Professor of Mathematics
Jacksonville State University
700 Pelham Road North
Jacksonville AL 36265
Office : 131 Ayers
Class Schedule for Fall 2022
Monday, Wednesday, and Friday:
MS 416 Advanced Calculus II
8:15 – 9:45 AM
MS 227 Calculus III
11:15 AM – 12:45 PM
Tuesday and Thursday:
MS 112 Precalculus Algebra
11:00 AM – 12:30 PM
Office Hours for Fall 2022
Students are welcome to
· Make an appointment (by telephone, by email, or in class) to see me either in-person or in Teams at some other mutually convenient time.
· Stop by my office at any time even if you do not have an appointment; I will always be happy to talk to you as long as I am not tied up with something.
· Ask me questions by email, through the ``Ask Your Teacher'' feature in WebAssign if applicable, or through the chat feature in Teams.
Please do not hesitate to contact me in any or all of these ways. I am here to help!
Thesis: “Convective Stability of Shock Profile Solutions of a
Ph.D. Thesis Advisor: Professor Robert L. Pego
MY CURRICULUM VITAE (pdf)
Publications, Presentations, and Scholarly Activity
“Why Curves Curve: The Geodesics on a Torus,” Mathematics Magazine, Vol. 95 No. 3 (2022), pp. 230--239.
“Extrinsic Ricci Flow on Surfaces of Revolution,” Geometriae Dedicata, Vol. 207 Issue 1 (2020), pp. 81--94.
“The Archimedean Projection Property,” Advances in Geometry, Vol. 17 No. 3 (2017), pp. 363--372.
“A Characteristic Averaging Property of the Catenary,” The American Mathematical Monthly, Vol. 123 No. 7 (2016), pp. 683--688.
“On the Smoothness of the Equizonal Ovaloids,” Journal of Geometry, Vol. 103 No. 3 (2012), pp. 409--416.
“Which Surfaces of Revolution Core Like a Sphere?” Mathematics Magazine, Vol. 83 No. 3 (2012), pp. 409--416.
“Generalizing the Equal Area Zones Property of the Sphere,” Journal of Geometry, Vol. 90 No. 1-2 (2008), pp. 47--55.
“Spectral Stability of Undercompressive Shock Profile Solutions of a Modified KdV-Burgers Equation,” Electron. J. Diff. Eqns., Vol. 2007 (2007), No. 135, pp. 1--13: http://ejde.math.txstate.edu/Volumes/2007/135/abstr.html
“Some Combinatorial Questions,” Alabama Journal of Mathematics, Vol. 24 No. 2, Fall 2000.
“A Novel Tournament: A New Combinatorial Design for the Final Round of the Alabama Statewide Mathematics Contest,” Alabama Journal of Mathematics, Vol. 23 No. 1, Spring 1999.
Master’s Degree Thesis Completed Under my Direction
``The Equal Area Zones Property,” by Kristopher Simino (2011)
Abstract: “In Chapter 1 we define and prove the equal area zones property for spheres. Then we discuss two versions of the equal area zones property that make sense in the context of more general, non-spherical ovaloids which we call the isotropic and weak versions. In Chapter 2 we show that an ovaloid satisfying either the isotropic or weak version of the equal area zones property must be a sphere. This theorem is due to Otto Stamm, who published it in German in 1951. To the best of our knowledge, our treatment of his result is the only one available in English.”
“The Napkin Ring Problem: Generalizations and Related Problems,” by Christopher Mount (2019)
Abstract: “Chapter I describes the classical napkin ring problem in three-dimensional
Euclidean space. This problem defines a special family of regions in the upper half of the xy-plane. These regions, when revolved around the x-axis, produce volumes of revolution that are surprisingly invariant with respect to a parameter defining the regions. New versions of the napkin ring problem are formulated and explored in three dimensions and in higher dimensions. Chapter II reviews lesser known generalizations of the classical napkin ring problem in three-dimensional Euclidean space; these generalizations suggest two new and still-unresolved questions. Chapter III defines a new class of mappings on the upper half plane: “volume of revolution-preserving mappings," under which any region that generates a volume of revolution when revolved around the x-axis is mapped to a region that generates the same volume of revolution when revolved around the x-axis. We derive a partial differential equation characterizing these mappings and explore a special class of these mappings related to the napkin ring problem and its generalizations. Chapter IV explores more examples of volume of revolution-preserving mappings and gives a general solution for the partial differential equation characterizing volume of revolution-preserving mappings.”
The following projects (exposition and exercises) appear, under my name and affiliation, in one or more of the 3rd, 4th, 5th, 6th, or 7th editions (copyright dates 2006, 2011, 2012, 2016, and 2020 respectively) of Advanced Engineering Mathematics by Dennis G. Zill and Warren S. Wright, Jones and Bartlett Learning (Burlington, MA):
“When Differential Equations Invaded Geometry: Inverse Tangent Problems in the 17th Century''
“Two Properties of the Sphere”
“Tricky Timing: The Isochrones of Huygens and Leibniz”
“Vibration Control: Vibration Isolation”
“Vibration Control: Vibration Absorbers”
“Making Waves: Convection, Diffusion, and Traffic Flow”
“The Uncertainty Inequality in Signal Processing”
“The Paris Guns: How the Science of Ballistics Entered the Space Age”
"Some Books on the Art of Problem Solving," Alabama Journal of Mathematics, Volume 26 No. 1, Spring 2002.
“Results of the Statewide Contest,” Alabama Journal of Mathematics: Vol. 22 No. 2 1998, Vol. 23 No. 2 1999, Vol. 24 No. 2 2000, Vol. 25 No. 2 2001, Vol. 26 No. 2 2002, Vol. 27 No. 2 2003.
Algebra II with Trigonometry Examination, 1999 - 2003: lead editor and contributing author, 2009: lead editor and co-author.
Geometry Examination, 1999 - 2003: lead editor and contributing author.
Final Round Ciphering Questions, 1998 - 2003: co-author and lead editor.
“What Else Cores Like a Sphere?” Annual Meeting of the Alabama Association of College Teachers of Mathematics (AACTM), February 28, 2009
“Generalizing Some Geometric Properties of the Sphere,” Colgate University Mathematics Department Seminar Series, November 12, 2007.
“Generalizing a Coring Property of the Sphere,” 2007 Annual Meeting of the Southeastern Section of the Mathematical Association of America, March 17, 2007.
“Rings and Things,” Mathfest 2006 (Summer Meeting of the Mathematical Association of America), Knoxville TN, August 12, 2006.
Panelist, “The No Child Left Behind Act,” a panel discussion at the Annual Meeting of the Southeastern Section of the Mathematical Association of America, March 26, 2004.
“Mathematics Program Assessment at Jacksonville State University,” an article in a report prepared and distributed by Bernie Madison of the University of Arkansas at his Assessment Workshop at the Annual Meeting of the Southeastern Section of the Mathematical Association of America, March 26, 2004.
Co-organizer, “Encouraging Underrepresented Groups of Students in Math Contests,” contributed paper session at the Annual Joint Meeting of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA), January 17, 2003.
“The Alabama Statewide Mathematics Contest: can one contest fit all?” Alabama Council of Teachers of Mathematics (ACTM) Annual State Conference, Auburn University at Montgomery, Montgomery AL, November 15, 2002.
“Using Challenging Problems from Elementary Mathematics to Stimulate and Motivate Preservice and Inservice Teachers,” Annual Meeting of the Southeastern Section of the Mathematical Association of America (MAA-SE), Huntingdon College, Montgomery AL, March 30, 2001.
“Generalizing the Equal Area Zones Property of the Sphere,” Annual Joint Meetings of the American Mathematical Society (AMS) and Mathematical Association of America (MAA), New Orleans LA, January 13, 2001.
“Some Combinatorial Questions,” Annual Meeting of the Alabama Association of College Teachers of Mathematics (AACTM), Troy State University, Troy AL, February 12, 2000.
“Convective Stability of Shock Profile Solutions of a Modified KdV-Burgers Equation,” Society for Industrial and Applied Mathematics (SIAM) Minisymposium on Dispersive Equations, Annual Joint Meetings of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA), Washington D.C., January 21, 2000.
Slices Like a Sphere?” Annual Meeting of the
“Vignettes From the History of the Mathematics of Voting,” JSU Math Department/JSU Math Club Colloquium, February 11, 1998.
“Alabama Commission on Higher Education (ACHE) Viability Standards” (with James Stagliano), Annual Meeting of the Alabama Association of College Teachers of Mathematics (AACTM), University of Mobile, Mobile AL, February 22, 1997.
“An Introduction to the Mathematics of Voting,” Fairview High School Mu Alpha Theta Math Club, Cullman AL, December 10, 1996.
Refereed five papers for Mathematics Magazine (a publication of the Mathematical Association of America) (2011, 2012, 2013, 2016, and 2018).
Refereed two papers for the Journal of the Alabama Academy of Science (2008, 2010).
Consulting: Mathematics Program Review
Coauthored with Jan Case a mathematics program review commissioned by the administration of the Donoho School in Anniston, Alabama. Contributed to the report three items in particular: a review of the current thinking on ``best practices'' in content and methodology, a study of the issue of when students should start the serious study of algebra (the ninth grade as is traditional or earlier), and an overview of math contests and other extracurricular activities for high school students. (The report was completed in March 2010.)
Developmental and Editorial Book Reviews
Partial Differential Equations, preliminary draft, by Michael V. Klibanov and Jingzhi Li, for Mansi Kabra, Editorial Department, Taylor & Francis Group of CRC Press, October 2021.
Finite Mathematics and Its Applications, 11th ed., by Larry J. Goldstein, David I. Schneider, and Martha J. Siegel for Joanne Wendelken and Alison Oehmen, Editorial Assistants for Applied Mathematics, Pearson Higher Education, September 2014 and September 2015.
Calculus by Jon Rogawski and Colin Adams, 3rd ed., for Katrina Wilhem, Development Editor, W.H. Freeman and Company, December 2013.
Algebra: Form and Function by William G. McCallum, Deborah Hughes-Hallett, and Eric Connally, for John Wiley and Sons Inc., Publishers, December 2009.
How to Read and Do Proofs, 4th ed., by Daniel Solow, for Shannon L. Corliss, Associate Editor for Mathematics, John Wiley and Sons Inc., Publishers, Spring 2008.
Prelude to Calculus, by Sheldon Axler, for Danielle Amico, Editorial Assistant, John Wiley and Sons Inc., Publishers, July 2006.
Algebra: Form and Function, 1st ed., by William G. McCallum, Deborah Hughes-Hallett, and Eric Connally, for John Wiley and Sons Inc., Publishers, December 2004.
Transcendental Functions, by Larson, Hostetler, and Edwards, one hour telephone
interview with Elizabeth Kassab, Editorial Assistant,
Houghton Mifflin Publishers,
Just in Time Algebra and Trigonometry for Students of
Calculus, 2nd ed., by Ronald I. Brent
and Guntram Mueller, for Rachel S. Reeve,
Senior Project Editor, Addison-Wesley,
Differential Equations and Mathematical Modeling (new book), for Amy Gembala, Development Editor, McGraw-Hill, San Francisco CA, July 2003.
Differential Equations and Mathematical Modeling (new book), for Michelle Munn, Development Editor, McGraw-Hill, San Francisco CA, October 2000.
Untitled new book on applied calculus, for Gale
Epps, Editorial Assistant, Prentice Hall,
Advanced Engineering Mathematics, 2nd ed. by Dennis G. Zill and Michael R. Cullen, for Barbara Lovenvirth, Developmental Editor, Jones and Bartlett Publishers, Norwood MA, December 1998.
Calculus, 5th ed. by C. Henry Edwards and David E. Penney, for Gale Epps, Editorial Assistant, Prentice Hall, Upper Saddle River NJ, March 1997.
Revised – August 10, 2022