William Johnston

"Dr. J." has taught mathematics to undergraduates for more than 35 years. He also served for 17 years in administrative posts ranging from department chair, associate dean, and academic affairs vice president at various institutions. The pinnacle of this work was from June 2011 to January 2018 as chair of Butler University's Department of Mathematics, Statistics, and Actuarial Science, which culminated in the Liberal Arts and Sciences award for outstanding faculty member in service to the College.  In this role he led the department into a host of improvements, including a more than doubling in student majors, an addition of a statistics major, and an establishment of a unique summer Mathematics Research Camp (MRC). The MRC is offered to any Butler department major to experience one-on-one research work in mathematics with department faculty members. He has developed and implemented new courses into the undergraduate curriculum at several institutions. They include: Integration Theory, which teaches the Lebesgue Integral to undergraduates; Foundations of Mathematics, which teaches how to prove mathematical theorems, much like an art course might teach how to paint; the FYS course Elementary, my Dear Watson, which looks at characters such as Sherlock Holmes in literature, drama, and film who illustrate the use of deductive and inductive reasoning; and Decision Making, which shows how many different disciplines -- such as mathematics, economics, ethics, and English literature -- can influence the way people make decisions.  His third textbook in mathematics, on the Lebesgue Integral, was published by the highly acclaimed MAA Press in fall 2015. His fourth book, on complex variables, is also published by the MAA Press and is newly available at the AMS Bookstore site https://bookstore.ams.org/cdn-1645193668088/text-71/ . It introduces complex analysis as a natural extension of the calculus of real-valued functions. A complimentary Teacher's Guide and the full Solutions Manual are available at that website for faculty members' review and upon adoption.   

Areas of Expertise

The Theory of Functions; in particular, Lebesgue Integration, Operator Theory, and Complex Functions

Education/Degrees

Ph.D. University of Virginia, 1988. B.S. Wake Forest University, 1982

Select Publications:

Books (* Signifies publication after peer review; ** after editor review):

Johnston, W., The Calculus of Complex Functions, MAA Press: An Imprint of the AMS, Washington, DC, 2022. ISBN 978-1-4704-6565-0*

Johnston, W., The Lebesgue Integral for Undergraduates, MAA Press: An Imprint of the AMS, Washington, DC, 2015. ISBN 978-1-93951-207-9.*

Johnston, W., and McAllister, A., A Transition to Advanced Mathematics: A Survey Course, Oxford University Press, New York, 2009. ISBN978-0-19-531076-4.*

4. Johnston, W., An Introduction to Statistical Inference, Mohican Publishing Co., February 2001. ISBN 0-923231-40-4.*

5. Johnston, W. and Perry, J., Solution Manual to Accompany An Introduction to Statistical Inference, Mohican Publishing Co., February 2001. ISBN 0-923231-41-2.**

Articles 6. Johnston, W., Makdad, C., A Comparison of Norms: Bicomplex Root and Ratio Tests and an Extension Theorem, The American Mathematical Monthly, 128:6, 525-533, 2021.*

7. Cowen, C., Johnston, W., Wahl, R., Constructing Invariant Subspaces as Kernels of Commuting Matrices, Linear Algebra and its Applications, 583:15, (December 2019): 46-62.* 

8. Johnston, W., Webster, J., and Wilson, C., An introductory research experience in mathematics for undergraduates, PRIMUS, 27 4-5, pp. 451-460, 2017.*

9. Johnston, W., The weighted Hermite polynomials form a basis for L2(R), The American Mathematical Monthly, 121(3),(March 2014):249-253.*

10. Johnston, W. and McAllister, A., A survey transition course, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22:1,(January 2012): 30-42.*

11. Johnston, W., McAllister, A.; Wilson, J., An experiment that worked: revising the calculus curriculum, Focus, XXI, No. 8 (November 2001): 8-9.**

12. Johnston, W., Hall, A., Reducing litigation: the mathematics of settling out of court, PRIMUS,VIII, No. 1 (March 1998): 93-96.*

13.McMahan, T. and Surrey, M. (student publication) with Johnston, W., A statistical analysis of baseball's 1987 home run phenomenon, Pi Mu Epsilon Journal 10, No. 4 (Spring 1996) 300-304.*

14. Johnston, W. and Wilson, J., Optimization using computer software and algebra, The Proceedings of the Fifth ICTCM - Technology in Collegiate Mathematics, Addison-Wesley, Chicago, Illinois (1994): 602-608.***

15. Allen, J. (student publication) with Johnston, W., Winning blackjack strategies, Undergraduate Journal of Mathematics 23, No. 2 (September 1991) 31-35.*

16.Johnston, W., A condition for absence of singular spectrum with an application to perturbations of self-adjoint Toeplitz operators, American Journal of Mathematics, 113 (1991): 243-267. *

Fillers 17. Farrell, J. and Johnston, W., A mathematics crossword puzzle: mathematical evolution, The American Mathematical Monthly, 124:5 (May 2017): 444-445. DOI: 10.4169/amer.math.monthly.124.5.479*