Department of Mathematics and Computer Science
Eastern Illinois University
Charleston, IL 61920
Office : 335 Old Main
Phone: (217) 581-7777
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Personal
Date of Birth: May 14, 1945
Home Address: 2617
Salem Road
Charleston, IL 61920
(217) 345-2357 (Think Primes!)
Family:
Susan (wife), Ruth Ellen (daughter), Jeremy (son)
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Education
Ph.D.
Mathematics (Topology), University of Wisconsin, 1972
Thesis: Absolute Endpoints and Open Maps
of Chainable Continua
under the supervision of Joseph M. Martin
M.A. Mathematics, University of Wisconsin, Madison, 1970
B.A. Mathematics, Brandeis University, Waltham, MA, 1967
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Teaching Experience
1996-present Professor,
Eastern Illinois University
1990-1996
Professor and Chairperson, Eastern Illinois University
1988-1989
Visiting Associate Professor, Middlebury College
1980-1990
Associate Professor, University of Wyoming
1973-1980
Assistant Professor, University of Wyoming
1972-1973
Assistant Professor, Grinnell College
1967-1971
Teaching Assistant, University of Wisconsin
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Honors and Awards
1. Winner of the Trevor Evans
Prize of the Mathematical Association of America for his article "ONE Point
Determines a Straight Line: A Geometric Axiom of Choice", which appeared
in the November 2000 issue of Math Horizons.
2. Faculty Achievement and
Contribution Award in Research/Creative Activity, Eastern Illinois University,
2001.
3. Eastern Illinois University
College of Sciences Teacher-Scholar Award, 2001.
4. PAI at EIU awarded in
2001.
5. Faculty Achievement and
Contribution Award in Teaching, Eastern Illinois University, 1997.
6. Winner of the Golden
Apple Teaching Award, University of Wyoming, 1988.
7. Runner-up for the Golden
Apple Teaching Award, Univ. of Wyoming, 1987.
8. Faculty Fellow at the
University of Wyoming Summer Institute, 1985, 1986, 1987, 1988, 1989,
and 1990.
9. Summer Research Grant,
University of Wyoming, 1975.
10. N.D.E.A. Title IV Fellowship,
University of Wisconsin, Sept. 1971-Aug. 1972.
11. Research Assistant, University
of Wisconsin, summers of 1968, 1969, and 1971.
12. Teaching Assistantship, University
of Wisconsin, Sept. 1967-June 1971 (including summer of 1970).
13. B.A. cum laude (with honors
in mathematics).
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Courses Taught
The Spirit of Mathematics, Pre-Calculus Algebra and Trigonometry, Business Mathematics, Problem Solving, the Calculus Sequence, BioCalc, Honors Calculus, Contemplating the Infinite, Linear Algebra, Finite Mathematics, Mathematics for High School Teachers, Abstract Algebra, Real Analysis, Complex Analysis, Fundamental Concepts of Mathematics, Numerical Analysis, Theory of Probability, Honors Seminar in Mathematics, Problem Solving Seminar for Students in the Honors and Scholars Program, Undergraduate and Graduate Topology, Problem Seminar in Group Theory, Theory of Retracts, Algebraic Topology, Topology Seminar
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Talks
1. Talk on "ONE Point Determines a Straight
Line: A Geometric Axiom of Choice" in the Great Theorems of
Mathematics Section at the National Joint Meetings in New Orleans, 2001.
Also spoke on this subject at the EIU Mathematics Colloquium on September
24, 2000, the Geometric Potpourri Seminar at the U of I on February 6,
and at the Annual Meeting of the Illinois Section of the MAA on March 24,
2001.
2. Invited Talks at Washington University
in St. Louis, 1984, at Swarthmore College, 1987, Rose-Hulman Institute
of Technology, 1991, 1992, 1994, 1996, and Middlebury College, 1998.
3. Featured speaker at the Regional
MAA Meeting at the Air Force Academy in Colorado Springs, 1984, and
the Illinois State MAA Meetings, 1992, 1996, 1998 and 2001.
4. Three National Merit Symposia and
two "Convo's" at the University of Wyoming. Featured Speaker at the
1986 U.W. National Merit Symposium.
5. Invited Talk at the Higher Education
Project, University of Wyoming, 1988.
6. Several talks at the annual combined
meetings, at the annual spring topology conferences, and the Annual
Conferences on Teaching Mathematics at EIU.
7. Speaker at Rose Hulman Young Scholars
Summer Program (2 talks given
1996) and speaker at Expanding Your Horizons Through Math and
Science Parents
and Teachers Workshop at EIU.
8. Several mathematics talks around
the State at junior colleges and high schools and Math Clubs.
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Other Activities
1. Beta Tester for Mathematica,
1998-present.
2. A Visiting Lecturer of the
Mathematical Association of America. (1995-1998).
3. A Board Member of the Illinois
Section of the Mathematical Association of America, 1990-1996.
4. Chairman of the Committee to
Re-Evaluate the Calculus Sequence, and the Calculus Text Committee, Univ.
of Wyoming.
5. Attended "Calculus for a New
Century" Conference in Washington, D.C. 1987.
6. Referee for the Math Monthly,
Math
Magazine, Proc. of the A.M.S., Trans. of the A.M.S.,
Houston
J. of Math and Rocky Mountain Journal, among others.
7. A Faculty Advisor for the Putnam
Competition, the Speakers Bureau Chair (1996-99), Friday Colloquium Chair
(1999).
8. Co-Director of the Wyoming
Mathematical Talent Search for eight years.
9. Member of the Department Advisory,
Undergraduate, Graduate, and Personnel Committees.
10. Department Librarian.
11. Member of the Honors Course Committee,
the Dean Review Committee, and the Department Review Committee.
12. Course and T.A. supervisor for Calculus
13. Director of Freshman Mathematics,
1984-85.
14. Faculty Advisor of the Wyoming Knights
Chess Club.
15. On numerous intramural teams with
math graduate students, including three championship slow-pitch softball
teams.
16. Member of the Mathematical Association
of America, 1967-present.
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Publications of Ira Rosenholtz
1. "Open Maps of Chainable Continua", PAMS, 42 (1974) p. 258 ff.
2. "Evidence of a Conspiracy Among Fixed Point Theorems", PAMS, 53 (1975) p. 213 ff.
3. "Local Expansions, Derivatives,
and Fixed Points", Fundamenta Mathematicae,
91 (1976) p. 1 ff.
4. "On a Fixed Point Problem of D.R. Smart", PAMS, 55 (1976) p. 252.
5. "Another Proof That Any Compact Metric Space Is The Continuous Image Of The Cantor Set", Am. Math. Monthly, 83 (1976) p. 646 ff.
6. "Imitating the Euclidean Metric", Math. Mag., 51 (1978) p. 125 ff.
7. "An Elementary Solution of the Monotone Mapping Problem" (with Joseph Martin), PAMS, 72 (1978) p. 352 ff.
8. "There Is No Differentiable Metric for Rn ", Am. Math. Monthly, 86 (1979) p. 585 ff.
9. "Calculating Surface Areas From a Blueprint", Math. Mag., 52 (1979) p. 252 ff.
10. "Mapping Theorems for Differentiable Operators" (with William O. Ray), Bull. de L'Acad. Polonaise des Sciences, 29 (1981) p. 265 ff.
11. "Counting Fixed Points", PAMS, 86 (1982) p. 341 ff.
12. "Tackling a Ticklish Type of
Tic-Tac-Toe (or The Case of the [Almost] Total Tactics)",
J. Recr. Math., 16 (1983) p. 12 ff.
13. "Tackling a Ticklish Type of Tic-Tac-Toe (or The Case of the [Almost] Total Tactics) II", J. Recr. Math., 17 (1984) p. 81 ff.
14. " 'The Only Critical Point
in Town' Test" (with Lowell Smylie), Math. Mag. , 58 (1985)
p. 149 ff.
15. "Two Mountains Without a Valley", Math. Mag., 60 (1987) p. 48.
16. "Absolute Endpoints of Chainable Continua", PAMS, 103 (1988) p. 1305ff.
17. "A Topological Mean Value Theorem
for the Plane", Am. Math. Monthly, 98 (1991)
p. 149 ff.
18. "A Pigeon-Hole Proof of Kaplansky's
Theorem", Am. Math. Monthly, 99(1992)
p. 132 ff.
19. "Solving Some Variations on a Variant of Tic-Tac-Toe Using Invariant Subsets", J. Recr. Math., 25(1993) p. 128 ff.
20. Solution of Problem 10284, "The Tarry-Escott Problem" (with Hillel Gauchman), Am. Math. Monthly, 102(1995) p. 843 ff.
21. “Quickie” Problem proposal
Q880 and its solution, Math. Mag., 71(1998)
p. 226 ff.
22. "Tangent Sequences, World Records, ?, and the Meaning of Life: Some Applications of Number Theory to Calculus", Math. Mag., 72 (1999) p. 367ff.
23. “Quickie” Problem proposal Q890 and its solution, Math. Mag., 72(1999) p. 149 ff.
24. Problem Proposal 1584, Math. Mag., 72 (1999) p. 408.
25. "A Very Simple, Very Paradoxical, Old Space-Filling Curve (or "Wrong-Way" Corrigan Rides Again!)", Math Horizons, 7(2000) p. 23ff.
26. "ONE Point Determines a Straight Line: A Geometric Axiom of Choice", Math Horizons, 8(2000) p. 20ff.
27. "Estimating Large Integrals:
The Bigger They Are The Harder They Fall", College Math Journal,
32(2001) p. 322ff.
28. "You Can't Go Wrong With Triangles", Math Horizons, 10(2002) p. 5ff.
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Some Citations of Ira Rosenholtz
On mappings contractive in the sense of Kannan, by Ludvik Janos, PAMS, 61(1976)171ff.
Local homeomorphisms onto tree-like continua, by T. Mackowiak, Colloq. Math., 38(1977)63ff.
Certain local homeomorphisms of continua are homeomorphisms, I and II, by August Lau, Bulletin de L'Academie Polonaise, Serie des sciences, math, astr. et phys., 26(1978)315ff., and 27(1979)381ff.
Fixed points of sequences of locally expansive maps, by Harvey Rosen, PAMS, 72(1978)387ff.
A characterization of the pseudo-arc, by Janusz J. Charatonik, Bulletin de L'Academie Polonaise, 26(1978)901ff.
Periodic and fixed points, and commuting mappings, by Gerald Junck, PAMS, 76(1979)333ff.
A fixed point principle for locally expansive multifunctions, by Solomon Leader, Funda. Math., 106(1980)99ff.
Which connected metric spaces are compact?, by Gerald Beer, PAMS, 83(1981)807ff.
Solvability of nonlinear operator equations, by William O. Ray and W.J. Cramer, Jr., Pacific J. of Math., 95(1981)37ff.
Arcwise connectivity and continuum chainability, by Charles L. Hagopian and Leland E. Rogers, Houston J. of Math., 7(1981)249ff.
Arcwise connectivity of continuum-chainable plane continua, by Charles L. Hagopian
A continuum-chainable aposyndetic plane continuum, by Lex G. Oversteegen, Houston J. of Math., 7(1981)271ff.
On local isometries and isometries in metric spaces, by Thakyin Hu and W.A. Kirk, Colloq. Math., 44(1981)53ff.
Global convergence of iterative processes, by Fam Kii An', Math. Notes (of the Academy of Science of the USSR), Nov. 1981, pp. 471ff.
On the dual of the linearly constrained multifacility location problem with arbitrary norms, by Henrik Juel and Robert F. Love, Transportation Science, 15(1981)329ff.
Open local expansions on graphs, by Stanislaw Miklos, Bulletin de L'Academie Polonaise, 29(1981)79ff.
Local expansions on graphs, by J.J. Charatonik and S. Miklos, Funda. Math., 113(1981)235ff.
On confluent mappings and essential mappings---a survey, by J. Grispolakis and E.D. Tymchatyn, Rocky Mtn. J. of Math, 11(1981)131ff.
Expanding maps on compact metric spaces, by William L. Reddy, Topology and its Appl., 13(1982)327ff.
Locally contractive and expansive mappings, by Thakyin Hu and Harvey Rosen, PAMS, 86(1982)656ff.
Mapping theorems for Gateux differentiable and accretive operators, by William O. Ray and Anita M. Walker, Nonlinear Analysis, Method and Applic., 6(1982)423ff.
Homeomorphic classification of certain inverse limit spaces with open bonding maps, by William Thomas Watkins, Pacific J. of Math., 103(1982)589ff.
Finite and compact actions on chainable and tree-like continua, by Juan A. Toledo, Ph.D. thesis, Univ. of Florida, 1982.
On local expansions, by J.J. Charatonik and M. Karlota, Funda. Math., 117(1983)187ff.
Generalized graphs and their open mappings, by J.J. Charatonik and S. Miklos
Normally solvable nonlinear operators, by William O. Ray, Contemp. Math., 18(1983)155ff.
On locally expansive selfcoverings of compact metrizable spaces., by Aleksander Calca, Funda. Math., 117(1983)15ff.
Continua whose local homeomorphisms are homeomorphisms, by Akira Tominaga, Funda. Math., 119(1983)1ff.
Confluent local expansions, by Krzysztof Omiljanowski, Funda. Math., 119(1983)36ff.
Finite-to-one open mappings on chainable continua. by E. Duda and P. Bartick, Proc. of the Intl. Conf. on Geometric Topology (Warsaw, 1978), PWN, Warsaw, 1980, 103-107.
Monotone and open mappings on circularly chainable continua. by E. Duda and J. Kell, Proc. of the Intl. Conf. on Geometric Topology (Warsaw, 1978), PWN, Warsaw, 1980, 109-111.
Finite-to-one open mappings on circularly chainable continua. by P. Bartick and E. Duda, Pacific J. of Math., 106(1983)17ff.
Confluent and related local expansions on graphs, by S. Miklos, Houston J. of Math., 10(1984)63ff.
Inducible periodic homeomorphisms of tree-like continua, by Juan A. Toledo, TAMS, 282(1984)77ff.
Fixed point property for local expansions on graphs, by S. Miklos, Math Seminar Notes and Kobe J. of Math 1(1984)103ff.
Fixed points of expanding maps, by Tetsuo Kaneko and Kazu-Hiro Sakai, Sci. Rep. Niigata Univ., Ser A, 20(1984)25ff.
Periodic points of positively expansive maps, by Kazu-Hiro Sakai, PAMS, 94(1985)531ff.
Vestpocket Bibliographies No 9: Games and Puzzles, by William L. Schaaf, J. of Recr. Math., 18(1985-86)161ff.
A fixed point theorem for locally nonexpansive mappings in normed spaces, by C. Waters, PAMS, 97(1986)695ff.
Review of a paper by Sidney A. Morris, by Richard M Schori, Math. Reviews., 86k:54041.
Small compact actions on chainable continua, by Juan A. Toledo, Can. J. of Math., 38(1986)563ff.
Local expansions on graphs and order of a point, by J.J. Charatonik and S. Miklos, Acta Mathematica Hungarica, 47(1986)287ff.
Nonextreme unique critical points, by Ole Jorsboe, Am. Math. Monthly, 93(1986)307.
Range of Gateaux differentiable operators and local expansions, by Jong Sook Bae and Sangsuk Yie, Pac. J. of Math., 125(1986)289ff.
Confluent and related mappings on arc-like continua---an application to homogeneity, by J.J. Charatonik and T. Mackowiak, Topology and its Appl., 23(1986)29ff.
The boundary characteristic and Pick's theorem in the Archemedian planar tilings, by Ding Ren and John R. Reay, J. of Combinatorial Theory, Ser. A, 44(1987)110ff.
The fascination of the elementary, by Paul R. Scott, Am. Math. Monthly, 94(1987)759ff.
On mappings and invariance of domain theorem and accretive operators, by J. Kolomy, Boll. Un Mat Ital B., 1(1987)235ff.
Expanding maps of solenoids, by Nobuo Aoki, Monatshefte fur Mathematik, 105(1988)1ff.
Calculus (Third Edition), by Howard Anton, 1988, pp. 1029 and 1030.
On some properties of span, by Kazuhiro Kawamura, J. Math. Soc. Japan, 40(1988)605ff.
A Mathematica sampler, by Stan Wagon.
Failure of the Only-Critical-Point-in-Town Test, by Stan Wagon, Doing Mathematics with Mathematica, W.H. Freeman, 1989, p. 62ff.
Open maps of circularly chainable continua (Russian), by A.A. Odintsov, Vestnik Mosk Univ Mat Mekh, 5(1989)76ff.
Positively expansive open maps of Peano spaces, by K. Hiraide, Topol. Appl., 37(1990)213ff.
Failure of the Only-Critical-Point-in-Town Test, by Stan Wagon, Mathematica in Action, W.H. Freeman, 1991, p. 67-91.
2-to-1 maps with hereditarily indecomposible images, by Jo Heath, PAMS, 113(1991)839ff.
Areas of lattice figures in the planar tilings with congruent regular pologons, by Krzysztof Kolodziejczyk, J. Comb Th. A, 58(1991)115ff.
2-to-1 maps on hereditarily indecomposible metric continua, by Jo Heath, TAMS, 328(1991)433ff.
The pseudo-arc, by W. Lewis, Continuum Theory and Dynamical Systems, (Arcata, CA, 1989), Contemp. Math, 117(1991)103ff.
Multivariable Calculus (Fourth Edition), by Howard Anton, 1992, pp. 1063 and 1064.
A complex Rolle's theorem, by J.-Claude Evard and F. Jafari, Am. Math. Monthly, 99(1992)858ff.
A Century of Calculus (Part II) 1969-1991, ed. by Tom Apostol, et al, The Raymond W. Brink Selected Mathematical Papers, Mathematical Association of America, 1992, p. 262ff.
A characterization of finitely-junctioned continua, by E. Duda and P. Krupski, PAMS, 116(1992)839ff.
2-to-1 maps on solenoids and Knaster continua, by W. Debski, Funda. Math., 141(1992)277ff.
A classification of homogeneous continua, by W. Lewis, Soochow J. of Math., 18(1992)85ff.
Counting critical points of real polynomials in two variables, by Alan Durfee, Nathan Kronenfield, Heidi Munson, Jeff Roy, and Ina Westby, Am. Math. Monthly, 100(1993)255ff.
Absolute end points of irreducible continua, by J.J. Charatonik, Mathematica Bohemica, 118(1993)19ff.
Absolute end points and their mapping properties, by J.J. Charatonik, P. Krupski, and J.R. Prajs, Mathematica Pannonica, 4(1993)103ff.
Degrees of closed curves in the plane, by Marko Kranjc, Rocky Mtn. J. of Math, 23(1993)951ff.
Singularities and self intersections of curves evolving on surfaces, by Jeffrey A. Oaks, Indiana Math J., 43(1994)959ff.
A Multidimensional Version of Rolle's Theorem, by Massimo Furi and Mario Martelli, Am. Math. Monthly, 102(1995)243ff.
Generalizations and applications of a complex Rolle's theorem, by J.-Cl. Evard, F. Jafari, and P. Polyakov, Nieuw Archief voor Wiskunde, 13(1995)173ff.
Games of No Chance, ed. by Richard J. Nowakowski, Mathematical Sciences Research Institute Publications, 1996, Cambridge Univ. Press
Open mappings and solvability of nonlinear equations in Banach space, by Stewart C. Welsh, Proc. of the Royal Academy of Edinburgh A, 126(1996)239ff.
General models in min-max continuous location---theory and solution techniques, by J.B.G. Frenk, J. Gromicho, and S. Zhang, J. Optim Th. and Appl., 89(1996)39ff.
Twisting behavior of conformal maps, by J.J. Carmona and C. Pommerenke, J. Lond. Math., 56(1997)16ff.
An Introduction to Banach Space Theory, by Robert E. Megginson, Graduate Texts in Mathematics #183, Springer-Verlag, 1998, p.234.
Optimization of Schur-convex functions, by X.M. Zhang, Math Inequal Appl, 1(1998)319ff.
Flett's mean value theorem for holomorphic functions, by R.M. Davitt, R.C. Powers, T. Riedel, and P.K. Sahoo, Math. Mag.,72(1999)304 ff.
The Pseudo-Arc, by Wayne Lewis, Bol. Soc. Mat Mex, 5(1999)p.25-77.
Efficient computation of continued fractions, by M. Sofroniou and G. Spaletta, Foundations of Comp. Math., Oxford, UK(1999).
mathworld.wolfram.com/OnlyCriticalPointinTownTest.html, (2000).
Confluent maps and spans, by E. Duda, Houston J. of Math., 27(2001), p. 845 ff.
The periodic points and the invariant set of an epsilon-contractive map, by C.M. Ding and S.B. Nadler, Appl. Math Letters, 15(2002) pp. 795ff.
Fixed points for some non-obviously contractive operators, by E. De Pascale and L. De Pascale, PAMS, 130(2002)3249 ff.
Life on the Edge, by Alf van der Poorten, Am. Math. Monthly, 109(2002), p. 850ff.
Various shadowing properties for postitively expansive maps, by K. Sakai, Topology and its Appl., 131(2003)15 ff.