Dr. David K. Neal

Department of Mathematics
Western Kentucky University
Bowling Green, Kentucky 42101

(270) - 745 - 6213



PhD, University of Florida, 1988
MS, University of Florida, 1985
BS, University of Florida, 1983

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
Random Walks
Mathematica Simulations
History of Mathematics


Crapoulette: Card Craps with One Deck (with Dustin Gentile), The Mathematical Gazette, Volume 99, Issue 545, (July 2015), 196 - 204.

Distribution of the Sum of Non-Identical Geometric Random Variables (with Lindsey Traughber), International Journal of Pure and Applied Mathematics accepted for publication.

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.
View Here

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

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 Mathematical Scientist, 35, No. 2 (2010), 101-110. (pdf available on request)

A Geometric Gambling Game (with Frank Polivka), The Mathematical Spectrum, 43, No. 1 (2010), 20-25. (pdf available on request)

A Generalized Martingale Betting Strategy (with Michael D. Russell), Missouri Journal of Mathematical Sciences, 21, No. 3 (2009), 183-197.  (pdf available on request)

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, Fibonacci Quarterly, 45, No. 1 (2007), 35-38.  (pdf available on request)

Average Lengths for the Two-Player Name Game, The Mathematical Gazette, 91, No. 520 (2007), 51-58.  (pdf available on request)
Preview Here

TI-83/84 Graphing Calculator Manual for David S. Moore's The Basic Practice of Statistics - 4th Edition, W.H. Freeman and Company, 2006.

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

Directed Masters Theses

"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.

Directed Senior Research Projects

"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

Grants Funded

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.

Undergraduate Courses Taught

MATH 109: General Mathematics
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: Elementary 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: 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: Probability and Statistics II
MATH 431:  Intermediate Analysis
MATH 475: Topics in Mathematics
MATH 498: Senior Project

Graduate Courses Taught

MATH 500: Readings in Mathematics (Research Tool)
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.

David Neal's Homepage

WKU Math Department

Western Online