
Current Position
Professor Emeritus Department of Mathematics and Statistics
710 North Pleasant Street
Lederle Graduate Research Center
University of Massachusetts
Amherst, MA 010039305
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

CoProject 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

CoProject 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 HeatActivated 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, AddisonWesley, 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 problemsolving: 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 APLCAM 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/SIGAPLACM, 1985, 92–98.
APL in linear algebra, in APL as a Tool of Thought II Conference Proceedings, NY/SIGAPLACM, 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 APLCAM 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, SpringerVerlag, 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 finitedimensional 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
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 PressureAssisted Thermal Preservation Processes, Wolfram Demonstrations Project, http://demonstrations.wolfram.com/IdealizedConventionalAndPressureAssistedThermalPreservationP/, 2011 (with Mark D. Normand and Micha Peleg).
Online teaching materials
This category includes various unrefereed MATHEMATICA notebooks and other materials published online 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/math331murray/demos/
http://blogs.umass.edu/math421murray/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.standrews.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 Talgebras, 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 spacespreliminary report, Notices Amer. Math. Soc., 14 (1967), 667.
Abstract: On certain universal minimal transformation groupspreliminary 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 webbased 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: Hightech and Low, Inclass


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

Coleader, Workshop on APL problemsolving, APL89 conference,


New York

1987

Coleader, 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/SIGAPLACM Professional Development Seminar

1985

Panellist, Math. Assoc. of Amer., Anaheim,


Computers in Upperlevel Courses

1984

Leader of workshop on linear algebra and APL,


NY/SIGAPLACM Professional Development Seminar

198488

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 196669, 199093)

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: 198183, 198586)

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 (196669, 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 Chautauquatype Short Course,


Computers as an Aid in Learning Science

1981

Planning conference participant and member, interim steering


committee, Consortium for Computerbased 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) Nonstandard 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 III 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
