenvalues" for The College Mathematics Journal, 1994.

"Using Mathematica to Find Minimal Length Confidence Intervals" for The Pentagon, 1993.

OTHER PROFESSIONAL ACTIVITIES:

Editor of The Problem Corner in The Pentagon magazine, Fall 2005-present.

Faculty sponsor of the EKU chapter of Kappa Mu Epsilon (national mathematics honor society), 1982-present.

Host of a national convention of KME at EKU in the spring of 1983.

Regional Director of the Southeast Region of KME, 1985-1997.

President-Elect of KME, 1993-1997

President of KME, 1997-2001.

Kentucky coordinator of the American High School Mathematics Exam, 1985-1993.

Judge for regional and state finals of the mathematics part of the Academic Sweet 16 Competition 1986-1987 and 1989-1992

Co-organizer of a departmental problem-solving group.

Organizer of students to participate in the Virginia Tech Regional Mathematics Exam and the national Putnam Mathematics Exam.

Faculty sponsor for Timothy Melvin's M.S. thesis (1987) entitled "Some New and Old Results Concerning Amicable Numbers."

Faculty sponsor for Lisa Whitis' undergraduate Honors Thesis (1991) entitled "Rediscovering Calculus."

Faculty sponsor for Kathy Lewis' M.S. thesis (1994) entitled "Smith Numbers: An Infinite Subset of N."

Faculty sponsor for Alexander Shaumayan's M.S. thesis (1998) entitled "Pollard's Number Field Sieve: A Modern Algorithm for Factoring Large Integers."

Faculty sponsor for Shannon Purvis' undergraduate Honors Thesis (2000) entitled "A New Look at Math: It Really Does Have a Purpose."

Faculty sponsor for Shawn Clift's M.S. thesis (2002) entitled "RSA Encryption."

Faculty sponsor for Michael Osborne's M.S. thesis (2007) entitled "Partitions."

Co-organizer of the EKU Mathematics Teachers' Workshop 1984-1986.

Academic advisor for both math majors (1982-present) and computer science majors (1982-1995).

Advisor to Tim Melvin, Kathy Ponder, Lisa Whitis, Onecia Gibson and Wally Siddiqui in the preparation and presentation of talks to national conventions of KME.

Advisor to Paulette Wilson, Paula Christian, and Kathy Lewis in the preparation and presentation of talks to the EKU Mathematical Sciences Symposium.

Transporter of students to national KME conventions in Dallas, TX(1985), San Luis Obispo, CA (1987), Topeka, KS (1989), Florence, AL (1991), Niagara University, NY (1993), Durango, CO (1995), Springfield, MO (1997), Lakeland, FL (1999), Topeka, KS (2001), Tulsa, OK (2003).

Organizer of EKU Summer Undergraduate Number Theory Institute held in June 2000.

HONORS:

Selected to teach the Honors Calculus I-IV classes during the 1988-1990, 1991-1993, and 1994-1996 school years.

Selected to be the speaker at the Lincoln County High School Academic Awards Banquet in 1987.

Received the 2008 Award for Distinguished College or University Teaching of Mathematics by the Kentucky Section of the Mathematics Association of America.