Tuesday, March 19, 2019

The Role of the Proof in Math Essay example -- Mathematics Mathematica

The Role of the Proof in Math The notion of proof has long played a key role in the theatre of mathematics. It is in my opinion the role of proof that separates mathematics from the sciences and other field of study. It is the existence of proofs that give mathematicians the confidence that their work is credible and thus allows them to tolerate to build upon prior work without the need to second guess what has antecedently been accomplished.Based upon this observation, it becomes natural to ask the questions pertaining to the use of proof in schooling and understanding mathematics. If the concept of proof is so important to the field of mathematics, hence is it possible that by writing proofs and studying proofs that an individual will be better equipped to understand the mathematics for which the proofs pertain? And if this is possible thus when should a person be first exposed to proofs and at what train? In this paper I will give my views pertaining to these questions , as well as, a few more of my views pertaining to some other topics related to these questions. beforehand discussing the virtues of proofs as a means of learning and understanding mathematics, I know that it is first necessary to begin with a brief discussion of the functions of proof within mathematics. Following I will give a tip of the functions of proof that I have comprised from three sources (Hanna 2, Knuth 3, Tucker 6)1.verification,the act of rock that a statement is true2.explanation,providing reasons for why a statement is true, which in turnmay lead to understanding3.systematization,organizing statements and definitions into a system ofaxioms, lemmas, theorems, and so forth4.discovery,creating knowledge and new results... ...ducation, V178 N1, pp. 35-452Hanna, Gila (2000), Proof, Explanation and Exploration An Overview, Educational Studies in maths, V44, pp. 5-233Knuth, Eric (2002), junior-grade School Mathematics Teachers Conceptions of Proof, Journal for look in Mathematics Education, V33, pp.379-4054Lester, stamp K. (1975), Developmental Aspects of Childrens Ability to Understand Mathematical Proof, Journal for Research in Mathematics Education, V6 N1, pp. 14-255Selden, Annie and Selden, John (2003), Validations of Proofs Considered as Texts Can Undergraduates Tell Whether an melody Proves a Theorem?, Journal for Research in Mathematics Education, V34 N1, pp. 4-366Tucker, Thomas (1999), On the Role of Proof in Calculus Courses, Contemporary Issues in Mathematics Education, MSRI Publications, Cambridge University Press, Cambridge, UK

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