Creative Mathematics Education

Author(s)
Edgar E. Escultura

ABSTRACT

Creativity and critical thinking are the core values of science. Since mathematics is its primary language, the student of mathematics must imbibe and consolidate them. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. Therefore, the student of mathematics must go through the twists and turns of the critique-recti- fication of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works.

Creativity and critical thinking are the core values of science. Since mathematics is its primary language, the student of mathematics must imbibe and consolidate them. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. Therefore, the student of mathematics must go through the twists and turns of the critique-recti- fication of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works.

Cite this paper

Escultura, E. (2012). Creative Mathematics Education.*Creative Education, 3,* 45-54. doi: 10.4236/ce.2012.31008.

Escultura, E. (2012). Creative Mathematics Education.

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.

[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.