Emre Tokgoz Home Page

Current Teaching - FALL 2011

• MATH 1823-003 - Calculus and Analytic Geometry I
, MWF 9:30-10:20, Sutton Hall, Room 111.

• MATH 2123-002 - Business Calculus II
, MWF 10:30-11:20, Sutton Hall, Room 111.

• MATH 2123-004 - Business Calculus II
, TR 3:00-4:15, PHSC, Room 356.

Classes I Taught Last Semester - Summer 2011 Semester

• MATH 1743-181 - Business Calculus I
, MTWRF 11:50-1:00

Teaching Experience at the University of Oklahoma

1) Department of Mathematics

MATH 2423 - Calculus/Analytic Geometry II (Summer 2008, Summer 2010)

MATH 2123 - Business Calculus II (Spring 2010, Fall 2010)

MATH 1743 - Business Calculus I (Spring 2008, Fall 2008, Spring 2009, Fall 2009, Summer 2011)

MATH 1823 - Calculus/Analytic Geometry I (Summer 2006, Summer 2009)

MATH 2423 - Calculus/Analytic Geometry II (Fall 2007, Spring 2007, Fall 2006)

MATH 1823 - Calculus/Analytic Geometry I (Spring 2006, Fall 2005)

Mathematics Help Center Tutor (Summer 2005, Spring 2005)

Grader (Fall 2004)

2) School of Computer Science

C.S. 3723 Numerical Methods for Engineering Computation (Spring 2011)

Grader (Spring 2010)

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Degrees Recieved

• Ph.D. in Mathematics, University of Oklahoma. My dissertation in Mathematics is titled "Separation and Fenchel-Type Duality Theorems for Functions with Integer and Real Variables." My advisor was Dr. Kevin A. Grasse.
• M.S. in Computer Science, University of Oklahoma.
My thesis in Computer Science is titled "Analysis of Default Probability of Corporate Bonds when the Interest Rates are Stochastic." My advisor was Dr. S. Lakshmivarahan.
• M.A. in Mathematics, University of Oklahoma.
• B.S. in Mathematics, University of Ankara, Ankara, Turkey.

Research Interests

• Operations Research: Applied Probability, Queueing Systems, Nonlinear Mixed Integer Convexity, Convex Optimization.
• Machine Learning: Support Vector Machines, Quadratic Programming Problem.
• Riemannian Geometry: Bernstein Type Theorems for Higher Codimension.
• Financial Mathematics: My Master's thesis in Computer Science is related to Corporate Bond Pricing with Stochastic Interest Rates.
• Pedagogy (Mathematics and Engineering): Investigating engineering and science students numerical methods/analysis and their pre-requisite course concept knowledge.

Publications

• Tokgoz, Emre and Kumin, Hillel. "Mixed Convexity and Optimization Results for an (S-1,S) Inventory Model Under a Time Limit on Backorders," to appear in the Journal of Computational Management Science, Springer, (Accepted on 03-08-2011).
• Tokgoz, Emre and Theodore B. Trafalis, “Mixed Convexity and Optimization of an SVM QP Problem for Nonlinear Polynomial Kernel Maps,” to appear in the Proceedings of the 15th World Scientific and Engineering Academy and Society CSCC Multiconference, Corfu Island, Greece, July 2011.
• Tokgoz, Emre, Nourazari, Sara and Kumin, Hillel. "Convexity and Optimization of Condense Discrete Functions," 2011 Symposium on Experimental Algorithms, Lecture Notes in Computer Science, Springer-Verlag, Vol. 6630, pg. 33-42, May 2011.
• Tokgoz, Emre and Kumin, Hillel. "A Mixed Integer Convexity Result with an Application to an M/M/s Queueing System," Accepted to the International Journal of Open Problems in Computer Science and Mathematics, Vol. 3. No. 5, 2010.
• Tokgoz, Emre. "The Number of Minimal Points, Minimal Values and Related Algorithms for Non-linear Mixed Convex Functionals with Unbounded Domain," published as a regular research paper in the Proceedings of the 2010 International Conference on Scientific Computing, pg. 307-313, July 2010.
• Tokgoz, Emre, and Adnan, Asif M. "The Number of Minimal Points, the Minimal Values and Related Algorithms of Non-linear Mixed Convex Functionals with Bounded Domain," published as a regular research paper in the Proceedings of the 2010 International Conference on Scientific Computing, pg. 314-319, July 2010.
• Tokgoz, Emre. "Mixed E-, E*-Convex Functions and Their Corresponding Mixed Hessian Matrices," International Journal of Pure and Applied Mathematics, Vol. 59, No. 2, pg. 145-155, 2010.
• Tokgoz, Emre. "Mixed T-, T*-Convex Functions and Their Corresponding Mixed Hessian Matrices," International Journal of Pure and Applied Mathematics, Vol. 56, No. 1, 2009.
• Lakshmivarahan, S., and Tokgoz, Emre. "On the Structure of Orthogonal Skew-Symmetric Matrices," published as a regular research paper in the Proceedings of the 2009 International Conference on Scientific Computing, pg. 371- 373, July 2009.
• Tokgoz, Emre, Maalouf, Maher, and Kumin, Hillel. "A Hessian Matrix for Functions with Integer and Continuous Variable," International Journal of Pure and Applied Mathematics, Vol. 57, No. 2, pg. 209-218, 2009.
• Tokgoz, Emre. "Algorithms for Mixed Convexity and Optimization of 2-Smooth Mixed Functions," International Journal of Pure and Applied Mathematics, Vol. 57, No.1, pg. 103-110, 2009.

Conference Presentations

• Tokgoz, Emre. "Analysis of Default Probability of Corporate Bonds When the Interest Rates are Stochastic," 6th Annual Computer Science Research Conference at the University of Oklahoma, April 2011.
• Tokgoz, Emre. "Separation and Fenchel-Type Duality Theorems for Functions with Integer and Real Variables," 73rd Annual Oklahoma-Arkansas MAA Sectional Meeting, March 2011.
• Tokgoz, Emre and Kumin, Hillel. A convexity Result for an (S-1,S) Inventory Model under Time limit with Backorders, 2010 INFORMS Annual Meeting, November 2010.
• Tokgoz, Emre. "On the Theory of Mixed Convex Functions," Joint Meetings of the AMS and the MAA, January 2010.
• Tokgoz, Emre. "The Number of Minimal Points, Minimal Values and Related Algorithms for Non-linear Mixed Convex Functionals with Unbounded Domain," 2010 World Congress in Computer Science, Computer Engineering, and Applied Computing: International Conference on Scientific Computing, July 2010.
• Tokgoz, Emre, and Adnan, Asif M. "The Number of Minimal Points, the Minimal Values and Related Algorithms of Non-linear Mixed Convex Functionals with Bounded Domain," 2010 World Congress in Computer Science, Computer Engineering, and Applied Computing: International Conference on Scientific Computing, July 2010.
• Tokgoz, Emre and Kumin, Hillel. "A Mixed Integer Convexity Result with an Application to an M/M/s Queueing System," 20th International Symposium on Mathematical Programming, August 2009.
• Lakshmivarahan, S. and Tokgoz, Emre. "On the Structure of Orthogonal Skew-Symmetric Matrices," 2009 World Congress in Computer Science, Computer Engineering, and Applied Computing: International Conference on Scientific Computing, July 2009.
• Tokgoz, Emre and Kumin, Hillel. "A Hessian Matrix for Functions with an Integer and Real Variable," 71st Annual Meeting of the Oklahoma-Arkansas Section of the Mathematical Association of America, March 2009.