Department of Mathematics

Western Kentucky University

Bowling Green, Kentucky 42101

(270) - 745 - 6213

Degrees
PhD, University of Florida, 1988 |
Memberships Mathematical Association of America Phi Beta Kappa |

Professional
Experience
Mathematics Professor, WKU, 1989-Present Post-Doctoral Associate, UF, 1988-89 Graduate Teaching Assistant, UF, 1983-1988 |
Research Interests
Probability Theory |

Average Extrema of a Random Walk with a Negative Binomial Stopping Time, International Journal of Pure and Applied Mathematics, 88, No. 3 (2013), 391 - 405.

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A Two-Sided Boundary Problem for Two-Dimensional Random Walks, International Electronic Journal of Pure and Applied Mathematics, 6, No. 2 (2013), 63 - 75.

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Mean Maximum Difference Between Simple Random Walks, Journal of Probability and Statistical Science, 10, No. 2 (2012), 111-124. (pdf available on request)

Collision of One-Dimensional Random Walks, The

A Geometric Gambling Game (with Frank Polivka), The

A Generalized Martingale Betting Strategy (with Michael D. Russell),

Limits of Mean and Variance of a Fibonacci Distribution, The Mathematical Scientist, 34, No. 1 (2009), 25-29. (pdf available on request)

Fibonacci Fractions from Heron's Square Root Approximation of the Golden Ratio,

Average Lengths for the Two-Player Name Game,

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TI-83/84 Graphing Calculator Manual for David S. Moore's

Binomial Bowling (with Patrick Brown), * Missouri Journal of
Mathematical Sciences,* 18,
No. 1 (2006), 17-25.

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Here

Approximating Pi with the Golden Ratio (with Stacy Linn), *The
Mathematics Teacher*, 99,
No. 7 (2006), 472-477. (pdf available on request)

TI-83 Graphing
Calculator Manual for Moore and McCabe's *Introduction to the
Practice of Statistics* - 5th Edition, W.H. Freeman and
Company, 2005.

Random Bowling, *The Journal of Recreational Mathematics,*
32, No. 2 (2004), 125-129.

TI-83 Graphing
Calculator Manual for David S. Moore's *The Basic Practice of
Statistics* - 3rd Edition, W.H. Freeman and Company,
2003.

TI-83 Graphing
Calculator Manual for Moore, McCabe, Duckworth, and Scove's *The
Practice
of Business Statistics* - W.H. Freeman and Company,
2003.

TI-83 Graphing
Calculator Manual for Moore and McCabe's *Introduction to the
Practice of Statistics* - 4th Edition, W.H. Freeman and
Company, 2002.

Generalized Random Walks with Negative Binomial Stopping Times
(with Mark W. Rogers), *New Zealand Journal of
Mathematics,* 30,
No. 1 (2001), 69-79.

Uniform Convergence of the T-Distributions, * Missouri Journal
of Mathematical Sciences,* 12,
No. 3 (2000), 193-203.

View
Here

Designing Payoffs for Some Probabilistic Gambling Games (with
Randall J. Swift), *Missouri Journal of Mathematical
Sciences,* 11, No. 2
(1999), 93 -102.

View
Here

TI-83
Graphing Calculator Manual for David S. Moore's *The Basic
Practice of Statistics*, W.H. Freeman and Company,
1999.

Quit When You Are Ahead, *The Mathematical Scientist,* 23, No. 1 (1998), 41-49.

TI-83 Graphing Calculator Manual for Moore and McCabe's *Introduction
to
the Practice of Statistics*- 3rd Edition, W.H. Freeman and
Company, 1998.

Generalized stochastic integration on nuclear spaces (with James
K. Brooks) Dedicated to Prof. C. Vinti. * Atti Sem. Mat. Fis.
Univ. Modena* 46,
Suppl. (1998), 83-98.

Generalized Stochastic Integral for Real and Hilbert Processes
(with James K. Brooks), *Atti. Sem. Mat. Fis. Univ.
Modena* 46, No. 1
(1998), 189-247.

Goodness of Fit Tests For Normality, *Mathematica in Education
and Research*, 5,
No. 2 (1996), 23-30.

Commutation of Variation and Dual Projection, *Proceedings of
the American Mathematical Society*, 123, No. 5 (1995), 1591-1595.

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Here

Generalized Boundary Problem For One-Dimensional Random Walks, *Mathematica
in Education*, 3,
No. 4, (1994), 11-16.

Stopped Random Walks: Areas and Lengths (with Lon Maynard), *The
Pi
Mu Epsilon Journal*, 9,
No. 10 (1994), 654-661.

View
Here

The Series n^m x^n and a Pascal-like Triangle, *The College
Mathematics Journal*, 25,
No. 2 (1994), 99-101.

Determining Sample Sizes for Monte Carlo Integration, *The
College Mathematics Journal*, 24, No. 3 (1993), 254-259.

Characterization of O-summable processes, *Journal of
Theoretical Probability*, 5,
No. 3 (1992), 585-596.

Preview
Here

A vector measure approach to the optional stochastic integral
(with James K. Brooks), *Ulam Quarterly* 1, No. 1 (1992), 18-26.

View
Here

A characterization of Hilbert stochastic integrals (with James K.
Brooks), *Atti. Sem. Mat. Fis. Univ. Modena* 39 (1991), 113-129.

The optional stochastic integral (with James K. Brooks), Seminar on Stochastic Processes 1988,
Birkhauser, Boston (1989), 45-54.

Preview
Here

**Dissertation**: Optional Stochastic Integration in Hilbert
Space with Applications to Nuclear Spaces (1988).

"Runs of Identical Outcomes in a Sequence of Bernoulli Trials" - Matthew Riggle, May 2018.

"Boundary Problems for One and Two-Dimensional Random Walks" - Miky Wright, May 2015.

"Random Walks with Elastic and Reflective Lower Boundaries" - Lucas Devore, December 2009.

"Generalized Probabilistic Bowling Distributions" - Jennifer Hohn, May 2009.

"A Generalized Random Walk with a Betting Scenario" - Michael Russell, May 2007.

"Uniform Convergence of Standardized Special Distributions" - Marcia Lami, May 2002."New Theories in Random Walks" - Lina Jichi, December 1998.

"Generalized One-Dimensional Random Walks With Negative Binomial Stopping Times" - Mark Rogers, May 1997.

"A Fibonacci Martingale Betting Strategy" - Sarah McDaniel, Fall 2019

"Alternate Proof and Variations of the Buffon Needle Problem" - Mary Lacy, Spring 2017

"Sums of Independent Geometric Random Variables" - Lindsey Traughber, Fall 2013

"Crapoulette: Full-Deck Craps" - Dustin Gentile, Fall 2013

"Four-Sided Boundary Problem for Two-Dimensional Random Walks" - Miky Wright, Summer 2013

"Sums of Independent Exponential Random Variables" - Chelsea Gelley, Spring 2013

"Craps: Rolling the Dice" - Sarah Long, Fall 2011

"Average Area Under a Stopped Random Walk" - Alyssa Surina, Spring 2011

"A Geometric Betting Challenge" - Frank Polivka, Spring 2008

"A Goodness of Fit Test on a Queue: Is It a Poisson
Distribution?" - Catherine Wilson, Spring 2008

"A Truncated Geometric Distribution" - Quinn Thomas, Fall 2007

"Using the Math: Satellite Orbits" - James Overton, Fall
2007

"Mean and Standard Deviation in Random Bowling" - Jennifer Hohn, Spring 2007

"Hypothesis Testing for Exponential Distributions" - Jennifer Jones, Spring 2007 "A One-Sided Boundary Problem for Two-Dimensional Simple Random Walks" - Aziz Bah, Summer 2005"Average Extrema of Geometric Random Walks" - Justin Grieves, Spring 2005

"A Distribution of Geometric Averages" - Jennifer Helm, Fall 2004

"Increasing the Accuracy of Confidence Intervals for Exponential Means" - Mark Mabry, Fall 2004

"Averages and Probabilities for Casino Betting Games" - Leslie Adams, Fall 2004

"Binomial Bowling" - Patrick Brown, Spring 2004

"Approximating Pi with the Golden Ratio" - Stacy Patrick, Fall 2003

Research Start-Up Fund Grant for a new faculty position in
probability and statisics. Funded by Kentucky EPSCoR and WKU (in a
2:1 ratio) for $25,000, 2007-09.

Statistical Inference on the TI-82/83 - Proposal to develop
calculator programs for the course Math 203. Funded by Kentucky
PRISM-UG Statewide Project for $6020.30, July - Dec. 1996.

Computer Experiments in Probability - Proposal to develop a Computer Lab Workbook to supplement the sequence Probability & Statistics I and II. Funded by Kentucky PRISM-UG Statewide Project for $5672.98, May - Dec. 1994.

MATH 116: College Algebra

MATH 116H: Honors College Algebra

MATH 117: Trigonometry

MATH 118: College Algebra and Trigonometry

MATH 126/136: Calculus I

MATH 126H: Honors Calculus

MATH 183/203: Introductory Statistics

MATH 137/227: Calculus II

MATH 275: Simple Random Walks

STAT 301: Applied Statistics

MATH 307: Linear Algebra

MATH 310: Discrete Mathematics

MATH 327: Multivariable Calculus

MATH 329/382: Probability and Statistics I

MATH 337: Elements of Real Analysis

MATH 398: Independent Study

MATH 403: Geometry for Middle School Teachers

MATH 409: History of Mathematics

MATH 411: Problem Solving for Elementary and Middle School Teachers

MATH 429/482: Probability and Statistics II

MATH 431: Intermediate Analysis

MATH 475: Topics in Mathematics

MATH 498: Senior Project

Graduate Courses Taught

MATH 501: Probability for High School Teachers

MATH 509: History of Modern Mathematics

MATH 529: Applied Probability

MATH 530: Mathematical Statistics

MATH 532: Measure Theory

MATH 540: Stochastic Processes

MATH 599: Thesis Direction

1. Department of Mathematics Lead Academic
Advisor: Fall 2008 - Present

2. Faculty Senator: Fall 1990 - Spring 1994, Fall 2004 -
Spring 2006.

(a) Faculty Status and Welfare
Committee: Fall 1990 - Spring 1993; Chair, Fall 1992 - Spring
1993.

(b) Chair of Academic Affairs
Committee: Fall 1993 - Spring 1994.

(c) Executive Council of the
Faculty Senate: Fall 1992 - Spring 1994.

3. University's Academic Quality Committee: Fall 2005 - Spring 2006.

4. University's Undergraduate Curriculum Committee: Fall 2004 - Spring 2005

5. Vice-Chair, Kentucky Section of the Mathematical Association of America: Spring 1995 - Spring 1998.

6. Academic Council: Fall 1994 - Spring 1998.

(a) Rules Committee: Fall 1994 -
Spring 1998.

7. Graduate Council: Fall 2001 - Spring 2003.

8. Teacher Education Committee: Fall 2001 - Spring 2003.

9. Department of Mathematics Director of Graduate Studies: Summer 2001 - Summer 2002.

10. Department of Mathematics Graduate Committee: Fall 2000 - Spring 2002, Fall 2004 - Spring 2006.

11. Department of Mathematics Majors Committee:

Chair: Fall 1992 - Spring 1994 and
Spring 1998 - Spring 2000. Member: Fall 2000 - Spring 2002.

12. Department of Mathematics Undergraduate Committee:

Member: Fall 1989 - Spring 1992, Fall
2005 - Present; Chair: Fall 1990 - Spring 1992.

13. Department of Mathematics Undergraduate Service Courses Committee: Chair: Fall 1994 - Spring 1996.

14. Department Headship Search Committee: Fall 1990 - Spring 1991, Fall 2000 - Spring 2001, Fall 2001 - Spring 2002.

15. Ogden College Dean Search Committee: Spring 1993 - Fall 1994.

16. Department of Mathematics SACS Accredidation Committee: Fall 1992.

17. Department of Mathematics Strategic Planning Committee: Spring 1998 - Spring 2002.

18. Mathematics Hiring Committee: Summer 1992 - Spring 1994; Fall 1998 - Spring 2000, Fall 2001-Spring 2002, Fall 2005 - Spring 2007.

19. Department of Mathematics Symposium Committee: 1990, 1991, 1995, 1997.

20. Academic Advisor: Spring 1991 - Present.

21. Mathematics Department Awards and Scholarship Committee (Chair): Fall 2003 - Spring 2013.

22. Johnson Award Committee: 1991, 1992, 1997, 1998.

23. Bueker Award Committee: 1992, 1995, 1996.

24. Quizmaster/Judge in Annual Junior High Math Bowl: 1990 - 1993, 1995 - 1998.

25. Grand Awards Judge at International Science and Engineering Fair: May, 1992

Rolling Dice Until All Become Six, 29th Annual Mathematics
Symposium, November 2009.

Limits of Mean and Variance of a Fibonacci Distribution - KY
Section of MAA, Western Kentucky University, March 2008.

Non-Equally-Likely Binomial Strings: Does P(WWWLL) = P(LLWWW) -
27th Annual Mathematics Symposium, October 2007

Generating Fibonacci Fractions from Heron's Method, 26th Annual
Mathematics Symposium, November 2006.

Technology Throughout The Curriculum - an invited two-hour short course presented at the KY Section MAA meeting at Morehead State University - March 1998.

Uniform Convergence of the T-Distribution - WKU Department of Mathematics Colloquium, March 1998.

Statistics Made Easy with a TI-83 - 17th Annual Mathematics
Symposium, Western Kentucky University, October 1997.

Interchange of Limits for Random Walk Areas. KY Section of MAA,
Western Kentucky University, April 1997.

Hyperbolic Trig Functions and The Real-Life Falling Object
Problem. WKU Department of Mathematics Colloquium, Feb. 1996.

A Model for a Foraging Animal Exposed to a Toxic Food Supply. KY
Section of MAA, Transylvania University, April 1995.

Statistical Inference on the TI-82. PRISM-UG Conclave,
Louisville, March, 1995.

Writing In Calculus With Challenge Problems. Writing in
Mathematics Workshop, Lexington, November 1994.

The Probability of Getting Ahead. WKU Department of Mathematics
Colloquium, October 1994.

A Poisson Parlour Game. KY Section of MAA, Morehead University,
April 1994.

Computer Experiments in Probability. PRISM-UG Conclave,
Louisville, March, 1994.

Variation of Dual Projection and Optional Stochastic Integration.
Joint Meetings of AMS/MAA, Cincinnati, Jan. 1994.

Computer Experiments in Probability. WKU Mathematics Symposium,
Nov. 1993.

On the series n^m x^n. KY Section of MAA, Center College, April
1993.

Computing Average Values with Random Samples. (with Lon Maynard)
Ninth Annual Symposium of Mathematics, Statistics, and Computer
Science, Eastern Kentucky University, March 1993.

Stopped Random Walks : Areas and Lengths. History of Mathematics
Conference, Miami University, October 1992.

Simulated Monte Carlo Integration. KY Section of MAA, Bellarmine
College, March 1992.

A closed form expansion of the series n^m x^n. WKU Department of
Mathematics Colloquium, March 1992.

Gambler's Ruin. WKU Department of Mathematics Colloquium, Jan. 1990.

Integration in Nuclear Spaces. WKU Department of Mathematics
Colloquium, Sept. 1989.

Co-author of an invited one-hour lecture Abstract Stochastic
Integration. International Congress of Analysis and Measure
Theory, Capri, Italy, Sept. 1988.