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Welcome to Khodr Shamseddine’s professional web page
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Contact Information
Education
Teaching Experience
- August 15, 2007- : Tenured
Associate Professor in the Department of Mathematics at Western Illinois
University.
- August, 2004- : Graduate
Program Director in the Department of
Mathematics at Western Illinois
University.
- August 18, 2003- August 15,
2007: Assistant Professor (tenure-track) in the Department of Mathematics
at Western Illinois University.
- January 1, 2001- August 15,
2003: Visiting Research Instructor in the Department of Mathematics, Michigan State University.
- January 1, 2000- December 31, 2000: Half-time
Visiting Research Instructor in the Department of Mathematics, Michigan State University
(complementing a half-time Research Associate appointment at the National Superconducting Cyclotron
Laboratory.)
- Spring 1994: Teaching
Assistant, Chemistry Department, Michigan State University.
- Fall 1993: Mathematics tutor,
Office of Supportive Services, Michigan
State University.
- 1988-1990: Teaching
Assistant, Department of Physics and Astronomy, Michigan State
University.
- Academic year 1987-1988:
Teaching Assistant, Department of Physics, American
University of Beirut.
Research
Experience
- August 15, 2007- : Tenured
Associate Professor in the Department of Mathematics at Western Illinois
University.
- August 18, 2003- August 15,
2007: Assistant Professor (tenure-track) in the Department of Mathematics
at Western Illinois University.
- August 4, 2000- Present:
Associate at the Center for Advanced Mathematical Sciences at the American University
of Beirut.
- May 29-July 23, 2007:
Visiting Professor in the Department
of Mathematics at the University
of Wisconsin- Eau Claire.
- July 1-July 31, 2006:
Visiting Assistant Professor in the
Department of Physics and Astronomy at Michigan
State University.
- July 1-July 31, 2005:
Visiting Assistant Professor in the
Department of Physics and Astronomy at Michigan
State University.
- June 1-June 30, 2005:
Visiting Research Scientist in the Department
of Mathematics at the University
of Wisconsin- Eau Claire.
- Summer 2002: Visiting
Assistant Professor in the Department of Physics and Astronomy at Michigan State University.
- January 1, 2001- August 15,
2003: Full-time Visiting Research Instructor in the Department of
Mathematics at Michigan
State University.
- January 1, 2000- December 31,
2000: Half-time Visiting Research Instructor in the Department of
Mathematics and half-time Research Associate at the National
Superconducting Cyclotron Laboratory at Michigan State
University.
- September 1993-December 1999:
Research assistant, Beam Physics Theory
group, National Superconducting Cyclotron Laboratory, Michigan State University.
- Summer 1989: Research
assistant, Department of Physics and Astronomy, Michigan State
University.
Refereed Publications
- Intermediate Value Theorem
for Analytic Functions on a Levi-Civita Field, Khodr Shamseddine and Martin Berz,
Bulletin of the Belgian
Mathematical Society, in press.
- Generalized Power Series on a
Non-Archimedean Field, Khodr Shamseddine and Martin Berz, Indagationes Mathematicae, Volume
17 # 3, 2006, pp. 457-477.
- Analytical
Properties of Power Series on Levi-Civita Fields, Khodr Shamseddine and Martin Berz,
Annales Mathématiques Blaise Pascal,
Volume 12 # 2, 2005, pp. 309-329.
- Constrained Second Order Optimization on
Non-Archimedean Fields, Khodr Shamseddine and Vera Zeidan, Indagationes Mathematicae, Volume
14 # 1, 2003, pp. 81-101.
- Measure Theory and Integration on the
Levi-Civita Field, Khodr Shamseddine and Martin Berz, Contemporary Mathematics, American
Mathematical Society, Volume 319 (Ultrametric Functional Analysis),
2003, ISBN: 0-8218-3320-0,
pp. 369-387.
- Intermediate Values and Inverse
Functions on Non-Archimedean Fields, Khodr Shamseddine and Martin Berz,
International Journal of
Mathematics and Mathematical Sciences, Volume 30 # 3, 2002, pp.
165-176.
- On the Existence and Uniqueness of Solutions
of Differential Equations on the Levi-Civita Field, Khodr
Shamseddine, International
Journal of Differential Equations and Applications, Volume 4 # 4,
2002, pp. 375-386.
- One-Dimensional Optimization on
Non-Archimedean Fields, Khodr Shamseddine and Vera Zeidan, Journal of Nonlinear and Convex
Analysis, Volume 2 # 3, 2001, pp. 351-361.
- Convergence on the Levi-Civita Field and
Study of Power Series, Khodr Shamseddine and Martin Berz, Lecture Notes in Pure and Applied
Mathematics, Marcel Dekker, Proceedings of the Sixth International
Conference on P-adic Analysis, July 2-9, 2000, ISBN 0-8247-0611-0, pp.
283-299.
- The Differential Algebraic Structure of
the Levi-Civita Field and Applications, Khodr Shamseddine and Martin Berz,
International Journal of Applied
Mathematics, Volume 3 # 4, 2000, pp. 449-464.
- New
Elements of Analysis on the Levi-Civita Field, PhD Dissertation, Khodr
Shamseddine, Department of Mathematics and Department of
Physics and Astronomy, Michigan State University, December 1999.
- Exception Handling in Derivative
Computation with Non-Archimedean Calculus, Khodr Shamseddine and Martin Berz,
Computational Differentiation: Techniques, Applications, and Tools, M.
Berz, C. Bischof, G. Corliss, A. Griewank, eds., SIAM, Philadelphia, Penn, 1996, pp. 37-51.
- COSY INFINITY and Its Applications to
Nonlinear Dynamics, Martin Berz,
Georg Hoffstätter, Weishi Wan, Khodr Shamseddine
and Kyoko Makino, Computational Differentiation: Techniques,
Applications, and Tools, M. Berz, C. Bischof, G. Corliss, A. Griewank ,
eds., SIAM, Philadelphia, Penn,
1996, pp. 363-367.
Work in Progress
- On the the topological
structure of Levi-Civita fields, Khodr Shamseddine, in preparation.
- Multi-variable Calculus on
Non-Archimedean Fields, the Implicit Function Theorem, Khodr Shamseddine,
in preparation.
Invited Talks at Conferences
- Intermediate Value Theorem
for Analytic Functions on a Levi-Civita Field, Ninth
International Conference on P-adic Functional Analysis, University of Concepcion,
Concepcion, Chile, July 10-14, 2006.
- Analytical Properties of
Power Series on Levi-Civita Fields, Eighth
International Conference on P-adic Functional Analysis, Aubiere-Cedex,
France, July 5-9, 2004.
- Measure Theory and
Integration on the Levi-Civita-Field, Seventh International
Conference on P-adic Functional Analysis, Nijmegen, The Netherlands, June 17-21, 2002.
- The Differential Algebraic
Structure of the Levi-Civita Field and Applications, Ninth International
Colloquium on Numerical Analysis and Computer Science with Applications,
Plovdiv, Bulgaria, August 12-17, 2000.
- Convergence on the
Levi-Civita Field and Study of Power Series, Sixth International Conference
on P-adic Functional Analysis, Ioannina, Greece, July 2-9, 2000.
- Power Series on the
Levi-Civita Field, Eighth International Colloquium on Numerical Analysis
and Computer Science with Applications, Plovdiv, Bulgaria, August 13-18,
1999.
Contributed Talks at Conferences
- The Non-Archimedean Field
R-script, Overview and Applications, International Conference on
Scientific Computations, LAU, Beirut,
Lebanon, March 1999.
- Non-Archimedean Structures as
Differentiation Tools, Second
LAAS International Conference on Computer Simulation, AUB, Beirut, Lebanon,
September 1997.
- Exception Handling in
Derivative Computation with Non-Archimedean Calculus, SIAM 96: Second International
Workshop on Industrial and Applied Mathematics, Santa Fe, New Mexico,
February 1996.
Invited Talks, Seminars and Colloquia at
Universities
- Department of Mathematics, University of Wisconsin- Eau Claire, July 7,
2007.
- Department of Mathematics, University of Wisconsin- Eau Claire, June 21,
2007.
- Department of Physics &
Astronomy, University
of Manitoba,
November 24, 2006.
- Department of Mathematics, University of Manitoba, November 24, 2005.
- Center for Advanced
Mathematical Sciences (CAMS), American
University of Beirut,
Beirut, Lebanon, August 12, 2005.
- Center for Research in
Applied Mathematics & Statistics (CRAMS), Business and Computer University College, Beirut, Lebanon, January 7, 2005.
- Center for Advanced
Mathematical Sciences (CAMS), American
University of Beirut,
Beirut, Lebanon, January 5, 2005.
- Department of Mathematics, Western Illinois University,
November 11, 2004.
- Department of Mathematics, University of Wisconsin- Eau Claire, July 13,
2004.
- Department of Physics and
Astronomy, Michigan
State University,
June 18, 2004.
- Department of Mathematics, University of Wisconsin- Eau Claire, April 30,
2004.
- Department of Mathematics, Western Illinois University,
February 5, 2004.
- Department of Mathematics, Western Illinois University,
February 14, 2003.
- Department of Mathematics
and Computer Science, Lawrence
Technological University, May 14, 2002.
- Department of Mathematics, Michigan State University,
October 8, 2001.
- Center for Advanced
Mathematical Sciences (CAMS), American
University of Beirut,
Beirut, Lebanon, July 19, 2000.
- National Superconducting
Cyclotron Laboratory, Michigan
State University,
November 24, 1999.
- Department of Mathematics, American University
of Beirut, Beirut, Lebanon,
March 24, 1999.
External Research Support
- Summer 2007-Summer 2010: NSF
Grant # 0552350 (www.fastlane.nsf.gov/a6/A6RC_6-18-2006.html)
in collaboration with four colleagues from the Department of Mathematics at UWEC to
support Summer Research in Pure and
Applied Mathematics for undergraduate students.
- Summer 2006: Collaborative
research with Professor Martin Berz (Department of Physics and Astronomy
at Michigan State University) which was supported by a United States
Department of Energy grant, and which led to two refereed publications.
- July 2005: Collaborative
research with Professor Martin Berz (Department of Physics and Astronomy
at Michigan State University) which was supported by a United States
Department of Energy grant, and which led to a refereed publication.
- Summer 2002: Collaborative
research with Professor Martin Berz (Department of Physics and Astronomy
at Michigan State University)
which was supported by an Alfred P. Sloan fellowship and by a United
States Department of Energy grant, and which led to a refereed
publication.
Student Supervision
As
the Graduate Program Director in the Department of Mathematics at Western Illinois University,
I am the academic advisor of all the graduate students; I advise them on what
courses to take and what research and career opportunities are available to
them. Moreover, I have helped in the supervision of five exchange graduate
students from Germany who visited my research group at different times during
my PhD studies at Michigan State University, I have served on the thesis
committees of two graduate students at Western Illinois University and one PhD
student at Howard University, and I have supervised undergraduate research
projects with two students at Western Illinois University and three at the
University of Wisconsin-Eau Claire.
Research Interests
My research interests and activities include various areas of non-Archimedean
Analysis: power series and analytic functions, measure theory and integration,
optimization, existence and uniqueness of solutions of differential equations,
complex analysis and multivariable analysis. The focus of my research has been
on the Levi-Civita fields which were first introduced by the Italian
mathematician Tullio Levi-Civita at the end of the nineteenth century. Of those
Levi-Civita fields, one (which we denote by R-script) is of particular
interest; it is shown to be the smallest non-Archimedean field extension of the
real numbers that admits roots of positive elements and that is complete in the
order topology. In fact, R-script is small enough so that the numbers of the
field can be implemented on a computer; and this allows for many useful
applications, one of which is the fast and accurate computation of the
derivatives of real-valued functions up to high orders.
We have studied convergence of sequences and series in two different
topologies, which led to an exhaustive study of power series. A handful of
people have investigated power series on the Levi-Civita fields before, but all
the previous studies were restricted to the special case of power series with
real coefficients. We have dropped that restriction and showed that power
series on Levi-Civita fields have all the nice smoothness properties that real
power series have. In particular, they satisfy the intermediate value theorem
and the mean value theorem, they are infinitely often differentiable and they
are re-expandable around any point within their domain of convergence.
While it is a known fact that conventional continuity or differentiability
are not sufficient to guarantee that a function on a closed interval of a
non-Archimedean field be bounded or satisfy any of the common theorems of real
calculus, we have shown that under mild conditions, differentiability is
sufficient for the function to assume all intermediate values and a
differentiable inverse function. We also showed that conventional
differentiability is not the right one to study optimization questions on
non-Archimedean fields in general; and based on a stronger concept of
differentiability, we studied finite-dimensional optimization both with and
without constraints. In both cases, we derived necessary and sufficient
conditions of first and second order for a function to have a local minimum at
a point of its domain.
We have developed a measure theory and integration on the Levi-Civita field
R-script. We introduced a measure that proved to be a natural generalization of
the Lebesgue measure on the field of the real numbers and have similar
properties. Then we introduced a family of simple functions from which we
obtained a larger family of measurable functions and derived a simple
characterization of such functions. We studied the properties of measurable
functions, we showed how to integrate them over measurable sets, and we showed
that the resulting integral satisfies similar properties to those of the
Lebesgue integral of Real Analysis.
Research currently in progress aims at understanding the topological
structure of the non-Archimedean Levi-Civita fields and developing a complete
calculus theory on such fields, extending all the common theorems of real
calculus. Multivariable analysis and complex analysis on non-Archimedean fields
are then two natural research projects to investigate and try to develop.
Moreover, now that an integration theory has been achieved, this will lead
naturally to investigating a general theory of differential equations on these fields
with possible applications in solving differential equations on the field of
real numbers. We have developed all the mathematical tools necessary to work on
all the projects above, any one of which (or a part thereof) may also
constitute a good research project to work on with a graduate student towards
an MS thesis or a PhD dissertation.
Teaching Philosophy
Like teaching all other subjects, teaching Mathematics
requires the instructor's thorough knowledge of the material as well as the
skills to transmit that knowledge to the students as efficiently as possible. I
believe that well-prepared and well-organized lectures are necessary to achieve
that goal. I also believe that teaching Mathematics has an additional component
as compared to teaching other subjects; namely, teaching the students how to
think in a logical way and how to write clear and rigorous proofs and solutions
for problems. I have always stressed that in my teaching.
A fundamental goal in all the courses that I teach is to
help my students learn and succeed, and to foster their interest in
Mathematics. My lectures, the examples I present in class, the homework
problems I assign after each lecture, the quizzes, and the exams all complement
each other to achieve the goal stated above. I am available during all my
office hours; and I constantly encourage my students to contact me and arrange
for other times to come to my office if they need help and they can't make it
to the office hours.
For presentation, clear organization and student participation
are two of my principal goals. While presenting the material in my low-level
courses, I encourage my students to understand the mathematical concepts and
master the techniques needed to solve problems through various examples of
different levels of complexity. I believe this is more helpful for the students
than trying to memorize formulas, equations, or ways to solve specific problems
without sufficient understanding of the concepts and techniques involved.
To facilitate the transfer of the information from the
instructor to the students, the WWW resources can be very useful and should be
taken advantage of. For each of the courses I have taught since Spring 2000, I
have designed a web page on which I posted all important announcements related
to the course as well as links to the syllabus, homework assignments, quizzes'
solutions, exams' solutions and grades. My students find that very helpful as
they state in their evaluation forms at the end of each semester.
My syllabi usually state clearly what material would be
covered in the course, what the grades would be based on, as well as the dates
of all quizzes and exams, my policies on make-ups, and my office
hours. The quizzes are usually based on the homework
assignments; and they then prepare the students for the in-class exams. By the
end of the semester, the students have access to the solutions for
up to ten quizzes and three one-hour exams on the web pages
of each of the courses; and that constitutes excellent review material for the
final exam since the problems on the quizzes and exams naturally
cover the main concepts and techniques that I want the
students to learn from the course.
Besides having the homework problems and the quizzes as good
review material for the exams, I also usually have a full review lecture in
class before each of the exams to prepare the students best for the exam, to
answer any questions from the students on the material covered on that
particular exam, and to do more review problems. Also, to further help the students,
I distribute a list of review problems about a week before each exam, including
the final exam; then I go over some of those review problems in class and post
the answers to all of them on the web.
In the senior level and graduate courses that I teach, I
normally put more emphasis on rigor both in my lectures and in my distributed
solutions of exams and homework sets (which replace weekly quizzes
in the lower level courses.) I encourage my students to work
independently on their homework problems, to acknowledge their fellow students'
contribution in case of collaboration, and to widen their interests in
Mathematics beyond the classroom through additional reading and attending
seminars and colloquia; and I foster my students' appreciation of mathematical
research. As the Graduate Program Director, I have succeeded in recruiting
several students from the undergraduate courses, who ended up doing very well
in the graduate program. Moreover, I have recruited two undergraduate students
to work with me on research projects, who later presented their work to the
whole Department.
Since my graduation with a dual PhD in Physics and
Mathematics in December 1999, I have been teaching in a Mathematics department
(Michigan State University:
January 2000-August 2003; and Western
Illinois
University: August 2003-
Present.) I have taught a wide range of Mathematics courses including Calculus,
Business Calculus, Linear Algebra, Differential Equations, Real Analysis,
Complex Analysis and Multi-variable Analysis. A list of my most recently taught
courses can be found on www.wiu.edu/users/kms117/#teachingatwiu.
Honor Societies and Awards
- Nominated for the J. S. Frame Teaching Excellence Award for Faculty,
Spring 2003, Department of Mathematics, Michigan State
University.
- Nominated for the J. S. Frame Teaching Excellence Award for
Faculty, Spring 2002, Department of Mathematics, Michigan State
University.
- Hariri Foundation alumnus.
- Member of The Honor Society of Phi Kappa Phi.
- Member of Phi Beta Delta, the
Honor Society for International Scholars.
- BS in Physics with High Distinction, American University of Beirut, June 1988.
- Philip Hitti Award, American University of Beirut, June 1988, for graduating with the highest
average in the Faculty of Arts and Sciences.
- Dean's Honor List, faculty of
Arts and Sciences, American University of Beirut, 1986-1988.
- Malcolm Kerr Award, American
University of Beirut, 1986-1988.
Professional Societies
Languages
- Arabic: fluent (reading,
speaking and writing).
- English: fluent (reading,
speaking and writing).
- French: good (reading,
speaking and writing).
Teaching at Western Illinois
University
Service
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2007-2008
(WIU)
·
University
Ø
University Research Council
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Evidence of English Proficiency and Minimum
TOEFL Requirements Committee
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College of Arts & Sciences
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College of Arts & Sciences Graduate
Studies Committee
·
Department of Mathematics
Ø
Graduate Committee (Chair)
Ø
Personnel Committee
Ø
Curriculum Committee
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2007-2008
(Outside WIU)
·
PhD Committee for Dodzi Attimu (Howard University)
·
Tenth International Conference on P-adic
Functional Analysis (June 30-July 3, 2008):
o Local
Organizing Committee
o Scientific
Committee
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2005-2006
·
College of Arts & Sciences
Ø
College of Arts & Sciences Graduate
Studies Committee
·
Department of Mathematics
Ø
Graduate Committee (Chair)
Ø
Colloquium Committee
Ø
Curriculum Committee
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2006-2007
·
University
Ø
University Research Council
Ø
Evidence of English Proficiency and Minimum
TOEFL Requirements Committee
·
College of Arts & Sciences
Ø
College of Arts & Sciences Graduate
Studies Committee
·
Department of Mathematics
Ø
Graduate Committee (Chair)
Ø
Colloquium Committee
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Computer Affairs Committee
Ø
Curriculum Committee
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2003-2004
·
Department of Mathematics
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High School Relations Committee
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Library Committee (Chairman)
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Upper Division Curriculum Committee
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Javed Siddique’s MS thesis committee
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Duygu Inceoz’s MS thesis committee
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2004-2005
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Department of Mathematics
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Graduate Committee (Chair)
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Colloquium Committee
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Curriculum Committee
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Upper Division Curriculum Committee
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As the Chairman of the Graduate Committee since Fall 2004, I
have led the efforts of that committee in recruiting new graduate students and
advising new and current graduate students as well as assisting the Department
Chair with various matters pertaining to the graduate program. I have also led
the efforts of the Graduate Committee in preparing the proposals for revisions
in the graduate program including new structure, courses and tracks to better
serve the needs of our incoming graduate students. I have gathered ideas,
thoughts and suggestions from the various groups in the Department about the
structure and the contents of the courses in the revised program and designed a
web page for that purpose to facilitate the discussions and the exchange of
ideas in the Department. As a result, proposals for a revised program have been
submitted and approved by the Dean and the Graduate Council; and the revised
program has started in Fall 2006.
Maintained by K. Shamseddine (last updated on 7/10/07). Top of page
