loadurl = window.location.href; // var args = "PaperID=" + 17266 + "&RefererUrl=" + refererrurl + "&DownloadUrl=" + downloadurl; // url = url + "?" + args + "&rand=" + RndNum(4); // // $(this).bind('click', function() { ShowTwo(url)}); // } // }); // } // //获取下载pdf注册的cookie // function getcookie() { // var cookieName = "pdfddcookie"; // var cookieValue = null; //返回cookie的value值 // if (document.cookie != null && document.cookie != '') { // var cookies = document.cookie.split(';'); //将获得的所有cookie切割成数组 // for (var i = 0; i < cookies.length; i++) { // var cookie = cookies[i]; //得到某下标的cookies数组 // if (cookie.substring(0, cookieName.length + 2).trim() == cookieName.trim() + "=") {//如果存在该cookie的话就将cookie的值拿出来 // cookieValue = cookie.substring(cookieName.length + 2, cookie.length); // break // } // } // } // if (cookieValue != "" && cookieValue != null) {//如果存在指定的cookie值 // return false; // } // else { // // return true; // } // } // function ShowTwo(webUrl){ // alert("22"); // $.funkyUI({url:webUrl,css:{width:"600",height:"500"}}); // } //window.onload = pdfdownloadjudge;
CE> Vol.3 No.1, February 2012
Share This Article:
Cite This Paper >>

Creative Mathematics Education

Abstract Full-Text HTML Download Download as PDF (Size:295KB) PP. 45-54
DOI: 10.4236/ce.2012.31008    6,506 Downloads   12,862 Views   Citations
Author(s)    Leave a comment
Edgar E. Escultura

Affiliation(s)

GVP College of Engineering, JNT University Kakinada, Visakhapatnam, India.

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.

KEYWORDS

Adjacent Decimals; Axioms; Banach-Tarski Paradox; Russell Paradox; Creativity; Critical Thinking; Dark Number; Decimal Integer; Goldbach’s Conjecture; G-Limit; G-Norm G-Sequnce; Lexicographic Ordering; Recurring 9s; Self-Reference; Vacuous Concept; Fermat’s Last Theorem

Cite this paper

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

Conflicts of Interest

The authors declare no conflicts of interest.

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.

  
comments powered by Disqus
CE Subscription
E-Mail Alert
CE Most popular papers
Publication Ethics & OA Statement
CE News
Frequently Asked Questions
Recommend to Peers
Recommend to Library
Contact Us

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.