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Articles 1 - 9 of 9
Full-Text Articles in Analysis
Nightmare In The Library, Charles A. Coppin
Nightmare In The Library, Charles A. Coppin
Journal of Humanistic Mathematics
Students of real analysis and calculus find that the completeness property of the real numbers is difficult to understand, especially, its importance. The word numbers denote real numbers throughout this piece. After all, the real numbers are not any less imaginary than the so-called imaginary numbers. Although, sometimes, it does gain some mention in calculus courses, its presence as a topic is a mere will-o’-the-wisp of bygone days when teachers would often reach deep into the big ideas of calculus as a mainstay of their courses. For the sake of cultural literacy and the development of mathematical maturity, we believe …
Dream Series, Jim Wolper
Dream Series, Jim Wolper
Journal of Humanistic Mathematics
Dream Series converge to numbers we cannot analyze. They exist, like dreams, but resist attempts to put them into order.
The Operator Algebras Mentor Network: Impact Of Community-Based Mentoring, Anna Duwenig, Kari Eifler, Priyanga Ganesan, Lara Ismert, Viviana Meschitti, Sarah Plosker, Karen Strung
The Operator Algebras Mentor Network: Impact Of Community-Based Mentoring, Anna Duwenig, Kari Eifler, Priyanga Ganesan, Lara Ismert, Viviana Meschitti, Sarah Plosker, Karen Strung
Journal of Humanistic Mathematics
The Operator Algebras Mentor Network (OAMN) is an international mentoring initiative that offers support in small groups to women and minority genders in the particularly male-dominated field of operator algebras (OA) in mathematics. Expected advantages of membership include raising awareness of the lack of gender diversity in this field, providing advice to mentees by mentors (e.g., pertaining to career or work/life balance), broadening one’s network in OA, etc. In this project, we set out to determine if membership within the OAMN is beneficial to its members. To this end we sent a questionnaire to OAMN members and a control group …
Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat
Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat
Journal of Humanistic Mathematics
What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?
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.
My Finite Field, Matthew Schroeder
My Finite Field, Matthew Schroeder
Journal of Humanistic Mathematics
A love poem written in the language of mathematics.
Harmonics In The Library, Charles Coppin
Harmonics In The Library, Charles Coppin
Journal of Humanistic Mathematics
Students of traditional calculus courses can discover significant mathematics original to themselves, especially if these courses are taught in a way that allows shafts of mathematical light to shine through. We tell a story of such an incident in the form of a dialogue between two fictional students. Our students, on their own, discover (or rediscover) a well-known problem based on the harmonic series. We believe opportunities for such discoveries are greater if students have had some experience with inquiry-based learning prior to entering a traditional course. More broadly, we aim to demonstrate what can occur when students feel no …
Math Moment, Paige S. Orland
Math Moment, Paige S. Orland
Journal of Humanistic Mathematics
A short poem comparing Exponential and Logistic functions.