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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Self-Reference And Diagonalisation, Joël A. Doat
Self-Reference And Diagonalisation, Joël A. Doat
Journal of Humanistic Mathematics
This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox.
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Journal of Humanistic Mathematics
Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …
The Rubbish Researchers Puzzle, Michael W. Lucht
The Rubbish Researchers Puzzle, Michael W. Lucht
Journal of Humanistic Mathematics
The Rubbish Researchers Puzzle is a humorous short story about the Blue-Eyed Islanders Puzzle, cultural insensitivity in logic problems, and the quality of research.
What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann
What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann
Journal of Humanistic Mathematics
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.
From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev
From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev
Journal of Humanistic Mathematics
In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.
On The Occasion Of Your Graduation, Robert Dawson
On The Occasion Of Your Graduation, Robert Dawson
Journal of Humanistic Mathematics
A letter from an absent supervisor to a doctoral student about to graduate reveals a terrible secret.
Prove It!, Kenny W. Moran
Prove It!, Kenny W. Moran
Journal of Humanistic Mathematics
A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.