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Ian Anderson Ph.D.

Profile Picture

Mathematics and Statistics

Professor

Professor

Contact Information

DialPhone: (435) 797-2822
SendEmail: Ian.Anderson@usu.edu


Educational Background

PhD, Mathematics, University of Arizona, 1976
MS, Mathematics, University of Waterloo, 1974
BS, Mathematics, University of Waterloo, 1973

Awards

Valedictorian Escort College of Science 2016, 2016

Top Professor Award, 2005

Utah State University Student Honors Program

Wynne D. Thorne Research Award, 1992

Utah State University

Wynne D. Thorne Research Award, 1992

Utah State University

Outstanding Teaching Assistantship Award, 1976

Dept. ofMathematics, Univ. of Arizona

Graduate Fellowship, 1973

Province of Ontario

National Research Council of Canada Postgraduate Scholarship, 1973

Research Assistantship, 1973

Univ. of Waterloo

Science Scholarship, 1973

National Research Council of Canada

Publications - Abstracts

    Publications - Books & Book Chapters

      Book Chapters

    • Anderson, I.M, (1976). The Uniqueness of the Neutrino Energy-Momentum Tensor and the Einstein- Weyl Equations: Topics in Differential Geometry. Academic Press

    * Has not been peer reviewed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      * Has not been peer reviewed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        * Has not been peer reviewed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, 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
        • Anderson, I.M, Nie, Z., Nurowski, P., (2015). Non-rigid parabolic geometries of Monge type. Advances in Mathematics, 277:4, 24--55.
        • Fels, M.E, Anderson, I.M, (2014). Backlund Transformations for Darboux Integrable Differential Systems: General Theory. Selecta Mathematica, New Series
        • Anderson, I.M, Torre, C.G, (2013). GR 20 Workshop, Warsaw, July 2013.
        • Anderson, I.M, Torre, C.G, (2013). Lessons from GR 20 Workshop, Warsaw, July 2013.
        • 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.
        • Torre, C.G, Anderson, I.M, (2012). New symbolic tools for differential geometry, gravitation, and field theory. Journal of Mathematical Physics, 53, 013511 (12 pages).
        • Torre, C.G, Anderson, I.M, (2011). New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory. preprint
        • Anderson, I.M, Fels, M.E, Vassiliou, P., (2009). Superposition Formulas for Darboux Integrable Exterior Differential Systems. Advances in Mathematics, 221:6, 1910-1963.
        • Anderson, I.M, Fels, M.E, (2005). Exterior Differential Systems with Symmetry. Acta Applicandae Mathematicae, 87, 3-31.
        • 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., Torre, C., (2001). Group invariant solutions in mathematical physics and differential geometry. Contemporary Mathematics, 285
        • 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.
        • Anderson, I.M, Fels, M.E, Torre, C.G, (1999). Symmetry Reduction Without Transversality. arXiv preprint math-ph/9910015
        • Anderson, I.M, Juras, M., (1997). Generalized Laplace Invariants and the Method of Darboux. Duke J. Math., 89, 351-375.
        • 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.
        • Anderson, I.M, Kamran, N., (1997). The Variational Bicomplex for Second Order Partial Differential Equa- tions in the Plane. Duke J. Math, 87, 265-319.
        • Anderson, I.M, Torre, C., (1996). Asymptotic Conservation Laws in Classical Field Theory. Phys. Rev. Lett., 77, 4109-4133.
        • Anderson, I.M, Torre, C.G, (1996). Asymptotic conservation laws in classical field theory. Physical review letters, 77:20, 4109.
        • Anderson, I.M, Torre, C.G, (1996). Classification of local generalized symmetries for the vacuum Einstein equations. Communications in mathematical physics, 176:3, 479–539.
        • Anderson, I.M, Torre, C.G, Fredenhagen, K., Jr, M., Guhr, T., Bogomolny, E., Leyvraz, F., Schmit, C., Jakšic, V., Pillet, C., others, , (1996). Miscellaneous front pages, Comm. Math. Phys., Volume 176, Number 3 (1996).
        • Anderson, I.M, Pohjanpelto, J., (1996). Symmetries, Conservation Laws, and Variational Principles for Vector Field Theories. Proc. Camb. Phil. Soc., 120, 369-384.
        • Anderson, I.M, Torre, C., (1996). The Classification of Local Generalized Symmetries for the Einstein Equations. Comm. Math. Physics, 176, 479-539.
        • Anderson, I.M, Pohjanpelto, J., (1995). Variational Principles for Differential Equations with Symmetries and Conservation Laws II: Polynomial Equations. Mathematische Annalen, 301, 627-653.
        • Anderson, I.M, Torre, C.G, (1994). Classification of generalized symmetries for the vacuum Einstein equations. arXiv preprint gr-qc/9404030
        • Anderson, I.M, Pohjanpelto, J., (1994). Variational Principles for Differential Equations with Symmetries and Conservation Laws I: Second Order Scalar Equations. Mathematische Annalen, 299, 191-222.
        • Anderson, I.M, Kamran, N., Olver, P., (1993). Internal, External and Generalized Symmetries. Advances in Mathematics, 100, 53-100.
        • Anderson, I.M, Torre, C., (1993). Symmetries of the Einstein Equations. Physical Rev. Let- ters, 70, 3525-3529.
        • Torre, C.G, Anderson, I.M, (1993). Symmetries of the Einstein equations. arXiv preprint gr-qc/9302033
        • Anderson, I.M, Thompson, G., (1992). The Inverse Problem in the Calculus of Variations for Ordinary Differen- tial Equations. Memoirs of the AMS, 473
        • Anderson, I.M, (1988). Aspects of the Inverse Problem to the Calculus of Variations. Archivum Mathematicum (Brno), 24, 329-370.
        • Anderson, I.M, Arms, J., (1986). Perturbations of Conservation Laws in Field Theories. Annals of Physics, 167, 354-689.
        • Anderson, I.M, Bezdek, J., (1985). An Application of the c-Varieties Clustering Algorithm to Polygonal Curve Fitting. IEEE Trans SMC, 15, doi: 637-641
        • Anderson, I.M, (1985). Determinantal Ideals and the Capelli Identities. Linear Algebra and its Applications, 69, 269-277.
        • Anderson, I.M, Bezdek, J., (1984). Curvature and Tangential Deflections of Discrete Arcs. IEEE Trans. PAMI, 6, 27-40.
        • Anderson, I.M, (1984). Natural Variational Principles on Riemannian Structures. Annals ofMath- ematics, 120, 329-370.
        • Anderson, I.M, Duchamp, T., (1984). Variational Principles for Second-Order Quasi-Linear Scalar Equations. J. Diff. Equations, 51, 1-47.
        • Anderson, I.M, (1981). The Principle of Minimal Gravitational Coupling. Arch. RationalMech. Anal., 75, 349-372.
        • Anderson, I.M, Duchamp, T., (1980). On the Existence of Global Variational Principles. Amer. J. Math., 102, 781-868.
        • Anderson, I.M, (1979). On the Characterization of Energy-Momentum Tensors. General Relativ- ity and Gravitation, 10, 461-465.
        • Anderson, I.M, (1978). On the Structure of Divergence-Free Tensors. J. Math. Phys, 19, 2570-2575.
        • Anderson, I.M, (1978). Tensorial Euler-Lagrange Expressions and Conservation Laws. Aequa- tiones Mathematicae, 17, 255-291.
        • Anderson, I.M, Lovelock, D., (1976). A Characterization of the Einstein Tensor in Terms of Spinors. J. Math. Phys., 17, 1001-1003.
        • Anderson, I.M, (1974). The Neutrino Energy-Momentum Tensor and the Weyl Equations in Curved Space-Time. General Relativity and Gravitation, 6, 621-642.
        • Professional Journal

        • Anderson, I.M, Pohjanpelto, J., (2012). Variational principles for natural divergence-free tensors in metric field theories. Journal of Geometry and Physics , 62, 2376--2388.
        • Anderson, I.M, Kruglikov, B., (2011). Rank 2 distributions of Monge equations: Symmetries, equivalences, extensions. Advances in Mathematics, 228, 1435-1465.

        * Has not been peer reviewed

        Publications - Literary Journal

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          Publications - MultiMedia

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          Publications - Technical Reports

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          Publications - Translations & Transcripts

            Publications - Other

              * Has not been peer reviewed

              Scheduled Teaching

              MATH 6120 - Differential Geometry, Spring 2017

              MATH 4200 - Foundations of Analysis, Spring 2017

              MATH 6110 - Differential Geometry, Fall 2016

              MATH 4310 - Introduction to Algebraic Structures, Spring 2016

              MATH 6350 - Multilinear Algebra and Matrix Theory, Spring 2016

              MATH 5910 - Directed Reading and Conference, Fall 2015

              MATH 6340 - Multilinear Algebra and Matrix Theory, Fall 2015

              MATH 4310 - Introduction to Algebraic Structures, Spring 2015

              MATH 6810 - Topics in Mathematics (Topic), Spring 2015

              MATH 5220 - Introduction to Analysis II, Spring 2014

              MATH 6350 - Multilinear Algebra and Matrix Theory, Spring 2014

              MATH 5210 - Introduction to Analysis I, Fall 2013

              MATH 6340 - Multilinear Algebra and Matrix Theory, Fall 2013

              MATH 5220 - Introduction to Analysis II, Spring 2013

              MATH 5210 - Introduction to Analysis I, Fall 2012

              MATH 5220 - Introduction to Analysis II, Spring 2012

              MATH 7820 - Topics in Mathematics (Topic), Spring 2012

              MATH 5210 - Introduction to Analysis I, Fall 2011

              MATH 5220 - INTRO TO ANALYSIS II, Spring 2011

              MATH 5210 - Introduction to Analysis I, Fall 2010


              Graduate Students Mentored

              Jacob Kullberg, Mathematics & Statistics, September 2016
              Mychelle Parker, Mathematics & Statistics, June 2016
              Hannah Lewis, Mathematics & Statistics, September 2013
              Jesse Hicks, Mathematics & Statistics 2016
              Jordan Rozum, Mathematics & Statistics, June 2014 - October 2015
              Spencer Sitton, Mathematics & Statistics, June 2009 - June 2014
              Jesse Hicks, Mathematics & Statistics, June 2011 - December 2013
              Tom Apedaile, Mathematics & Statistics, June 2011 - December 2013
              Francesco Strazzullo, 2009
              Alan Perry, 2007
              Matt Biesecker, 2004
              Adam Bower, 2002
              Charles Miller, 1999
              Martin Juras, 1997
              Cinnamon Hillyard, 1992
              Hiroshi Nagao, 1981