Welcome to Khodr Shamseddine’s professional web page

 

The information on this page will not be updated after May 12, 2008. For more current information, please see my Web page at the University of Manitoba.

 

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

Work in Progress

  • On 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

  • Analysis on the Levi-Civita Field, a Brief Overview, Tenth International Conference on P-Adic and Non-Archimedean Analysis, Michigan State University, East Lansing, Michigan, USA, June 30- July 3, 2008.
  • 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

 

Spring 2006

Fall 2006

Spring 2007

Fall 07

Spring 08

Math 133

Math 137

Math 133

Math 137

Math 133

Math 391

Math 551

Math 391

Math 651

Math 391

 

Fall 2003

Spring 2004

Fall 2004

Spring 2005

Fall 2005

Math 137

Math 137

Math 137

Math 137

Math 137

Math 311

Math 435

Math 430

Math 599

Service

 

2007-2008 (WIU)

·         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       Personnel Committee

Ø       Curriculum Committee

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

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

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

Ø       Computer Affairs Committee

Ø       Curriculum Committee

2003-2004

·         Department of Mathematics

Ø       High School Relations Committee

Ø       Library Committee (Chairman)

Ø       Upper Division Curriculum Committee

Ø       Javed Siddique’s MS thesis committee

Ø       Duygu Inceoz’s MS thesis committee

2004-2005

·         Department of Mathematics

Ø       Graduate Committee (Chair)

Ø       Colloquium Committee

Ø       Curriculum Committee

Ø       Upper Division Curriculum Committee

 

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 5/10/08). Top of home page.