Mark Fels Ph.D.

Mathematics and Statistics

Professor


Mark Fels

Contact Information

Office Location: Animal Science (ANSC) 303
Phone: (435) 797-0774
Email: 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 | Book Chapters

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

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Journal Articles

Academic Journal

  • Fels, M.E, (2017). 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.

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Other

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Teaching

MATH 5110 - Differential Geometry, Spring 2021
MATH 2210 - Multivariable Calculus, Spring 2021
MATH 2210 - Multivariable Calculus, Fall 2020
MATH 5340 - Theory of Linear Algebra, Fall 2020
MATH 4310 - Introduction to Algebraic Structures, Spring 2020
MATH 6350 - Multilinear Algebra and Matrix Theory, Spring 2020
MATH 6340 - Multilinear Algebra and Matrix Theory, Fall 2019
MATH 5340 - Theory of Linear Algebra, Fall 2019
MATH 5110 - Differential Geometry, Spring 2018
MATH 2210 - Multivariable Calculus, Spring 2018
MATH 5340 - Theory of Linear Algebra, Fall 2017
MATH 6810 - Topics in Mathematics (Topic), Fall 2017
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

Illia Hayes, Mathematics & Statistics, August 2020
Nick Graner, Mathematics & Statistics, November 2016
Russel Saddler, 2009
Robert Reem, 2008
Brian Gleason, 2007
Andrew Renner, 2004
Kimberli Cole-Tripp, 2002