# Todor Todorov

### Professor

Mathematics Department
California Polytechnic State University
San Luis Obispo, CA 93407

### CV

Educational Preparation

Ph.D. in Mathematical Physics from University of Sofia - Bulgarian Academy of Sciences, 1982.
Ph.D. Thesis: Asymptotic Functions, Nonstandard Analysis and Multiplication of Schwartz Distributions: Generalized Eigen-States in Quantum Mechanics

Employment
1982-1986
Research Fellow at the Bulgarian Academy of Sciences, Department of Mathematical Physics and Elementary Particles of the Bulgarian Academy of Sciences, Sofia, Bulgaria.
1986-1987
Visiting Research Fellow at the International Center for Theoretical Physics, Trieste, Italy.
1987-88
Visiting Research Fellow at the Functional Analysis Department of International School for Advanced Studies, Trieste, (SISSA), Italy.
1989-90
Visiting Associate Professor at the Mathematics Department of University of California, Santa Barbara.
1990-2002
Lecturer at the Mathematics Department of California Polytechnic State University, San Luis Obispo.
Since September 2003
A tenure-track position of Assistant Professor in the Mathematics Department of California Polytechnic State University, San Luis Obispo.
Since September 2009
A tenure Associate Professor in the Mathematics Department of California Polytechnic State University, San Luis Obispo.
Since September 2014
A Full Professor of Mathematics in the Mathematics Department of California Polytechnic State University, San Luis Obispo.

### Published Work

• Chr. Ya. Christov, T. D. Todorov, Asymptotic Numbers: Algebraic Operations with Them, In: Serdica, Bulgaricae Mathematicae Publicationes, Vol.2, 1974, p.87--102.
• Todor D.Todorov, Asymptotic Numbers: I. Algebraic Properties, In: Bulgarian Journal of Physics, 7 (1981), 5, p.450--468.
• Todor D.Todorov, Asymptotic Numbers: II. Order Relation and Interval Topology, In: Bulgarian Journal of Physics, 7 (1981), 6, p.547--562
• T.D. Todorov, Asymptotic Functions and the Problem of Multiplication of Schwartz Distributions, In: Bulgarian Journal of Physics, Vol. 8 (1982), 2, p.109--120.
• T. D. Todorov, Extended Asymptotic Functions - Some Examples, In: Bulgarian Journal of Physics, 8 (1981), 3, p.216-225
• T. D. Todorov, Quasi-Extended Asymptotic Functions, In: Bulgarian Journal of Physics, 8 (1981), 4, p.313--328
• T. D.Todorov, Asymptotic Functions as Kernels of Schwartz Distributions, In: Bulgarian Journal of Physics, Vol. 12 (1981), 5, p.451--464
• T. D.Todorov, The Products $\delta^2(x),\, \delta(x)\, x^{-n},\ H(x)\, x^{-n}$ in the Class of the Asymptotic Functions, In: Bulgarian Journal of Physics, Vol.12 (1981), 5, p.465--480
• T.D.Todorov, Application of Non-Standard Hilbert Space to Quantum Mechanics, In: Proceedings of the International Conference on Complex Analysis and Applications, Varna, May 5-11, 1985, Bulgarian Academy of Sciences Publ., 1986, p.689--704
• T. D.Todorov, Sequential Approach to Colombeau's Theory of Generalized Functions, In: Internal Publication of International Centre for Theoretical Physics, International Atomic Energy Agency, UNESCO, IC/87/126 (1987), Trieste, Italia.
• B. Fisher and T. D. Todorov, Operations with Distribution Vectors, In: Demonstratio Mathematica, Vol. XX, No 3-4, 1987, p.401--412.
• T.D. Todorov, Colombeau's Generalized Functions and Non-Standard Analysis, In: B. Stankovic, E. Pap, S. Pilipovic, V.S. Vladimirov (editors), Generalized Functions, Convergence Structures and their Applications, Plenum Press, New York (1988), p.327--339.
• S. Salbany, T. Todorov, Alexander's Subbase Lemma, In: Proceedings of the American Mathematical Society, Vol. 105, Number 1, Jan. 1989
• Todor Todorov, A Nonstandard Delta Function, In: Proceedings of the American Mathematical Society, Vol. 110, Number 4, 1990, p.1143--1144
• B. Fisher and T. Todorov, A Commutative Product with Distribution Vectors, In: Journal of Mathematical and Physical Sciences, Vol. 25, No 2, April 1991, p.138--151.
• Todor Todorov, Pointwise Kernels of Schwartz Distributions, In: Proceedings of the American Mathematical Society, Vol. 114, No 3, March 1992, p.817--819
• S. Salbany and T. Todorov, Nonstandard and Standard Compactifications of Ordered Topological Spaces, In: Topology and its Applications, Vol. 47 (1992), p.35--52
• S. Salbany and T. Todorov, Monads and Realcompactness, In: Topology and its Applications, Vol. 56 (1994), p.99--104
• Todor Todorov, An Existence Result for a Class of Partial Differential Equations with Smooth Coefficients, In S. Albeverio, W.A.J. Luxemburg, M.P.H. Wolff (Eds.), Advances in Analysis, Probability and Mathematical Physics; Contributions to Nonstandard Analysis, Kluwer Academic Publishers, Dordrecht/Boston/London, Vol. 314, 1995, p. 107--121.
• Todor Todorov, An Existence of Solutions for Linear PDE with $C^{\infty}$-Coefficients in an Algebra of Generalized Functions, In: Transactions of the American Mathematical Society, Vol. 348, 2, Feb. 1996, p. 673--689
• T. Todorov, Pointwise Values and Fundamental Theorem in the Algebra of Asymptotic Functions, In: Non-Linear Theory of Generalized Functions (Eds: M. Grosser, G\"{u}nther H\"{o}rmann, M. Kunzinger and M. Oberguggenberger), Chapman & Hall/CRC Research Notes in Mathematics, 401, 1999, p.369-383 (available at arXivMathematics: (https://arxiv.org/abs/math/0601723)
• M. Oberguggenberger and T. Todorov, An Embedding of Schwartz Distributions in the Algebra of Asymptotic Functions, In: International Journal of Mathematics & Mathematical Sciences, Vol. 21, No. 3 (1998), p.417--428.
• S. Salbany and T. Todorov, Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications, In: Journal of Symbolic Logic, 65, 4 (2000), p.1836-1840 (available at arXivMathematics: https://arxiv.org/abs/math/0601724)
• T. Todorov and R. Wolf, Hahn field representation of A. RobinsonÕs asymptotic numbers, In: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF) 2000, Edited by A. Delcroix, M. Hasler, J.-A. Marti, and V.Valmorin, Cambridge Scientific Publishers, Cottenham, Cambridge, 2004, pp. 357-374 (available at arXivMathematics: https://arxiv.org/abs/math/0601722)
• TodorD. Todorov, Back to Classics: Teaching Limits through Infinitesimals, In: International Journal of Mathematical Education in Science and Technology, 2001, vol. 32, no. 1, p. 1-20 (available at arXivMathematics: https://arxiv.org/abs/1108.4657)
• TodorD.Todorov, Radius of Convergence of Power Series, In: International Journal of Mathematical Education in Science and Technology, Vol. 34, Number 2, March-April, 2003 (p. 277-280)
• Todor D. Todorov, Existence and uniqueness of $v$-asymptotic expantions and Colombeau's generalized numbers, In: Journal of Mathematical Analysis and Applications, 312 (2005), p. 261-279 (available at arXivMathematics: (https://arxiv.org/abs/math/0601720)
• Angel P. Popov and Todor D. Todorov, Exponentiation of $2\times 2$ and $3\times 3$ Matrices without Canonization, In: Mathematics and Education in Mathematics, 2006, Proceedings of the Thirty Fifth Spring Conference of the Union of Bulgarian Mathematicians, Borovets, April 5-8, 2006, pp. 344-353 (available at arXivMathematics: https://arxiv.org/abs/0712.2632)
• Ray Cavalcante and Todor D. Todorov, A Lost Theorem: Definite Integrals In Asymptotic Setting, In: The American Mathematical Monthly, Volume 115, Number 1, January, 2008, pp. 45-56 (available at arXivMathematics: https://arxiv.org/abs/0804.3156v1)
• Todor Todorov and Hans Vernaeve, Full Algebra of Generalzed Functions and Non-Standard Asymptotic Analysis, In: Logic and Analysis, Springer, Vol. 1, Issue 3, 2008, pp. 205-234 (available at arXivMathematics: https://arxiv.org/abs/0712.2603)
• Todor D. Todorov, An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms, In: Integral Transforms and Special Functions, Volume 22, Issue 9, September 2011, p. 695-708 (available at arXivMathematics: https://arxiv.org/abs/1101.5740)
• Todor D. Todorov, Algebraic Approach to Colombeau Theory, In: San Paulo Journal of Mathematical Sciences, 7 (2013), no. 2, 127-142 (https://arxiv.org/abs/1405.7341)
• James F. Hall and Todor D. Todorov, Ordered Fields, the Purge of Infinitesimals from Mathematics and the Rigorousness of Infinitesimal Calculus, Bulgarian Journal of Physics, Vol. 42 (2015) 99-127 - An issue dedicated to the centenary of the birth of Prof. Christo Yankov Christov (available at https://arxiv.org/abs/1509.03798)
• Todor D. Todorov, Steady-State Solutions in an Algebra of Generalized Functions: Lightning, Lightning Rods and Superconductivity, Novi Sad Journal of Mathematics, Volume 45, Number 1, 2015 (available at (http://www.dmi.pmf.uns.ac.rs/nsjom/framepaper.htm)
• {or} https://arxiv.org/abs/1509.03796)).

### Master's Students

• Guy Berger, Non-Standard Analysis, Multiplication of Schwartz Distributions and Delta-Like Solution of Hopf's Equation , Master Thesis, Cal Poly Library, San Luis Obispo, LD729.6.S52 M3 B47, 2005 (Available at: arXiv:0809.4322v1). Remark: This work was reported in the International Conference on Non-Standard Mathematics, Pisa, Italy, May 25-31, 2006 (http://www.dm.unipi.it/~nsm2006), in which Guy was rewarded with a scholarship from the Organizing Committee.
• Ray Cavalcante, Reduction of the Number of Quantifiers in Real Analysis through Infinitesimals, Master Thesis, Mathematics Department, California Polytechnic State University, San Luis Obispo, 2007 (Available at: arXiv:0809.4814v1).

### Senior Projects under Todor Todorov:

• Ray Cavalcante, Axiomatic approach to integration: an alternative method of teaching integrals, Senior Project # 05-0323 (2005) in Kennedy Library of the California Polytechnic State University, San Luis Obispo, CA-93407 (see also: arXiv:0804.3156v1).
• Mark Ireland, v-Asymptotic Analysis with Applications, Senior Project \# 07-0668 (2007) in Kennedy Library of the California Polytechnic State University, San Luis Obispo, CA-93407.
• James F. Hall, Completeness of Ordered Fields, MS #1004, 2011 (http://digitalcommons.calpoly.edu/mathsp/3/).
• Max Garcia, Filters and Ultrafilters in Real Analysis.