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

The Role of the Proof in Math The notion of proof has long play a key role in the study of mathematics. It is in my opinion the role of proof that separates mathematics from the sciences and other fields of study. It is the existence of proofs that give mathematicians the corporate trust that their work is credible and thus allows them to continue to build upon prior work without the need to second guess what has previously been accomplished.Based upon this observation, it becomes natural to ask the questions pertaining to the drill of proof in learning and understanding mathematics. If the concept of proof is so important to the field of mathematics, then is it possible that by writing proofs and studying proofs that an undivided will be better equipped to understand the mathematics for which the proofs pertain? And if this is possible then when should a person be first exposed to proofs and at what level? In this paper I will give my views pertaining to these questions, as w ell as, a few more of my views pertaining to some other topics related to these questions. to begin with discussing the virtues of proofs as a means of learning and understanding mathematics, I feel that it is first necessary to begin with a brief discussion of the functions of proof at heart mathematics. Following I will give a list of the functions of proof that I have comprised from three sources (Hanna 2, Knuth 3, Tucker 6)1.verification,the act of arguing that a financial 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, etc.4.discovery,creating knowledge and new results... ...ducation, V178 N1, pp. 35-452Hanna, Gila (2000), Proof, description and Exploration An Overview, Educational Studies in maths, V44, pp. 5-233Knuth, Eric (2002), Secondary School Mathematics Teachers Conceptions of Proof, Journal for Resear ch in Mathematics Education, V33, pp.379-4054Lester, Frank K. (1975), Developmental Aspects of Childrens Ability to register 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 Argument 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