Abstract
There are two ways to learn mathematics: to discover (research) and to rediscover. Inspiring exercises are used to guide students at all levels to rediscover the essential meaning of various individual pieces of mathematics. Their role has become all the more important at atime when Bourbakization is the dominating fashion. While mathematics is decorated with a thick layer of cosmetics, such as utmost generalities, excessive formalism and rigour, subtle proofs, etc., its natural beauty (intuitive ways of thinking, simplicity of ideas, etc.) is obscured. From apedagogical point of view, to say the least, it would be most desirable if a theorem, or an idea, could be fully explained by one or two simple examples. These kinds of illustrative examples actually exist everywhere, and at all levels. We can use them as inspiring exercises. In this paper, five sets of examples are given, beginning with asimple one on Abel's identity, followed by examples on Hensel's lemma, finitely generated Abelian groups, Baire's category theorem and the Weierstrass preparation theorem. Solutions, hints and discussions are provided in the final section.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical Education in Science and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
