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Houssein El Turkey
Houssein
El Turkey
Assistant Professor
Arts & Sciences
Mathematics and Physics - Math
About

    After receiving my doctorate degree, I joined the University of New Haven as an assistant professor in fall 2014. One of the main reasons that attracted me was the emphasis on experiential learning. This philosophy of learning goes side by side with the recent innovations in Mathematics Education such as the Inquiry-Based Learning (IBL) method, the discovery method, and the guided reinvention method.

    TEACHING PHILOSOPHY

    My primary goals as an educator are to help my students develop a full conceptual understanding of mathematical ideas and assist them in improving their problem solving skills. In other words, I want to help them communicate effectively, be able to reason through a problem, and develop the technical expertise needed to solve interesting problems.  These goals are largely independent of the level of the course being taught. As an instructor, I implement the techniques which I found were the most exciting and thought-provoking as a student. These styles formed a basis for my pedagogical philosophy and the design of my courses, lectures, homework, and exams. I have built on this basis as I gained experience as an instructor. The more I taught, the more I became aware of how important it is to be able to adapt to suit the class.  In addition, I actively search for new teaching methods because I believe that one's teaching style should always be evolving.

    To achieve the goals outlined above, I modify my approach based on the level of the course being taught and the mathematical maturity of the students enrolled. At the more basic course level, I spend a significant amount of time demonstrating methods for solving problems; this seems to help students develop an appreciation for thinking about and solving interesting problems.  At intermediate and advanced course levels, I teach students to hone their technical abilities and how to identify and extract the mathematical structure from an object or problem. I usually alternate between the lecture-based method, the ACE (Activities, Classroom discussion, Exercise) Teaching Cycle, and the Inquiry-Based Learning method (IBL).

    RESEARCH INTERESTS

    My research revolves around the study of different aspects of Lie superalgebras, and in particular their representations. The representation theory in the super setting follows a similar trajectory to that in Lie theory. We have a similar classification of simple Lie superalgebras. Root systems and root decompositions are defined similarly and simple modules are described by their highest weights. However, there are also important differences. For example, the finite dimensional representations are usually not semisimple even over the complex numbers. This leads to the use of tools from positive characteristic representation theory such as complexity, cohomology, and support varieties. I have also studied the Type A Schur superalgebra and currently I am looking at the Type B Schur algebra.

    In addition, I am very interested in research in undergraduate mathematics education (RUME). Currently I am working with a research group on creating a Creativity in Proving Rubric (CPR). This rubric can be used to help instructors and students to assess and value creativity in proving.

    Keywords: Representation Theory, Lie Theory, Lie Superalgebras, Undergraduate Mathematics Education.

More

    Education

    Ph.D. in Mathematics, 2014: University of Oklahoma, Norman, Oklahoma

    Adviser: Dr. Jonathan Kujawa http://www2.math.ou.edu/~kujawa

    M.S. in Mathematics, 2008: The American University of Beirut, Beirut, Lebanon

    B.S. in Mathematics, 2006: Beirut Arab University, Beirut, Lebanon

    Publications

    Complexity of modules over Lie superalgebras, in preparation.

    How can we access undergraduate students’ creativity in proof and proving? (with Milos Savic, Gulden Karakok, Gail Tang, and Molly Stubblefield), Proceedings of the 8th Conference of MCG, International Group for Mathematical Creativity and Giftedness, July 2014, 107–111.

    Presenting Schur superalgebras, (with J. Kujawa), Pacific Journal of Mathematics, 262 (2013), no. 2, 285–316.

    Talks

    Conferences:

    17th Annual Legacy of R.L. Moore IBL Conference, June 19-21, 2014, Utilizing a research-based rubric to assess students’ creativity in proof and proving.

    Southeastern Lie Theory Workshop 2014, University of Georgia, May 16-17, 2014
    Complexity of modules over Lie superalgebras.

    Joint Mathematics Meetings, Baltimore, MD, January 15-18, 2014:
    Complexity of modules over Lie superalgebras.

    The Third Graduate Research Conference in Algebra and Representation Theory, Kansas State University, April 12-14, 2013:
    Presenting Schur superalgebras.

    TORA IV : Texas - Oklahoma Representations and Automorphic Forms IV, U. of North Texas, March 23-24, 2013:
    Complexity of the simple and Kac modules over osp(2j2n):

    AMS Southeastern Sectional Meeting, Tulane University, LA, October 13-12, 2012:
    Presenting Schur superalgebras.

    TORA III : Texas - Oklahoma Representations and Automorphic Forms III, U. of Oklahoma, Sept. 28-30, 2012:
    Complexity of g-modules.

    TORA I : Texas - Oklahoma Representations and Automorphic Forms I, U. of North Texas, Sept. 17-18, 2011:
    Presenting Schur superalgebras.

    Math. Dept. - OU:
    February 24th, 2013: Left and right derived functors, Student Algebra Seminar.

    February 13th, 2012: Connection between projective representations and the second cohomology group, Graduate Student Seminar.

    December 9th, 2011: projective spaces and projective algebraic sets, Student Algebra Seminar.

    May 6th, 2011: A presentation of the Schur algebra and superalgebra, Algebra 3 Curriculum Vitae for Houssein El Turkey and Representation Theory Seminar.

    March 21st, 2011: A presentation of the Schur algebra S(2; d), Graduate Student Seminar.

    February 22nd, 2011: Algebraic groups, basic constructions, Student Algebra Seminar.

    December 5th, 2011: Generalities on superalgebras, Graduate Student Seminar.

    October 7th, 2010: Schur-Weyl Duality between partition algebras and the symmetric group, Student Algebra Seminar.

    October 4th, 2010: Partition Algebras, Graduate Student Seminar.

    September 23rd, 2010: Schur-Weyl Duality between the general linear group and the symmetric group, Student Algebra Seminar.

    Math. Dept. - The American University of Beirut:
    June 7th, 2008: Generalizations of Boolean rings.

    Professional Memberships

    American Mathematical Society