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John Gill: Career as a Teacher and Mathematician



mathart1

Instructor in Mathematics
@ Murray State University, Murray, KY [1964-1967]

Assistant/Associate/Full Professor of  Mathematics
@ Colorado State University at Pueblo [1971-2000]. 






I taught a variety of math courses at the undergraduate and graduate level [Intermediate and College Algebra , Trigonometry, Calculus, Math for Business, Math for Applied Science & Technology, Intro. to Mathematical Thought, Topics in Discrete Mathematics, Math for Computers, Topology, Advanced Calculus, Complex Variables, Graduate Real Analysis (for MSANS Program)].

Served as Department Chairman, President of Sigma Xi Club, Regional Chair of Mathematical Association of America (MAA), Board of Governors of the MAA. Given Outstanding Faculty Award and Provost's Award for Scholarship.

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onducted mathematical research in Classical Complex Analysis. Member of a small international group of research mathematicians working in the Analytic Theory of Continued Fractions and Related Topics (1970-1999). Participated in a number of research meetings in the USA, France, Hungary, and Norway. Founded and edited (with John McCabe of the U. of St. Andrews) the minor specialty journal Communications in the Analytic Theory of Continued Fractions (1991-1998).







Research Publications  (Single Author) :


· Infinite Compositions of Mobius Transformations, Transactions of the Amer. Math. Soc., Vol. 176
 
· Attractive Fixed Points and Continued Fractions, Mathematica Scandinavica , Vol. 33
 
· Use of Attractive Fixed Points to Accelerate the Convergence of Limit Periodic Continued Fractions, Proc. Amer. Math. Soc., Vol. 47
 
· A Generalization of Certain Continued fractions, Bull. Calcutta Math. Soc., Vol. 69
 
· Modifying Factors for Sequences of Linear Fractional Transformations , Proc. Royal Norwegian Soc. of Sci. & Letters, No. 3, 1978
 
· Enhancing the Conv. Region of a Seq. of Bilinear Transformations , Mathematica Scandinavica, Vol. 43
 
· Conv. Acceleration of Cont. Frac. K(a n /1) with Lim a n = 0, Springer-Verlag Lecture Notes in Math ., Vol. 932
 
· Truncation Error Analysis for Cont. Frac.K(a n /1) Where. . . , Springer-Verlag Lecture Notes in Math , Vol. 932
 
· Converging Factors for Cont. Frac. K(a n /1), Lim a n = 0 , Proc. Amer. Math. Soc., Vol. 84
 
· Converging Factors for Certain Cont. Frac. K(a n /1) Where . . . , Bull. Calc. Math. Soc., Vol. 75
 
· A Note on Fixed Point Cont. Frac. & Aitkin's Method, Rocky Mtn. J. of Math., Vol. 14
 
· An Error Estimate for Cont. Frac., Proc. Amer. Math. Soc., Vol. 96
 
· Limit Periodic Iteration, J. of Applied Numerical Math 4 (1988)

· Compositions of Analytic Func. of the Form F n (z) = F n-1 (f n (z)), Lim f n = f , J. of Computational & Applied Math.4(1988)
 
· Use of Repulsive Fixed Points to Analytically Continue Certain Func. , Rocky Mtn. J. of Math., Vol. 21
 
· Complex Dynamics of the System F n (z) = F n-1 (f n (z)), Lim f n = f , J. Comp. & Appl. Math., 32(1990)
 
· Inner Compositions of Anal. Func. on the Unit Disc, Intl. J. of Math. & Math. Sci., Vol 14
 
· Use of the Seq. F n = f n o. . . o f 1 to Compute Fixed Points of Cont. Frac., Products, & Series , J. Appl. Num. Math., 8(1991).
 
· Approximations of Iteration, Intl. Conf. Approximation theory, Kecskemet, Hungary
 
· Partial Limit Periodic Behavior in Cont. Frac., Bull. Calc. Math. Soc., Vol. 84
 
· A Tannery Trans. of Cont. Frac. & Other Expansions, Comm. Anal. Th. Cont. Frac., Vol. I
 
· Basic Dynamics of {F n }, F n = f n o. . . o f 1 , Comm. Anal. Th. Cont. Frac., Vol. I
 
· Outer Compositions of Hyperbolic/Loxodromic Mobius Trans., Intl. J. of Math. & Math. Sci., Vol. 15
 
· A Note on the Num. Dynamics of Modified Cont. Frac. and Other Expansions , Comm. Anal. Th. Cont. Frac., Vol. III
 
· Sequences of Linear Frac. Trans. and Reverse Cont. Frac. , Continued Fractions & Orthogonal Functions , Marcel Dekker
 
· Dynamics of Inner and Outer Composition Seq. of Functions {f n }, Lim f n = 0 , Intl. J. of Math. & Math. Sci. , Vol. 20
 
· A Note on Bounds for Derivatives of Cont. Frac., J. Comp. & Appl. Math., 72(1996).
 
· A Natural Continuous Interpolating Structure for Cont. Frac. , J. Comp. & Appl. Math., 105(1999).
 
· The Analogy Between Periodic Cont. Frac. and Geometric Series , Comm. Anal. Th. Cont. Frac., Vol. VI
 
· A Note on Extending Euler's Connection Between Cont. Frac. & Power Series, J. Comp. & Appl. Math., 106(1999).

.    .    .   After Retirement(2000) - Just for fun!   .    .    .

  • Generalizations of the Classical Tannery's Theorem  ,  Comm. Anal. Th. Cont. Frac., Vol. XIX (2012)
  • Covergence of Infinite Compositions of Complex Functions  ,  Comm. Anal. Th. Cont. Frac., Vol. XIX
  • Zeno's Arrow: A Mathematical Speculation  ,  Comm. Anal. Th. Cont. Frac.,  Vol. XIX
  • Zeno Contours and Vector Fields ,  Comm. Anal. Th. Cont. Frac.,  Vol. XIX
  • Zeno Contours & Attractors ,     www.johngill.net
  • Notes on a Zeno Integral ,   www.johmgill.net
  • Expanding Functions as Infinite Compositions ,  www.johngill.net
  • Images of Singularities in the Complex Plane , Comm. Anal. Th. Cont. Frac.,  Vol. XIX, www.johngill.net
  • Images of Continued Fractions , Comm. Anal. Th. Cont. Frac.,  Vol. XIX,  www.johngill.net






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