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Mark Fels Ph.D.

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Mathematics and Statistics

Professor

Professor

Contact Information

DialPhone: (435) 797-0774
SendEmail: mark.fels@usu.edu


Educational Background

PhD, Mathematics, McGill University, 1993
MS, Mathematics, University of Waterloo, 1989
BS, Computer Science/Mathematics, University of Waterloo, 1986

Awards

National Research Council of Canada Scholarship, 1996

ISM Montreal Scholarship, 1993

National Research Council of Canada Scholarship, 1991

Research Scholarship, 1987

Tomalla Institute Zurich

National Research Council of Canada Scholarship, 1985


Publications - Abstracts

    Publications - Books & Book Chapters

      Book Chapters

    • Fels, M.E, (2002). Differential Invariants,. Encyclopedia of Mathematics

    * Has not been peer reviewed

    Publications - Fact Sheets

      * Has not been peer reviewed

      Publications - Curriculum

        * Has not been peer reviewed

        Publications - Journal Articles

          Academic Journal

        • Fels, M.E, (2016). On the Construction of Simply Connected Solvable Lie Groups. Journal of Lie Theory, 27, 193–215.
        • Fels, M.E, Anderson, I.M, (2015). Backlund Transformations for Darboux Integrable Systems: Examples and Applications. Journal of Geometry and Physics, 102, 1-31. doi: doi:10.1016/j.geomphys.2015.12.005
        • Fels, M.E, Anderson, I.M, (2014). Backlund Transformations for Darboux Integrable Differential Systems: General Theory. Selecta Mathematica, New Series
        • Fels, M.E, Anderson, I.M, (2013). The Cauchy Problem for Darboux Integrable Systems and non-linear D'Alembert Formulas. Symmetry, Integrability and Geometry: Methods and Applications, 9:17, 1-22.
        • Anderson, I.M, Fels, M.E, Vassiliou, P., (2009). Superposition Formulas for Darboux Integrable Exterior Differential Systems. Advances in Mathematics, 221:6, 1910-1963.
        • Fels, M.E, (2007). Integrating ordinary differential equations with symmetry revisited. Foundations of Computational Math, 7:4, 417-454.
        • Fels, M.E, Renner, A.G, (2006). Non-reductive four dimensional homogeneous pseudo-Riemannian Mani- folds,. Canadian Journal of Mathematics, 58:2, 282-311.
        • Anderson, I.M, Fels, M.E, (2005). Exterior Differential Systems with Symmetry. Acta Applicandae Mathematicae, 87, 3-31.
        • Fels, M.E, Torre, C.G, (2002). The principle of symmetric criticality in general relativity. Classical and Quantum Gravity, 19:4, 641-675.
        • Anderson, I.M, Fels, M.E, (2002). Transverse Group Actions on Bundles. Topology and its Applications, 123:3, 443-459.
        • Anderson, I.M, Fels, M.E, Torre, C.G, (2000). Group invariant solutions without transversality. Comm. Math. Phys., 212:3, 653-686.
        • Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Department of Mathematics Utah State University Logan, Utah 84322.
        • Fels, M.E, Olver, P.J, (1999). Moving coframes II. Regularization and theoretical foundations. Acta. Appl. Math., 55, 127-208.
        • Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Symmetry Reduction Without Transversality. arXiv preprint math-ph/9910015
        • Fels, M.E, Olver, P.J, (1998). Moving coframes I. A practical algorithm. Acta. Appl. Math., 51, 161-213.
        • Fels, M.E, Olver, P.J, (1997). On relative invariants. Mathematische Annalen, 308:4, 701-732.
        • Fels, M.E, Anderson, I.M, (1997). Symmetry reduction of variational bicomplexes and the principle of sym- metric criticality. Amer. Jour. Math., 119:3, 609-670.
        • Fels, M.E, (1996). The Inverse Problem of the Calculus of Variations for Scalar Fourth Order Ordinary DiŽerential Equations. Trans. Amer. Math Soc., 348:12, 5007-5029.
        • Fels, M.E, (1995). The equivalence problem for systems of second order ordinary diŽerential equations. Proc. London Math. Soc., 71:3, 221-240.
        • Fels, M.E, (1990). Non-factorizable separable systems and higher-order symmetries of the Dirac operator. N. Kamran, Proc. R. Soc. Lond. A, 428, 229-249.
        • Fels, M.E, Kamran, N., (1990). Systemes separables non-factorisables et symetries de dieuxieme ordre de l' operateur de Dirac. C. R. Acad. Sci. Paris, 331:1, 825-830.

        * Has not been peer reviewed

        Publications - Literary Journal

          * Has not been peer reviewed

          Publications - MultiMedia

            * Has not been peer reviewed

            Publications - Technical Reports

              * Has not been peer reviewed

              Publications - Translations & Transcripts

                Publications - Other

                  * Has not been peer reviewed

                  Scheduled Teaching

                  MATH 5110 - Differential Geometry, Spring 2017

                  MATH 6810 - Topics in Mathematics (Topic), Spring 2017

                  MATH 6110 - Differential Geometry, Fall 2016

                  MATH 4310 - Introduction to Algebraic Structures, Fall 2016

                  MATH 2210 - Multivariable Calculus, Spring 2016

                  MATH 2210 - Multivariable Calculus, Spring 2016

                  MATH 4310 - Introduction to Algebraic Structures, Fall 2015

                  MATH 5340 - Theory of Linear Algebra, Fall 2015

                  MATH 5110 - Differential Geometry, Spring 2015

                  MATH 5310 - Introduction to Modern Algebra, Spring 2015

                  MATH 6110 - Differential Geometry, Fall 2014

                  MATH 5340 - Theory of Linear Algebra, Fall 2014

                  MATH 2210 - Multivariable Calculus, Spring 2014

                  MATH 2210 - Multivariable Calculus, Spring 2014

                  MATH 2210 - Multivariable Calculus, Fall 2013

                  MATH 5340 - Theory of Linear Algebra, Fall 2013

                  MATH 5270 - Complex Variables, Spring 2013

                  MATH 2250 - Linear Algebra and Differential Equations, Fall 2012

                  MATH 6110 - DIFFERENTIAL GEOM, Spring 2011

                  MATH 2210 - MULTIVARI CALCULUS (QI), Spring 2011

                  MATH 7810 - ST: DIFFERENTIAL GEOMETRY, Spring 2011

                  MATH 5110 - Differential Geometry, Fall 2010

                  MATH 2210 - Multivariable Calculus, Fall 2010


                  Graduate Students Mentored

                  Nick Graner, Mathematics & Statistics, November 2016
                  Russel Saddler, 2009
                  Robert Reem, 2008
                  Brian Gleason, 2007
                  Andrew Renner, 2004
                  Kimberli Cole-Tripp, 2002