Current Position

Professor Emeritus
Department of Mathematics and Statistics
710 North Pleasant Street
Lederle Graduate Research Center
University of Massachusetts
Amherst, MA 01003-9305

murray <at> math <dot> umass <dot>edu

Personal Data

Birthdate: May 23, 1939

Formal Education

1956	The Central High School, Philadelphia	B. A.
1960	University of Pennsylvania	B. A.	Mathematics
1962	University of Pennsylvania	M. A.	Mathematics
1965	Wesleyan University	Ph. D.	Mathematics
			Topological dynamics

Professional Experience

2012–	University of Massachusetts	Professor Emeritus
1981–2011	University of Massachusetts	Professor
1970–81	University of Massachusetts	Associate Professor
1974 (Spring)	University of Warwick Mathematics Institute	Visiting Scholar
1972–73	University of Massachusetts	Acting Department Head
1971 (Spring)	University of Massachusetts	Associate Department Head
1965–70	University of Massachusetts	Assistant Professor

Interests

Topology of dynamical systems
Use of computers in teaching college mathematics
Mathematica
J and APL programming languages

Grants

2001–03	Co-Project Director, NSF Course, Curriculum, and Laboratory
	Improvement Grant, Guided Discovery and Intelligent
	Tutoring Materials for Calculus and their Electronic Delivery
	on the World Wide Web.  Project Director, Jan.–Dec., 2003
1993–96	Co-Project Director, NSF Instructional Laboratory Improvement
	Grant, A Computer Laboratory to Teach Calculus to a Large
	Number of Students
1989–91	Educational software grants, STSC, Inc.
1981–84	Project Director, NSF Local Course Improvement Grant,
	Materials for Teaching Linear Algebra through APL
1979–82	Project Director, NSF Instructional Scientific Equipment
	Program Grant, Terminal Equipment for Demonstrations and
	Instruction in Undergraduate Mathematics
1966–71	Faculty Associate, NSF Research Grants, Topological
	Transformation Groups, Topological Dynamics, and Infinite
	Dimensional Manifolds

Publications

Books

The Mathematical Method: A Transition to Advanced Mathematics, Prentice Hall, Upper Saddle River, New Jersey, 1996, xvi + 350.

Topology, Holt, Rinehart and Winston, New York, 1974, xvi + 427.

Axiomatic Theory of Sets and Classes, Holt, Rinehart and Winston, New York, 1970, xv+ 336.

Articles

Evaluation of a Stochastic Inactivation Model for Heat-Activated Spores of Bacillus spp., Appl. Environ. Microbiol., 76, no. 13 (July 2010), 4402–4412 (with Maria G. Corradini, Mark D. Normand, and Micha Peleg).

Visualizing complex functions with the Presentations application, The Mathematica Journal, 11, no. 2 (2009), 226–252 (with David J. M. Park, Jr.).

Beyond elementary calculus with Mathematica 6, Mathematica in Education and Research, 12, no. 3 (2007), 185–191.

Visualizing complex functions with the Cardano3 application, in eProccedings of the 8th International Mathematica Symposium, Yves Papegay, editor, INRIA, 2006, 15 pp. (with David J. M. Park, Jr.).

Hero's method: an introduction to Mathematica programming, in Challenging the Boundaries of Symbolic Computation: Proceedings of the 5th International Mathematica Symposium, Peter Mitic, Philip Ramsden, and Janet Carne, editors, Imperial College Press, London, 2003, 263–270.

Active learning in sophomore mathematics: a cautionary tale, Journal of Mathematics and Science: Collaborative Explorations, 4, no. 1 (2001), 143–164.

Hill ciphers: a linear algebra project with Mathematica, in Proceedings of the Twelfth Annual International Conference on Technology in CollegiateMathematics, Gail Goodell, editor, Addison-Wesley, Boston, Mass., 2001, 100–104.

Confessions of two APL educators learning J, APL93 Conference Proceedings (Toronto, August 15–19, 1993), APL Quote Quad, 24 (1993), 78–87 (with H. A. Peelle).

Learning and teaching linear algebra with APL, Proceedings APL*PLUS Users Conference (Palo Alto, 8–9 August 1991), STSC, Inc., Rockville, MD, 1991, 125–135.

A survey of APL thinking, APL Quote Quad, 21 (1990), 5–8 (with H. A. Peelle).

Using the programming language APL in linear algebra, Spring Conference on the First Two Years: Teaching the Mathematical Core (March 31–April 1, 1989, Univ. of Hartford), Univ. of Hartford, 1989, 56–71.

APL problem-solving: a tutorial, APL Techniques and Applications: Session Tutorials, APL89, ACM, 1989, 1–30 (with H. A. Peelle).

Is the unified keyboard better?, APL Quote Quad, 18 (1988), 13–14.

APL thinking: examples, APL Conference Proceedings (Dallas, Texas, May 10–14, 1987), APL Quote Quad, 17 (1987), 433–440 (with H. A. Peelle).

APL teaching bugs, APL85 Conference Proceedings (Seattle, Wash., May 12–15, 1985), APL Quote Quad, 15 (1985), 86–93 (with H. A. Peelle); reprinted in APL-CAM Journal, 8 (1986), 75–88.

Least squares curve fitting viewed geometrically: an application of linear algebra with APL, in APL as a Tool of Thought III Conference Proceedings, NY/SIGAPL-ACM, 1985, 92–98.

APL in linear algebra, in APL as a Tool of Thought II Conference Proceedings, NY/SIGAPL-ACM, New York, 1984, VII.1–9.

APL learning bugs, APL83 Conference Proceedings (Washington, D. C., April 10–13, 1983), APL Quote Quad, 13 (1983), 11–16 (with H. A. Peelle); reprinted in APL-CAM Journal, 6 (1984), 58–67.

Zero divided by zero: zero or one—or neither?, APL Quote Quad, 11 (1981), 9–10.

A proof of the hairy ball theorem, Amer. Math. Monthly, 86, (1979) 571–574 (with Robert Guy).

A theorem on extensions of minimal sets, in Global Differentiable Dynamics (Proc. Conference, Case Western Reserve Univ., 1969), Lecture Notes in Math., 235, Springer-Verlag, New York, 1971, 61–64.

Expansive automorphisms of Banach spaces, Pacific J. Math., 34 (1970), 647–656 (with James H. Hedlund).

Embedding a transformation group in an automorphism group, Proc. Amer. Math. Soc., 23 (1969), 276–281.

Maximally almost periodic and universal equicontinuous minimal sets, Mich. Math. J., 14 (1967), 101–105.

A note on positively expansive endomorphisms, Math. Scand., 19 (1966), 217–218.

Expansive transformation semigroups of endomorphisms, Fund. Math., 59 (1966), 313–321.

Expansive automorphisms of finite-dimensional vector spaces, Fund. Math., 59 (1966), 307–312.

A theorem on Riemann integration, J. London Math. Soc., 37 (1962), 285–286 (with R. Cantor and E. M. Mandelbaum).

Software

Homeomorphism of a Disk Mapping the Origin to Another Interior Point, https://demonstrations.wolfram.com/HomeomorphismOfADiskMappingTheOriginToAnotherInteriorPoint, 2022.

Dynamic Germination of Seeds and Microbial Spores, Wolfram Demonstrations Project, http://demonstrations.wolfram.com/DynamicGerminationOfSeedsAndMicrobialSpores, 2013 (with Mark D. Normand and Micha Peleg).

Choosing Initial Parameter Values for Nonlinear Regression, Wolfram Demonstrations Project, http://demonstrations.wolfram.com/ChoosingInitialParameterValuesForNonlinearRegression/, 2012 (with Mark D. Normand and Micha Peleg).

Idealized Conventional and Pressure-Assisted Thermal Preservation Processes, Wolfram Demonstrations Project, http://demonstrations.wolfram.com/IdealizedConventionalAndPressureAssistedThermalPreservationP/, 2011 (with Mark D. Normand and Micha Peleg).

On-line teaching materials

This category includes various unrefereed MATHEMATICA notebooks and other materials published on-line at the following URLs and with Murray Eisenberg identified as author:

http://www.math.umass.edu/~murray/Math_135/Files/

http://www.math.umass.edu/~murray/Math_136/Files/

http://www.math.umass.edu/~murray/Math_236/Files/

http://blogs.umass.edu/math331-murray/demos/

http://blogs.umass.edu/math421-murray/files/

http://www.math.umass.edu/~murray/Math_455_Eisenberg/Files/

http://www.math.umass.edu/~murray/

Miscellaneous

Mathematica notebook:  Conformal mapping: solving the Laplace equation on a lens shaped region, http://www.st-andrews.ac.uk/~pl10/c/djmpark/Assets/8EB7C389/ConformalMapping.nb, November 2012 (with David Park).

Book review: C. Reiter and W. Jones,APL with a Mathematical Accent; review in APL News, 23, no. 1 (1991), 4–6 (with H. A. Peelle).

Letter, Computer Language, 8, no. 3 (1991), 11.

Course notes: APL for Linear Algebra, Math./Stat. Dept., Univ. of Mass., Amherst, 1986, 217 pp.

Book review: L. Gilman and A. J. Rose, APL: An Interactive Approach, 3rd ed.; review in APL Quote Quad, 14 (1984), 17.

Mimeograph notes: Guide to Using FORTRAN 5, Math./Stat. Dept., Univ. of Mass., Amherst, 1980, 21 pp.

Monograph review: I. U. Bronstěĭn, Extensions of minimal transformationgroups (Russian); review in Math. Reviews, 56 (1978), 1746–1747.

Abstract: Expansiveness of T-algebras, preliminary report Notices Amer. Math. Soc., 16 (1969), 848.

Review: D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature (Russian); review in Math. Reviews, 36 (1968), 1373–1374.

Abstract: Expansive automorphisms of Banach spaces--preliminary report, Notices Amer. Math. Soc., 14 (1967), 667.

Abstract: On certain universal minimal transformation groups--preliminary report, Notices Amer. Math. Soc., 13 (1966), 711.

Abstract: Positively expansive endomorphisms of compact groups, Notices Amer. Math. Soc., 13 (1966), 333.

Reviews of some 75 papers in Math. Reviews and Zentralblatt für Math., 1967–1984.

Presentations

2006	Selected paper, 8th International Mathematica Syposium, Avignon, Visualizing complex functions with the Cardano3 application (with David J.M. Park, Jr.)
2005	Selected paper, Wolfram Technology Conference, Champaign, IL, Embedding Mathematica in a web-based learning system (wth Stephen Battisti).  Eisenberg, presenter.  Abstract accepted.
2004	Selected paper, MathFest 2004 (Math. Assoc. Amer.), Providence, RI, Special Session on Uses of the WWW that Enrich and Promote Learning, The OWL system with webMathematica in applied calculus (with David M. Hart, Alan R. Peterfreund, and  Kenneth A. Rath).  Eisenberg, presenter.
2003	Selected paper, 5th International Mathematica Symposium, Imperial College,
	Heros method: an introduction to Mathematica programming
2000	Contributed paper, Pathways to Change: A Research Conference
	on Science and Mathematics Teaching and Learning, The Science,
	Technology, Engineering, and Mathematics Teacher Education
	Collaborative, Hampshire College, Reforming Sophomore Math:
	What Worked, What Didn't, and Why
2000	Invited paper, Special Session on Teaching Mathematics in the
	New Millennium, Amer. Math. Society Regional Meeting, Univ. of
	Mass./Lowell, Mathematical Software: Making Math Harder?
2000	Invited presentation, North East Regional Computing Program
	(NERCOMP), Instructional Special Interest Group,Mathematica
	for New Users: The Second Day
2000	Contributed paper, Twelfth Annual International Conference on
	Technology in Collegiate Mathematics, San Francisco, Hill Ciphers:
	A Linear Algebra Project with Mathematica
1999	Invited paper, Northeastern Section, Math. Assoc. of Amer.,
	Colby College, Active Learning: High-tech and Low, In-class
	and Out
1998	Workshop, Amherst College, Introduction to Mathematica
1998	Workshop, Science, Technology, Engineering, and Mathematics
	Education Collaborative, Univ. of Mass./Amherst,Mathematica
1998	Selected paper, Worldwide Mathematica Conference 1998, Chicago,
	My Favorite MathematicaProjects for Teaching Linear Algebra
1997	Selected paper, APL97 Conference (Toronto), J vs. Mathematica
1997	Invited presentation, Pioneer Valley PC Users Group, Amherst,
	MA, Teaching Mathematics with Computer
1995	Panellist, International Conference on APL, San Antonio,
	Improving J
1993	Contributed paper, APL93 (Toronto), Confessions of Two
	APL Educators Learning J
1992	Contributed paper, Conference on Computing in Calculus
	(Rensselaer Polytechnic Institute), Calculus with
	Computing: Some Tips and Traps
1991	Invited paper, STSC APL*PLUS Users Conference
	(Palo Alto), Learning and Teaching Linear Algebra
	with APL
1989	Contributed paper, Spring Conference on the First Two Years
	(Univ. of Hartford), Using the Programming Language APL
	in linear algebra

1989	Co-leader, Workshop on APL problem-solving, APL89 conference,
	New York
1987	Co-leader, Workshop on APL thinking, APL87 conference, Dallas
1987	Contributed paper, APL87 (Dallas), APL Thinking: Examples
	(with H. A. Peelle)
1986	Invited lecture, New England APL Users Group (Cambridge,
	Mass.), Thinking about APL Thinking (with H. A. Peelle)
1985	Contributed paper, APL85 (Seattle), APL Teaching Bugs
1985	Leader of workshop on linear algebra and APL,
	NY/SIGAPL-ACM Professional Development Seminar
1985	Panellist, Math. Assoc. of Amer., Anaheim,
	Computers in Upper-level Courses
1984	Leader of workshop on linear algebra and APL,
	NY/SIGAPL-ACM Professional Development Seminar
1984-88	Program chairman, Pioneer Valley PC Users Group
1983	Contributed paper, APL83 (Washington, D. C.),
	APL Learning Bugs (with H. A. Peelle)
1982	Contributed paper, session on Use of Computers in Under-
	graduate Math., Math. Assoc. of Amer., Toronto, Learning
	Linear Algebra through APL
1982	Contributed paper, Society of College Science Teachers,
	Chicago, Learning Mathematical and Statistical Concepts
	through A Programming Language
1980	Invited address, Conference for University Mathematics Faculty,
	Univ. of Maine, Orono, Use of Computers in Undergraduate
	Mathematics Courses

Dissertation and Thesis Committees

1990–91	Member, Senior Honors Thesis committee
1970–89	Member, Ph. D. dissertation committees (5 within department,
	2 outside department)
1969–72	Ph. D. dissertation supervisor, Mark D. Wochele, Flows on
	Unicoherent Spaces
1968–69	Senior Honors Thesis supervisor

Departmental and University Service

2003	Calculus restructuring committee
2002	Faculty Senate Executive Advisory Committee
	(ex officio as Senate committee chair)
2001-	University Computer and Electronic Communications
	Committee (chair: 2001–02)
2001–02	Provost's Instructional Technology Council
2001–02	University Teaching, Learning and Instructional Technology
	Council
1999–00	NSF/STEMTEC Teaching Scholar Mentor
1999–00	Departmental Undergraduate Program Review Committee
1997–00	University Faculty Senate (also 1966-69, 1990-93)
1990–93	University General Education Council
1988–89	Academic Computing Services Task Force
1984–87	College of Arts and Sciences Curriculum Committee
1980–86	University Computer Committee
	(chair: 1981-83, 1985-86)
1978–	In charge of Mathematics and Statistics Departments
	undergraduate computer facilities
1978–81	University Space and Calendar Committee (chair: 1980–81)
1976–77	Honors preceptor
1974–76, 2004–06	Departmental Personnel Committee (chair: 1975–76)
1972 (Fall)	FNSM Personnel Policy Committee
1971	Teaching advisor for TAs (sporadic)
1969–06	Departmental Undergraduate Curriculum Committee
	(1969–72, 1974–75, 1977–81, 1988–93, 2002–2006; chair: 1970–71)
1969–	Member or chair, graduate examining committees (sporadic)
1970	Moderator, Departmental Council
1969–70	Departmental Planning Committee
1966–69	University Library Committee
1966–76	Departmental Library Committee (1966-69, 1974–75)
1965–	an undergraduate mathematics major advisor

Miscellaneous Activities

1999	Review panel, NSF Course, Curriculum and Laboratory
	Improvement Program, Arlington, VA
1998–00	Participant, Faculty workshop series of The Science,
	Technology, Engineering and Mathematics Education
	Collaborative, Univ. of Mass./Amherst
1995–99	Software beta testing, Personal TeX, Inc. (consulting)
1993–95	Reviewer, Yankee Ingenuity Initiative, Connecticut Department
	of Higher Education (consulting)
1994	Staff, Workshop on Calculus in a Real and Complex World,
	Univ. of Mass.
1984–89	Program chair, Pioneer Valley PC Users Group
1983–92	Reviewer of submitted papers, APL84 and APL92 conferences
1980–81	Selected participant, NSF Chautauqua-type Short Course,
	Computers as an Aid in Learning Science
1981	Planning conference participant and member, interim steering
	committee, Consortium for Computer-based Education in
	Mathematics, Univ. of Delaware
1971–	Publishers reviewer for undergraduate math textbook
	manuscripts (consulting)
1970–72	Research proposal reviewer, National Science Foundation
1966–	Referee, Amer. Math. Monthly, Math. Systems Theory, Duke
	Math. J., Proc. Amer. Math. Soc., J. Australian Math. Soc.,
	Bull. Inst. Math. Acad. Sinica, Pacific J. Math., Canadian
	Math. Bull., College Math. J., APL Quote Quad, COMAP

Memberships

American Mathematical Society
Mathematical Association of America
Sigma Xi
Phi Beta Kappa

Courses Taught

Mathematics in the Modern World
Math Talent Affinity Program Seminar
Calculus I–II (for engineering, science, and math majors)
Non-standard calculus (with infinitesimals)
Calculus for Life and Social Sciences
Calculus with Computer I–II
Multivariate Calculus
Multivariable Calculus, Linear Algebra, and Ordinary Differential Equations with Computer I-II
Statistics for Business
Linear Algebra with Computer Programming
Honors Linear Algebra
Vector Analysis
Ordinary Differential Equations for Scientists and Engineers
Ordinary Differential Equations for Scientists and Engineers with Computer
Discrete Structures
Fundamental Concepts of Mathematics (for math majors)
Special Topics: Visualization of fractals, chaos and iteration
Introductory Modern Analysis
Introduction to Modern Algebra I–II
Set Theory
Topics in Ordinary Differential Equations
Complex Analysis
Numerical Analysis I–II
Applied Analysis I–II
Topology (undergraduate)
Seminar on APL Thinking (CompSci, undergrad./graduate, jointly taught)
Number Theory
Introduction to Theory of Statistics I–II
Probability
Topology I–II (graduate)
Algebraic Methods in Topology (graduate)
Topological Dynamics (graduate)
Advanced Applied Mathematics: Mathematical Systems Theory (graduate)
Current Research in Differential Topology (graduate)

8 December 2012