Creative Mathematics Education

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References

[1] Davies, P. J., & Hersch, R. (1981). Chapter 3: Famous problems. In The Mathematical Experience (pp. 207-316). Boston: Birkh?user.

[2] Escultura, E. E., (1970) The trajectories, reachable set, minimal levels and chain of trajectories of a control system, Ph.D. Thesis, Madison: University of Wisconsin.

[3] Escultura, E. E. (1997). The solution of the gravitational n-body problem. Journal of Nonlinear Analysis, A-Series: Theory, Methods and Applications, 30, 5021-5032.

[4] Escultura, E. E. (1998). Exact solutions of Fermat’s equation (A definitive resolution of Fermat’s last theorem). Journal of Nonlinear Studies, 5, 227-254.

[5] Escultura, E. E. (2002). The mathematics of the new physics. Journal of Applied Mathematics and Computations, 130, 149-169.

[6] Escultura, E. E. (2003). The new mathematics and physics. Journal of Applied Mathematics and Computation, 138, 145-169.

[7] Escultura, E. E. (2007). The Pillars of the new physics and some up- dates. Journal of Nonlinear Studies, 14, 241-260.

[8] Escultura, E. E. (2008). Extending the reach of computation. Journal of Applied Mathematics Letters, 21, 1074-1081.
doi:10.1016/j.aml.2007.10.027

[9] Escultura, E. E. (2009a). The mathematics of the grand unified theory (GUT). Journal of Nonlinear Analysis, A-Series: Theory: Method and Applications, 71, e420-e431. doi:10.1016/j.na.2008.11.003

[10] Escultura, E. E. (2009b). The new real number system and discrete computation and calculus. Journal of Neural, Parallel and Scientific Computations, 17, 59-84.

[11] Escultura, E. E. (2009c). Qualitative model of the atom, its components and origin in the early universe. Journal of Nonlinear Analysis, B- Series: Real World Applications, 11, 29-38.
doi:10.1016/j.nonrwa.2008.10.035

[12] Escultura, E. E. (2011). Scientific natural philosophy. Chapter 3: The grand unified theory. Bentham Ebooks, 60-107.
http://www.benthamscience.com/ebooks/9781608051786/index.htm

[13] Escultura, E. E. (2011). Scientific natural philosophy. Chapter 2: The mathematics of grand unified theory. Bentham Ebooks, 10-59.
http://www.benthamscience.com/ebooks/9781608051786/index.htm

[14] Escultura, E. E. (in press). The generalized integral as dual of Schwarz distribution. Journal of Nonlinear Studies.

[15] Horgan, H. (1993). The death of proof. Scientific American, 5, 74-82.

[16] Kiyosi, I. (Ed.), (1993). Encyclopedic Dictionary of Mathematics, Corporate Mathematical Society of Japan. Chapter 5: The integers (2nd ed.). Cambridge, MA: MIT Press, 393-400.

[17] Kline, M. (1980). Mathematics: The loss of certainty. Chapter 7: The axiom of choice (pp. 170-271). Oxford: Oxford University Press.

[18] Lakatos, I. (1976). Proofs and refutations. Chapter 2: Counterexamples to Cauchy’s proof of Euler’s formula on the polyhedron (pp. 70-99, J. Worral & E. Zahar Eds.). Cambridge: Cambridge University Press.

[19] Lakshmikantham, V., Escultura, E. E. & Leela, S. (2009). The Hybrid Grand Unified Theory. Chapter 2: The mathematics of the HGUT. Paris: Atlantis (Elsevier Science, Ltd), 70-93.

[20] Royden, H. L. (1983). Real analysis. Chapter 1: The real number system (3rd ed.). New York: MacMillan, 31-32.

[21] Young, L. C. (1969). Lectures on the Calculus of Variations and Optimal Control Theory. Volume II: The integrated Pontrjagin maximum principle. Philadelphia: W. B. Saunders, 410-498.

[22] Young, L. C. (1980). Mathematicians and their times. Chapter 3: Some paradox. Amsterdam: North-Holland, 122-123.