Showing posts from February 6, 2022

Python-Based Introduction to Mathematical Proofs

Scroll down for video lectures 1. What is a Mathematical Proof?   Mathematical proof is a method of discourse which allows a human being to:  discover new mathematical knowledge, analyze existing mathematical knowledge, verify truthfulness of a piece of mathematical knowledge.  The ability to construct a mathematical proof is part of human nature. It is closely related to the ability to form thoughts and reason. Mathematical knowledge is knowledge of abstract principles about our universe. As such, it requires use of symbols to represent entities that are inherently abstract. For example, the symbol 2 may represent 2 apples or 2 pears . The number 2 is an abstract entity, since it is not confined to any of these concrete representations.  Mathematics functions at different levels of abstraction too. For instance, we may write a symbol, such as n , to represent any number. In one case we could have n = 2 , and in another case we could have n = 3 . This is a second layer of abstractio