Название: Theoremus: A Student's Guide to Mathematical ProofsАвтор: Lito Perez Cruz
Издательство: Springer
Год: 2021
Страниц: 139
Язык: английский
Формат: pdf (true), epub
Размер: 16.4 MB
A compact and easily accessible book, it guides the reader in unravelling the apparent mysteries found in doing mathematical proofs. Simply written, it introduces the art and science of proving mathematical theorems and propositions and equips students with the skill required to tackle the task of proving mathematical assertions.
Theoremus - A Student's Guide to Mathematical Proofs is divided into two parts. Part 1 provides a grounding in the notion of mathematical assertions, arguments and fallacies and Part 2, presents lessons learned in action by applying them into the study of logic itself. The book supplies plenty of examples and figures, gives some historical background on personalities that gave rise to the topic and provides reflective problems to try and solve. The author aims to provide the reader with the confidence to take a deep dive into some more advanced work in mathematics or logic.
Today in the teaching of mathematically oriented subjects, students are taught the computational techniques and methods rather than the process of constructing proofs. Unfortunately, when these students are asked to prove a proposition, they are at their wits end. Groping in the dark, they fall all over the place having no clue as to how to proceed. Some attempt to prove but they employ questionable proof methods that make their proofs implausible.
Yet the computational algorithms students are made to learn come from proved theorems. Thus if there is no appreciation of how theorems are proved, mathematics becomes a magical art fogged in mystery. The students may work through the process but they have no idea why the steps they follow work and are valid.
What does it mean then when you are asked to prove a theorem? Essentially, one is asked to write out a proof by argumentation. A proof is a written product, thus writing therefore, is essentially the work involved in the task of proving.
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